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Entangled Macroscopic Quantum States in Two Superconducting Qubits
Abstract
We present spectroscopic evidence for the creation of entangled macroscopic quantum states in two current-biased Josephson-junction qubits coupled by a capacitor. The individual junction bias currents are used to control the interaction between the qubits by tuning the energy level spacings of the junctions in and out of resonance with each other. Microwave spectroscopy in the 4 to 6 gigahertzrange at 20 millikelvin reveals energy levels that agree well with theoretical results for entangled states. The single qubits are spatially separate, and the entangled states extend over the 0.7-millimeter distance between the two qubits.
... Nonclassical correlations are necessary to enhance the performance of a variety of quantum technological tasks, including sensing [1], communications and cryptography [2], quantum computing [3][4][5], quantum thermodynamics [6][7][8], as well as having significance for foundational questions in quantum physics [9]. Such correlations have been observed in a variety of physical platforms including optical photons [10][11][12][13], cold atoms [14][15][16], trapped ions [17][18][19], superconducting circuits [20,21], nitrogen-vacancy centres [22] and, the platform we address here, optomechanics. ...
... To test this idea in simulation, in which the full covariance matrix V is computed by numerically solving Eq. (16), Var X gen is calculated as per Eq. (20). The optimisation algorithm is given only θ c , θ m as variables, and the figure of merit is calculated from a fixed V. In an experiment this is equivalent to running with identical driving parameters. ...
... The simulations compute the covariance matrix V, either analytically or numerically, as described in Appendix B 1, and so Var X gen is calculated using Eq. (20). As d d φ (Var X gen ) and d 2 d φ 2 (Var X gen ) can be derived, then a Newton-Raphson based method is efficient for determining the optimal φ. ...
Nonclassical correlations provide a resource for many applications in quantum technology as well as providing strong evidence that a system is indeed operating in the quantum regime. Optomechanical systems can be arranged to generate quantum entanglement between the mechanics and a mode of travelling light. Here we propose automated optimisation of the production of quantum correlations in such a system, beyond what can be achieved through analytical methods, by applying Bayesian optimisation to the control parameters. Two-mode optomechanical squeezing experiment is simulated using a detailed theoretical model of the system, while the Bayesian optimisation process modifies the controllable parameters in order to maximise the non-classical two-mode squeezing and its detection, independently of the inner workings of the model. The Bayesian optimisation treats the simulations or the experiments as a black box. This we refer to as \emph{theory-blind} optimisation, and the optimisation process is designed to be unaware of whether it is working with a simulation or the actual experimental setup. We find that in the experimentally relevant thermal regimes, the ability to vary and optimise a broad array of control parameters provides access to large values of two-mode squeezing that would otherwise be difficult or intractable to discover. In particular we observe that modulation of the driving frequency around the resonant sideband, when added to the set of control parameters, produces strong nonclassical correlations greater on average than the maximum achieved by optimising over the remaining parameters. We also find that using our optimisation approach raises the upper limit to the thermal regime in which squeezing can be achieved. This extends the range of experimental setups in which non-classical correlations could be generated beyond the region of high quantum cooperativity.
... Nonclassical correlations are necessary to enhance the performance of a variety of quantum technological tasks, including sensing [1], communications and cryptography [2], quantum computing [3][4][5], quantum thermodynamics [6][7][8], as well as having significance for foundational questions in quantum physics [9]. Such correlations have been observed in a variety of physical platforms including optical photons [10][11][12][13], cold atoms [14][15][16], trapped ions [17][18][19], superconducting circuits [20,21], nitrogen-vacancy centers [22] and, the platform we address here, optomechanics. ...
... The homodyne measurement angles θ c , θ m are experimental settings that could be determined through theory-blind type optimization. This would require repeated driving with the same pulse parameters, taking measurements to calculate Var X gen as per equation (20), and using the optimization algorithm to find the values of θ c , θ m that minimize Var X gen . ...
Nonclassical correlations provide a resource for many applications in quantum technology as well as providing strong evidence that a system is indeed operating in the quantum regime. Optomechanical systems can be arranged to generate nonclassical correlations (such as quantum entanglement) between the mechanical mode and a mode of travelling light. Here we propose automated optimization of the production of quantum correlations in such a system, beyond what can be achieved through analytical methods, by applying Bayesian optimization to the control parameters. A two-mode optomechanical squeezing experiment is simulated using a detailed theoretical model of the system and the measurable outputs fed to the Bayesian optimization process. This then modifies the controllable parameters in order to maximize the non-classical two-mode squeezing and its detection, independently of the inner workings of the model. We focus on a levitated nano-sphere system, but the techniques described are broadly applicable in optomechanical experiments, and also more widely, especially where no detailed theoretical treatment is available. We find that in the experimentally relevant thermal regimes, the ability to vary and optimize a broad array of control parameters provides access to large values of two-mode squeezing that would otherwise be difficult or intractable to discover via analytical or trial and error methods. In particular we observe that modulation of the driving frequency around the resonant sideband allows for stronger nonclassical correlations. We also observe that our optimization approach finds parameters that allow significant squeezing in the high temperature regime. This extends the range of experimental setups in which non-classical correlations could be generated beyond the region of high quantum cooperativity.
... For the existing coherent phonon-photon interaction, the pertinent entanglement has been studied in various optomechanical systems by transferring the quantum behavior of photons to movable mirrors of coupled optical cavities. In this respect, different authors have studied the entanglement of two dielectric membranes suspended inside a cavity [10], optomechanical force-sensing [11,12], macroscopic quantum states in two superconducting qubits [13], dynamical quantum steering [14], nano-mechanical oscillators in a ring cavity by feeding squeezed light [15], and optomechanically induced transparency [16]. Furthermore, the bipartite entanglement between the cavity mode and the mode of oscillating mirrors has also been demonstrated with the help of an optomechanical array in which the optical cavities are connected to one oscillating end mirror via a photon hopping mechanism [17]. ...
... 2G mj α js . Since the steady-state amplitudes α js of the cavity fields (see Eq. (13)) are proportional to laser driving amplitude E j , then it should be realized that the g j factor in the drift matrix A is essentially determined by g j ∝ G mj E j . This shows that the behavior of coupling rate g j on the entanglement consistent with recent experiment [38]. ...
In this paper, we investigate the degree of steady-state entanglement using a hybrid optomechanical system, where the separate cavities contain a degenerate optical parametric amplifier (DOPA). Particularly, under the linearization approximation, the steady-state entanglement is quantified through logarithmic negativity. The bipartite entanglement between cavity-mechanical oscillator modes and two cavity modes is analyzed through the applicable choice of nonlinear gain of OPA, optical cavity detuning, and cavity-cavity coupling strength. It is found that the steady-state entanglement increases with the nonlinear gain of OPA medium and normalized detuning. We further emphasize the influence of cavity-cavity coupling parameter on the bipartite entanglement, and the generation of entanglement can be transferred entirely due to the coupling strengths. The main contribution of coupling parameters on the entanglement of the two modes of mechanical oscillators significantly altered and increased. The observed possibility of transferring the emerging entanglement of the states of light in the two cavities to the modes of the accompanying mechanical oscillators is expected to be a valuable asset in the practical realization of quantum information processing.
... As a strict subset of entanglement, quantum steering [4] has attracted extensive attention due to its unique asymmetry, which has been applied in many aspects, for instance, quantum key distribution [5], secure quantum communication [6], one-way quantum computing [7], etc. Although quantum entanglement and quantum steering have been able to be implemented in various systems up to now [8][9][10][11][12][13][14][15][16][17], the preparation of quantum correlations between two macroscopic, massive objects has been a task of paramount importance. ...
... Notice that in the absence of feedback, we have u j = n j = 0, ( j = 1, 2); in the case of a single feedback loop (assuming only the first feedback loop), we have u 1 , n 1 = 0 and u 2 = n 2 = 0; when both feedback loops are presented, there is u j , n j = 0. The values of both u j and n j are controlled by feedback gain g fb j according to Eqs. (9) and (12). Without loss of generality, we assumed ...
We propose a scheme to generate and enhance the quantum correlations between two magnons separated in two microwave cavities with feedback control of the cavity field. In each cavity, the magnon is coupled to the cavity mode by magnetic dipole interaction, and the interaction between two microwave cavities is realized via linear beam splitter interaction without any nonlinear interaction in the system. We show that the quantum entanglement, as a special quantum correlation, between the two magnons is improved in the system with double-feedback control, and the entanglement is highly robust to temperature. It is always possible to optimize the entanglement by modulating the gain of the other feedback loop if the parameters of one of the feedback loops are given. Also, there is one-way steering between two magnons of the system in the presence of a single feedback loop.
... While it is most commonly associated with the microscopic world, for sufficiently coherent systems and using states that are relatively robust under decoherence, it has been observed also at the larger scale [6][7][8][9]. Entanglement in the mesoscopic regime has been achieved in experiments with superconductors, resulting in the recent fast progress of superconducting quantum computers [10][11][12][13]. Entanglement plays a central role in quantum technologies to obtain practical advantages over devices based on classical physics. ...
... is the projector on the N-particle subspace. The denominator in (12) is needed such as to normalize the state properly. The probability of projection on the N-particle sector is defined as ...
We propose a method of generating and detecting entanglement via spin squeezing in an exciton-polariton condensate. Spin squeezing is a sensitive detector of entanglement because any squeezing below shot noise implies entanglement. In our scheme, two polariton spin species are resonantly pumped, forming a particle number fluctuating effective spin. The naturally occurring nonlinear interactions between the polaritons produce an effective one-axis squeezing interaction, which drives the system toward a spin-squeezed state at steady-state. We investigate the squeezing level that is attainable at the steady state for realistic experimental parameters and show the favorable parameters for strong squeezing. The amount of squeezing tends to improve with larger pumping, due to the bosonic enhancement of the one-axis twisting Hamiltonian. Using number-fluctuating versions of the Wineland squeezing criterion and optimal spin inequalities, we show how multipartite entanglement can be detected.
... In particular, it has been predicted that topological defects can be in quantum superposition states (18,19), with their coherent oscillation governed by the property of the quantum phase transition. However, although quantum superposition has been tested in a wide range of physical systems from elementary particles to mesoscopic and macroscopic objects like ensembles of cold atoms (20), large organic molecules (21), mechanical oscillators (22), and superconducting quantum circuits (23), its demonstration for topological defects remains an experimental challenge. This is because, while topological defects can be viewed as localized quasiparticles, their detection requires measuring global properties of the system and is thus subjected to decoherence and state-preparationand-measurement (SPAM) errors of the whole system. ...
Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a “Schrodinger kink” that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics.
... Quantum entanglement, as a significant resource for quantum information science, has been extensively studied in many sorts of systems [1][2][3][4][5][6]. It has potential applications in verifying fundamental theories of quantum mechanics [7][8][9], quantum information processing [10,11], and constructing quantum networks [12,13]. ...
... Se trata de un comentário a un artículo y la correspondiente respuesta, notándose en el contexto general de lo abordado una confusión común relacionada con el entrelazamiento cuántico, la que podemos aclarar. De un lado, Wójcik, refiriéndose a un reporte de Berkley et al., [8], en el que se afirma que los resultados que ellos presentan proporcionan evidencias de la creación del entrelazamiento en un sistema de dos q-bits del tipo contactos Josephson acoplados, a través de la implementación de los estados de Bell, comenta lo siguiente 6 : "... El misterio del entrelazamiento se origina en la existencia de correlaciones entre dos sistemas fisicamente no acoplados. Se debe enfatizar, sin embargo, que aunque las correlaciones entre sistemas entrelazados sean generalmente llamadas no locales, es la pérdida del acoplamiento y no la separación espacial entre ellas la que debería ser considerada como la condición necesaria para que la noción de no localidad puede ser usada. ...
In this article, we emphasize some aspects related to the difficulty encountered when identifying physical entanglement in quantum systems. We offer some comments that can alert us when it comes to distinguishing the purely mathematical aspects of entanglement from the physical aspects in real-world quantum systems. We show the case of an unusual type of entanglement, recently identified, as well as an example of this, considering a system composed of four particles, where the differences in relation to the usual case of entanglement are evident. Finally, we consider an example of how classical entanglement (if it existed) would develop in the world described by classical physics.
Resumen. En este artículo destacamos algunos aspectos relacionados con la dificultad encontrada al intentar identificar el entrelazamiento físico en sistemas cuánticos. Ofrecemos algunos comentarios que pueden alertarnos a la hora de distinguir los aspectos puramente matemáticos del entrelazamiento de los aspectos físicos en los sistemas cuánticos del mundo real. Mostramos el caso de un tipo de entrelazamiento inusual recientemente identificado, así como un ejemplo del mismo, considerando un sistema compuesto por cuatro partículas, donde las diferencias con el caso habitual de entrelazamiento son evidentes. Finalmente, consideramos un ejemplo de cómo se desarrollaría el entrelazamiento clásico (si existiera) en el mundo descrito por la física clásica.
... Quantum computers utilize large arrays of qubits with controlled interactions (typically either inductive or capacitive) between many pairs of qubits [58][59][60][61]. For charge and phase qubits, the nearest-neighbour interactions are enabled by capacitors, rather than inductors [60,[62][63][64][65]. Of recent interest is the design of a tunable coupler transmon that is capacitively coupled to a pair of qubits to achieve high-fidelity twoqubit gates [66][67][68][69]. ...
We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency Superconducting Quantum Interference Devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N × N × 2 overlapping metamaterial array, where we develop an understanding of the many (8N ² -8N+3) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant response of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10-30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
... Quantum entanglement, the phenomenon whereby quantum particles exhibit correlated properties even when separated by large distances, is a crucial resource for quantum information processing and communication [1,2]. Various theoretical and experimental works on entanglement have been studied, such as atomic ensembles [3,4], quantum dots [5,6], superconducting circuits [7,8], and cavity quantum electrodynamics [9][10][11]. An ongoing goal in the field of quantum optics is achieving controllable entanglement between microwave and optical photons. ...
We theoretically investigate entanglement in a hybrid quantum system comprising two optical cavities coupled to a shared microwave cavity via optomechanical interactions. Our results demonstrate that increasing the microwave input power and frequency in the allowed range enhances entanglement between the microwave–optical and optical–optical modes. We also show by change frequency of the one optical cavity in the communication domain that we still have entanglement. This ability to generate robust microwave–optical photon entanglement shows promise for various quantum technologies. Optical photons could enable secure quantum communication in optical fibers, while microwave photons allow transmission to satellites. Overall, this hybrid cavity optomechanical system offers prospects as an efficient source of entangled photon pairs, vital for implementing long-distance quantum communication networks.
... Also, it has been shown that under the low-excitation limit, a Josephson junction with a small dc-current bias could be effectively treated as a linear harmonic oscillator [10], which can quantized as a simple-mode boson and thus could serve as the quantum data bus to implement the couplings between distant superconducting qubits. If the biased dc current is sufficiently large (e.g., approaching its critical current), the quantized CBJJ device has only a few bound states [11] and thus can be treated as a macroscopic qubit (i.e., a fermion), called the CBJJ qubit [12], for superconducting quantum information computing [13]. This implies that a current-biased Josephson junction (CBJJ), acting as an artificially macroscopic quantum system, can serve as either a boson or a fermion, depending on its biased current. ...
It is well known that elementary particles in the real 3 + 1 -dimensional world are either bosons or fermions, without exception, and not both. Here, we show that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic “particle,” can serve as either a boson or a fermion or the combination, depending on the amplitude of the biased dc current. By using high vacuum two-angle electron beam evaporations, we fabricated CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. At 50 mK temperature environment, the microwave transmission characteristics of the fabricated CBJJ devices were measured at the low power limit. The experimental results verify the relevant theoretical predictions, i.e., when the bias current is significantly lower than the critical ones of the junctions, the device works in a very linear regime and thus behaves as a harmonic oscillator “boson”; while if the biased current is sufficiently large (especially approaching the junctions' critical currents), the device works manifestly in the nonlinear regime and thus behaves as a two-level artificial atom “fermion.” Therefore, by adjusting the biased dc current, the CBJJ device can be effectively switched from a Bose-type macroscopic particle to a Fermi-type one and thus might open an approach for quantum technology applications at a macroscopic scale.
Published by the American Physical Society 2024
... In recent years, there has been a scientific focus on optimizing classical devices by leveraging quantum phenomena, such as quantum superposition and entanglement [1][2][3][4][5]. This optimization has found widespread applications on large scales, including quantum computers that fundamentally differ from classical ones [4,5], as well as quantum sensors and quantum radars [6][7][8][9]. ...
The present article primarily focuses on the design of an ultra-low-noise amplifier specifically tailored for quantum applications. The circuit design places a significant emphasis on improving the noise figure, as quantum-associated applications require the circuit's noise temperature to be around 0.4 K. This requirement aims to achieve performance comparable to the Josephson Junction amplifier. Although this task presents considerable challenges, the work concentrates on engineering the circuit to minimize mismatch and reflection coefficients, while simultaneously enhancing circuit transconductance. These efforts aim to improve the noise figure as efficiently as possible. The results of this study indicate the possibility of achieving a noise figure of approximately 0.009 dB for a unique circuit design operating at 10 K. In a departure from traditional approaches, this study employs quantum mechanical theory to analyze the circuit comprehensively. By employing quantum theory, the researchers derive relationships that highlight the crucial quantities upon which the circuit design should focus to optimize the noise figure. For example, the circuit's gain power, which depends on the circuit's photonic modes, is theoretically derived and found to affect the noise figure directly. Ultimately, by merging quantum theory with engineering approaches, this study successfully designs a highly efficient circuit that significantly minimizes the noise figure in a quantum application setting.
... Quantum computers utilize large arrays of qubits with controlled interactions (typically either inductive or capacitive) between many pairs of qubits [57][58][59][60]. For charge and phase qubits, the nearest-neighbour interactions are enabled by capacitors, rather than inductors [59,[61][62][63][64]. Our rf SQUID metamaterials differ in that multiple coupling capacitors are included, creating a highly integrated network of both capcitive and inductive coupling between all of the SQUIDs. ...
We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency Superconducting Quantum Interference Devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion containing the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved which include the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N ×N ×2 overlapping metamaterial array, where we develop an understanding of the many (8N 2 − 8N + 3) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant response of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10-30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
... Qubits, as we all know, serve as a fundamental element in new application fields such as quantum computation and communication, for which the interest in the theoretical analyses and actual implementations of two-level systems has been further stimulated. Several methods are available to create qubits with current quantum technologies, including quantum optics, microscopic quantum objects (electrons, ions, atoms) in traps, quantum dots and quantum circuits [20][21][22][23]. However, the different implementations of qubits are unavoidably subject to environmental noise. ...
... Also, it has been shown that under the low-excitation limit, a Josephson junction with the small dc-current bias could be effectively treated as a linear harmonic oscillator [10], which can quantized as a simple-mode boson and thus could be severed as the quantum data bus to implement the couplings between the distant superconducting qubits. While, if the biased dccurrent is sufficiently large (e.g., approaching to its critical current), the quantized CBJJ device has only a few bound states [11] and thus can be treated as a macroscopic qubit (i.e., a fermion) called as the CBJJ one [12] for the superconducting quantum information computing [13]. This implies that, a current-biased Josephson junction (CBJJ), acted as one of the artificially macroscopic quantum system, can be served as either the boson or the fermion, depending on its biased current. ...
According to the statistical distribution laws, all the elementary particles in the real 3+1-dimensional world must and only be chosen as either bosons or fermions, without exception and not both. Here, we experimentally verified that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic "particle", can be served as either boson or fermion, depending on its biased dc-current. By using the high vacuum two-angle electron beam evaporations, we fabricated the CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. The microwave transmission characteristics of the fabricated CBJJ devices are analyzed by using the input-output theory and measured at 50mK temperature environment under low power limit. The experimental results verify the theoretical predictions, i.e., when the bias current is significantly lower than the critical one of the junction, the device works in a well linear regime and thus works as a harmonic oscillator, i.e., a "boson"; while if the biased current is sufficiently large (especially approaches to its critical current), the device works manifestly in the nonlinear regime and thus can be served as a two-level artificial atom, i.e., a "fermion". Therefore, by adjusting the biased dc-current, the CBJJ device can be effectively switched from the boson-type macroscopic particle to the fermion-type one, and thus may open the new approach of the superconducting quantum device application.
... Furthermore, dissipative preparation has been generalized to high-dimensional, [35,36] multipartite, [37][38][39][40][41] and distant entanglements. [42] According to the previous reports, dissipative preparation has been realized in various experimental platforms, including superconductors, [43,44] photons, [45,46] quantum dots, [47] nitrogen-vacancy centers, [48] neutral atoms, [49,50] and trapped ions. [51] Neutral atoms are known to be an appealing candidate among numerous physical systems due to the long-lived encoding in atomic hyperfine states and extremely large dipole moments. ...
A scheme for dissipatively preparing bipartite Knill-Lafamme-Milburn (KLM) entangled state in the neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the coherent population trapping, is actively exploited to engineer a steady KLM state from an arbitrary initial state. Instead of commonly used antiblockade dynamics of two Rydberg atoms, we particularly utilize the Rydberg-Rydberg interaction (RRI) as the pumping source to drive the undesired states so that it is not necessary to satisfy a certain relation with laser detuning. The numerical simulation of the master equation signifies that both the fidelity and the purity above 98% is available with the current feasible parameters, and the corresponding steady-state fidelity is robust to the variations of the dynamical parameters.
... Qubits, as we all know, serve as a fundamental element in new application fields such as quantum computation and communication, for which the interest in the theoretical analyses and actual implementations of two-level systems has been further stimulated. Several methods are available to create qubits with current quantum technologies, including quantum optics, microscopic quantum objects (electrons, ions, atoms) in traps, quantum dots and quantum circuits [20][21][22][23]. However, the different implementations of qubits are unavoidably subject to environmental noise. ...
The Time-Fractional Schr\"odinger Equation (TFSE) is well-adjusted to study a quantum system interacting with its dissipative environment. The Quantum Speed Limit (QSL) time captures the shortest time required for a quantum system to evolve between two states, which is significant for evaluating the maximum speed in quantum processes. In this work, we solve exactly for a generic time-fractional single qubit open system by applying the TFSE to a basic open quantum system model, namely the resonant dissipative Jaynes-Cummings (JC) model, and investigate the QSL time for the system. It is shown that the non-Markovian memory effects of the environment can accelerate the time-fractional quantum evolution, thus resulting in a smaller QSL time. Additionally, the condition for the acceleration evolution of the time-fractional open quantum system at a given driving time, i.e., a tradeoff among the fractional order, coupling strength, and photon number, is brought to light. In particular, a method to manipulate the non-Markovian dissipative dynamics of a time-fractional open quantum system by adjusting the fractional order for a long driving time is presented.
... Likewise, the coupling of superconducting qubits (SQs) as artificial atoms [27,28] with quantized fields can be mediated by exchanging microwave photons [29]. Such qubit systems play a vital role in quantum information processing [30][31][32][33]; for instance, one may refer to their remarkable usefulness in quantum state teleportation [34], quantum information transfer [35], and entanglement generation [36][37][38]. In this line, authors in [39] have investigated the entanglement generation of two remote SQs and quantum information transfer via performing appropriate measurements. ...
... Entanglement, one essential feature of quantum mechanics, is an indispensable resource for quantum information processing. This phenomenon has been demonstrated in various systems, such as superconducting qubits [1], atomic ensembles [2,3], individual atoms [4] and ions [5], and electron spins [6]. In the past few decades, mechanical oscillators with high resonance frequencies and quality factors have been extensively explored. ...
We present a scheme for realizing phase-controlled entanglement in a microwave optomechanical system comprising two microwave cavities and two mechanical oscillators. Under specific driving conditions, we show that this optomechanical interface can be exploited to generate simultaneously the stationary cavity–cavity entanglement, mechanical–mechanical entanglement, and cavity–mechanical entanglement. Due to the closed loop interaction, we find that the entanglement can be controlled flexibly by tuning the phase difference between the optomechanical coupling strengths. The dependence of the entanglement on the amplitudes of the optomechanical coupling strengths is also explored in detail. Moreover, the bipartite entanglements are robust against temperature, and it is shown that the mechanical oscillators are cooled to the ground state in the parameter regimes for observing entanglement.
... Importantly, this increase of the QFI is accompanied with a significant growth of entanglement, as quantified by the concurrence 41 , as we demonstrate in Fig. 4(b). The connection between the QFI and the entanglement of such a coupled-qubit setting (see Supplementary Note 3) is known to arise from the level anticrossing 42,43 , which represents a general feature in systems beyond the single-qubit context. These results suggest that a large QFI is linked to strong entanglement upon measuring the QFI based on parametric modulations as introduced here. ...
The quantum Cramér–Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We experimentally demonstrate near saturation of the quantum Cramér–Rao bound in the phase estimation of a solid-state spin system, provided by a nitrogen-vacancy center in diamond. This is achieved by comparing the experimental uncertainty in phase estimation with an independent measurement of the related quantum Fisher information. The latter is independently extracted from coherent dynamical responses of the system under weak parametric modulations, without performing any quantum-state tomography. While optimal parameter estimation has already been observed for quantum devices involving a limited number of degrees of freedom, our method offers a versatile and powerful experimental tool to explore the Cramér–Rao bound and the quantum Fisher information in systems of higher complexity, as relevant for quantum technologies.
... Here z σ α are Pauli matrices, α is the identity in qubit-α Hilbert space ( 1, 2 α = ), we put 1 = . This model applies in particular to the fixed, capacitive or inductive, coupling of superconducting qubits [29][30][31][32][33][34][35], where individual-qubit control allows an effective switch on/off of the interaction [5,6]. Eigenvalues and eigenvectors of equation (1) ...
Achieving high-fidelity universal two-qubit gates is a central requisite of any implementation of quantum information processing. The presence of spurious fluctuators of various physical origin represents a limiting factor for superconducting nanodevices. Operating qubits at optimal points, where the qubit-fluctuator interaction is transverse with respect to the single qubit Hamiltonian, considerably improved single qubit gates. Further enhancement has been achieved by dynamical decoupling (DD). In this article we investigate DD of transverse random telegraph noise acting locally on each of the qubits forming an entangling gate. Our analysis is based on the exact numerical solution of the stochastic Schrödinger equation. We evaluate the gate error under local periodic, Carr–Purcell and Uhrig DD sequences. We find that a threshold value of the number, n, of pulses exists above which the gate error decreases with a sequence-specific power-law dependence on n. Below threshold, DD may even increase the error with respect to the unconditioned evolution, a behaviour reminiscent of the anti-Zeno effect.
... These studies encourage us to further explore novel nonclassical effects based on the macroscopic quantum medium of photons, magnons, and phonons. Entanglement, characterized by quantum mechanics, has become a significant resource for quantum information science and thus raised widespread interest in various physical branches and has been realized in many kinds of systems at both the microscopic level [18] and macroscopic level [19,20]. In optomechanics, the entanglement between the cavity and macroscopic vibrating mirror can be generated by means of radiation pressure [21][22][23][24]. ...
We propose a simple scheme to generate quantum entanglement and one-way steering between distinct mode pairs in a generic cavity magnomechanical system, which is composed of a microwave cavity and a yttrium iron garnet sphere supporting magnon and phonon modes. The microwave cavity is pumped by a weak squeezed vacuum field, which plays an important role for establishing quantum entanglement and steering. It is found that when the magnon mode is driven by the red-detuned laser, the maximum entanglement between cavity mode and phonon mode and the maximum phonon-to-photon one-way steering can be effectively generated via adjusting the ratio of two coupling rates. While under the much weaker magnomechanical coupling, the quantum entanglement and one-way steering between cavity mode and magnon mode can be achieved, where the steering direction is determined merely by the relative dissipation strength of the cavity to the magnon mode. More interestingly, we reveal that the robustness to the temperature for entanglement and steering between any mode pairs can be evidently enhanced by selecting the squeezing parameter appropriately.
... Entanglement is when two or more subsystems cannot be described independently of each other. Whilst entanglement has been shown to exist in many systems, notably superconducting circuits [26] and atoms [239], entangled photons are by far the system easiest to generate experimentally, requiring a relatively simple setup. Traditionally, entangled photons are produced via a process known as spontaneous parametric down conversion (SPDC). ...
Microscale and nanoscale optics has seen rapid development over the past few years. There is a variety of reasons for this growth, chief among them are the breakthroughs in nano-fabrication and promise of fully intergratable optical chips and circuits. In parallel to this, the field of quantum optics has seen similar advances. Again, there are a variety of reasons for this, most predominantly is the prospect of new fully quantum technologies such as quantum communication, computing and imaging. This thesis ties these two hugely popular fields together. Specifically, it will cover the possibility of generating non-classical states of light via non-linear optics on the microscale and nanoscale. This would constitute a great advancement in both the fields of quantum optics and nanophotonics, as it would provide a source capable of generating quantum light whilst simultaneously being miniaturisable. In this thesis, the experimental procedure undertaken to observe photon pairs generated via spontaneous parametric down conversion (SPDC) from a microscale layer of lithium niobate is outlined. The entire source had an effective volume of 3.4 μm x 10 μm x 10 μm, the smallest source of SPDC ever reported. With a total emission rate of 1500 coincidences per second from the source, the experiment sets the standard for which other microscale devices can be compared and is a clear indication that SPDC will eventually be observed from nanoscale devices. The properties of SPDC generated from microscale and nanoscale lengths differ fundamentally from SPDC generated in bulk materials. At the microscale and (or) nanoscale level, one does not need to worry about phase matching. This phenomena is a manifestation of the Heisenberg principle. Reducing the interaction length localises the region from which the photon pairs can be produced. This leads to an increase in the uncertainty of net momentum of the photon pairs. This principle, taken to the extreme case of nanoscale interaction lengths, means the uncertainty in momentum becomes so large that phase matching no longer needs to be satisfied. Like blackbody or bremsstrahlung emission that generate photons that occupy a continuum of modes, SPDC creates photon pairs that can occupy a broad continuum of modes. However, phase matching limits the number of modes the photon pairs can occupy to those that satisfy momentum conservation. Without phase matching, the limit is lifted and the photon pairs produced via SPDC can populate a full continuum of modes. The total number of possible modes the photon pairs can occupy is directly related to the degree of entanglement between the photons. In this work, the degree of entanglement for non-phase matched SPDC is measured in frequency variables and angular variables using several methods designed to specifically work for weak sources such as this one. In angular variables, a degree of entanglement as large as 1100 pm 200 is measured, making the non-phase matched photon pair state suited for highcapacity quantum information. The third-order analogue of SPDC, a process called third-order spontaneous parametric down conversion (TOPDC) that produces photon triplets as opposed to pairs, is also considered as a quantum optical process that can miniaturised. Whilst TOPDC has yet to be observed experimentally in the optical regime, estimates show that in the non-phase matched regime the expected rate of photon triplets is fairly large, with respect to the phase matched regime. By utilising a highly non-linear sample of 230 nm silicon, the first attempts are made to try and observe photon triplets on the nanoscale.
... Over the recent years, the scientific focus has been laid on the optimization of classic devices with quantum phenomena, such as quantum superposition and quantum entanglement [1][2][3][4][5]. Optimization can be widely applied in large scales, like in quantum computers, which are fundamentally different from the classic ones [4,5], quantum sensors, and quantum radars [6][7][8][9]. ...
The present article mainly emphasizes the design of a low-noise amplifier that can be used for quantum applications. For this reason, the design circuit specifically concentrates on the noise figure and its improvement to be used in quantum applications at which the noise added due to the circuit designed should be strongly limited. If the designed low noise amplifier could have quantum-associated applications, its noise temperature should be around 0.4 K, in which the designed circuit is comparable with the Josephson Junction amplifier. Although this task seems to be highly challenging, this work focuses on engineering the circuit, minimizing the mismatch and reflection coefficients in the circuit, and enhancing the circuit transconductance to improve the noise figure in the circuit as efficiently as possible. The results indicated the possibility of reaching the noise figure around 0.008 dB in the circuit operating at 10 K. Additionally, the circuit is analyzed via quantum mechanical analysis, through which some important quantities, such as noise figure, is theoretically derived. In fact, the derived relationship using quantum theory reveals that on which quantities the design should focus in order to optimize the noise figure. Thus, merging quantum theory and engineering the approach contributed to designing a highly efficient circuit for strongly minimizing the noise figure.
... The parameters ∆ 1 , ∆ 2 , J are fixed by device design and 0 can be controlled experimentally. This type of Hamiltonian can be realized, for instance, in superconducting qubits [32,[42][43][44][45][46][47] where the qubit-qubit interaction term gives rise to non trivial entangled (eigen) states of H 0 . The additional term ...
We report on a mechanism to optimize the generation of steady-state entanglement in a system of coupled qubits driven by microwave fields. Due to the interplay between Landau-Zener-St\"uckerlberg pumping involving three levels and a subsequent fast relaxation channel, which is activated by tuning the qubits-reservoir couplings, a maximally entangled state can be populated. This mechanism does not require from the fine-tuning of multiphoton-resonances but depends on the sign of the qubit-qubit coupling. In particular, we find that by a proper design of the system parameters and the driving protocol, the two-qubits steady-state concurrence can attain values close to 1 in a wide range of driving amplitudes. Our results may be useful to gain further insight into entanglement control and manipulation in dissipative quantum systems exposed to strong driving.
... The superconducting nanodevices are in the focus of modern experimental research, especially since they are a promising platform for various qubit realizations like Josephson-based qubits [1][2][3][4][5] or Majorana bound states [6][7][8][9][10]. These structures containing superconductor-semiconductor and superconductor-insulator junctions host Andreev bound states which can also be used as a qubit [11,12]. ...
... As a vital quantum-mechanical phenomenon, entanglement has been realized in many sorts of systems at the mesoscopic level [38][39][40] or the microscopic level [41][42][43]. It is regarded as a key resource required to operate a quantum computer and to communicate with security guaranteed by physical laws [44]. ...
We propose a hybrid cavity magnomechanical system to realize and transfer the bipartite entanglements and Einstein-Podolsky-Rosen (EPR) steerings between magnons, photons, and phonons in the regime of stability of the system. As a parity-time-symmetric-like structure exhibiting the natural magnetostrictive magnon-phonon interaction, our passive-active cavity system can be explored to enhance the robust distant quantum entanglement and generate the relatively obvious asymmetric (even directional) EPR steering that is useful for the task with the highly asymmetric trusts of the bidirectional local measurements between two entangled states. It is of great interest that, based on such a tunable magnomechanical system, the perfect transfer between near and distant entanglements and steerings of different mode pairs is realized by adjusting the coupling parameters; in particular, we propose a perfect transfer scheme of steerings. These transferring processes suggest indeed an alternative method for quantum information storage and manipulation. In addition, the entanglements and steerings can also be exchanged between different mode pairs by adjusting the detunings between different modes. This work may provide a potential platform for distant and asymmetric quantum modulation.
... I show there are two characteristic times inversely proportional to each other: decoherence time, and probability decay time, with second often mistaken for the first. I present formulas for decoherence and decay times While decoherence has been extensively studied, surprisingly little is available in terms of numeric results, either calculated from formulas [1,2] or measured in experiments [3,4]. The reason for researchers shying away from publishing numbers becomes apparent once these numbers are estimated from widely quoted expressions [5,1]. ...
I critically assess some published values for decoherence times. I show there are two characteristic times inversely proportional to each other: decoherence time, and probability decay time, with second often mistaken for the first. I present formulas for decoherence and decay times
... There are different physical systems for which entanglement has been realized experimentally such as superconductors [1] and photons [2] for example. Bose Einstein Condensates are currently being investigated to achieve entanglement between two BEC clouds. ...
In the present paper, a quantum teleportation protocol for split-squeezed Bose-Einstein Condensates is proposed that transfers a spin coherent state between two locations using entanglement introduced by squeezing interactions. One axis squeezing is used for this purpose, two axis anti squeezing further reduces the noise. The protocol uses continuous variable quadrature measurements that works for short interaction times in the Holstein-Primakoff approximation. The performance of the protocol is also analyzed by calculating the fidelity to show that it exceeds the classical bound.
Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a ``Schrodinger kink'' that manifests non-locality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for non-equilibrium dynamics in quantum Kibble-Zurek physics.
Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.
By considering the local quantum uncertainty (LQU) as a measure of quantum correlations, the thermal evolution of a two-qubit-superconducting system is investigated. We show that the thermal LQU can be increased by manipulating the Hamiltonian parameters such as the mutual coupling and Josephson energies, however, it undergoes sudden transitions at specific temperatures. Furthermore, a detailed analysis is presented regarding the impact of decohering channels on thermal LQU. This controllable LQU in engineering applications can disclose the advantage enabled in the superconducting charge qubits for designing quantum computers and quantum batteries.
Superconducting qubits were initially developed with the goal of realizing a superposition of macroscopically distinct quantum states by exploiting superconducting circuits. This basic idea resulted from the quantum mechanical description of the Josephson junction, the key element for producing superconducting qubits. Because the phase across a Josephson junction and its charge are canonical conjugates, there are two alternative realizations of superconducting qubits. The first one is based on the charge degree of freedom, termed charge qubit. The second utilizes the phase (or flux) degree of freedom and correspondingly are called phase (flux) qubits. Nowadays, the most robust superconducting qubit is the transmon. In practical applications, quantum state initialization and manipulations are heavily restricted by the quantum coherence of the qubit itself and of the qubit‐based systems. The main source of decoherence is interactions with the environment. Their relatively large values result from the macroscopic size of the quantum bits. Still, their circuit architecture enables the implementation of different types of coupling schemes between superconducting qubits and qubit‐resonator systems. The handling of superconducting quantum structures requires special experimental methods, including qubit fabrication, cooling to milliKelvin temperatures, experimental characterization, and readout. Concerning applications, superconducting qubits are promising candidates for both quantum simulators and universal quantum computing. This article covers a description of basic types of superconducting qubits and gives a general description of their use that includes dissipation and decoherence, coupling schemes, experimental realization, and basic measurement techniques. Finally, their use as building blocks for the realization of quantum computation is discussed.
Gaussian quantum steering is a type of quantum correlation in which two entangled states exhibit asymmetry. An efficient theoretical proposal is presented for the control of quantum steering and enhancement of entanglement in a Laguerre–Gaussian (LG) cavity optomechanical system. The system contains two rotating mirrors and a coherently driven optical parametric amplifier (OPA). The numerical results show significantly improved mirror‐mirror and mirror‐cavity entanglements by controlling the system parameters such as parametric gain, parametric phase, and the frequency of the two rotating mirrors. In addition to bipartite entanglement, our system also exhibits mirror‐cavity‐mirror tripartite entanglement as well. Another intriguing finding is the control of quantum steering, for which several results were obtained by investigating it for various system parameters. It is shown that the steering directivity is primarily determined by the frequency of two rotating mirrors. Furthermore, for two rotating mirrors, quantum steering is found to be asymmetric both one‐way and two‐way. Therefore, it can be asserted that the current proposal may help in the understanding of non‐local correlations and entanglement verification tasks.
We analyze the entanglement between optical and mechanical modes in a hybrid optomechanical system. A mechanical resonator is coupled to a single-mode cavity field with thermal pressure and a two-level atomic system coupled through Jaynes-Cummings model. The cavity field is coupled with the mechanical resonator by nonlinear coupling parameters. The mechanical mode can be dressed by the probe and control laser field. We observe that with increasing Rabi frequency the intensity of the Energy Eigen-value first increases quickly and reaches a maximum value. By varying the input-laser phase slowly the maximum entanglement is achieved. The maximum entanglement is achieved at the crossing frequency between the optical mode and mechanical mode. The entanglement is more vigorous against the thermal temperature. Due to the presence of nonlinear coupling strength addition with an atom between the cavity field and the mechanical resonator optical bistability is achieved easily. We can control the optical bi-stability of the steady state photon number using control field detuning and Rabi frequency. By increasing, cavity detuning strength and using a different set of coupling strengths bistability becomes wider. The present study has much more experimental applications: in high-power low-frequency signal generators in microcomputers, and detectors for detecting small functions.
A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system-environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can leverage on available experimental data and replace first-principles simulations with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we propose a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows, on the one hand, capturing the most important characteristics of open quantum systems such as the effective dimension of the environment and the spectrum of the joint system-environment quantum dynamics, and, on the other hand, reconstructing a predictive model of non-Markovian quantum dynamics, and denoising the measured quantum trajectories. We demonstrate the performance of the proposed approach with various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.
Entanglement generation via optimal drivings is of significance for quantum information science and engineering. Here, an efficient scheme is proposed for creating entangled states between two transmon qubits via shortcuts to adiabaticity with constant Rabi drivings. Two three-level atoms of Cooper-pair box circuits are coupled to a common cavity field of transmission-line resonator and individually driven by adjustable classical microwaves. In the regime of large detuning, we obtain an effective three-state system consisting of qubits and cavity photons. By the invariant-based shortcuts with time-independent Rabi drivings, two-qubit entangled states can be rapidly induced from an easily prepared product state. Compared to the entanglement creation with time-dependent Rabi drivings, our protocol not only becomes more feasible in experiment but also needs shorter times. Moreover, high-fidelity quantum operations can be realized with the accessible decoherence rates. The scheme could pave a promising avenue towards optimal generation of entangled states between superconducting qubits.
Generation of entanglement between macroscale mechanical oscillators is challenging yet important for future quantum technologies. Here, the possibility of creating a steady‐state entanglement between two rotating mirrors in a Laguerre–Gaussian (LG) rotational‐cavity optomechanical system by placing an especially tuned degenerate optical parametric amplifier (OPA) inside the cavity is theoretically explored. In the resolved‐sideband regime, a LG cavity mode is driven by a Gaussian laser beam tuned to the first lower mechanical sideband. The Duan quantity and the logarithmic negativity is used to study the stationary entanglement between two rotating mirrors. The influence of the parametric gain and phase of the OPA, the input laser power, the temperature of the environment, and the topological charge of the LG cavity mode on the mechanical entanglement are investigated. The achievable maximal degree of entanglement is limited by the parametric gain of the OPA. Generation of entanglement between macroscale mechanical oscillators is challenging yet important for future quantum technologies. Here, the possibility of creating a steady‐state entanglement between two rotating mirrors in a Laguerre‐Gaussian rotational‐cavity optomechanical system by placing an especially tuned degenerate optical parametric amplifier inside the cavity is theoretically explored.
We investigate the static and the dynamical behavior of localizable entanglement and its lower bounds on nontrivial loops of topological quantum codes with parallel magnetic field. Exploiting the connection between the stabilizer states and graph states in the absence of the parallel field and external noise, we identify a specific measurement basis, referred to as the canonical measurement basis, that optimizes localizable entanglement when measurement is restricted to single-qubit Pauli measurements only, thereby providing a lower bound. In situations where computing even the lower bound is difficult, we propose an approximation of the lower bound that can be computed for larger systems according to the computational resource in hand. Additionally, we compute a lower bound of the localizable entanglement that can be computed by determining the expectation value of an appropriately designed witness operator. We investigate the behavior of these lower bounds in the vicinity of the topological to nontopological quantum phase transition of the system, and perform a finite-size scaling analysis. We also investigate the dynamical features of these lower bounds when the system is subjected to Markovian or non-Markovian single-qubit dephasing noise. We find that in the case of the non-Markovian dephasing noise, at large time, the canonical measurement-based lower bound oscillates with a larger amplitude when the initial state of the system undergoing dephasing dynamics is chosen from the nontopological phase, compared to the same for an initial state from the topological phase. On the other hand, repetitive collapses followed by revivals to high value with time are observed for the proposed witness-based lower bound in the nontopological phase, which is absent in the topological phase. These features can be utilized to distinguish the topological phase of the system from the nontopological phase in the presence of dephasing noise.
In a system of two charge-qubits that are initially prepared in a maximally entangled Bell’s state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast.
By virtue of the canonical quantization method, the Hamilton operator for the charge qubits coupled by the variable capacitor is given. Based on this system, the realization scheme of the controlled-phase-shift gate is proposed. Meanwhile the quantum entanglement phenomena exiting in the system are discussed. An interesting conclusion is obtained, i.e., if one desires to change the quantum entanglement, the coupling capacitance should be considered first, but it is also a good choice to tune symmetric and asymmetric combination of two external magnetic fluxes respectively through the two loops.
Quantum entanglement in optomechanical systems plays an important role in the progress of quantum science and technology, such as the exploration of fundamental physics and quantum information processing. Although the physical law of quantum mechanics does not specifically limit the size of objects that carry the entangled states, the experimental preparation and detection of quantum entanglement in the macro world still face great challenges. Fortunately, with the experimental advances in recent years, several pioneering works have demonstrated non-local correlation and entanglement among mechanical oscillators or between oscillators and electromagnetic fields. In this perspective, we summarize the theoretical and experimental progress related to the macro entanglement states in optomechanical systems and outlook its future direction and potential applications.
We report on a mechanism to optimize the generation of steady-state entanglement in a system of coupled qubits driven by microwave fields. Due to the interplay between Landau-Zener-Stückelberg-Majorana pumping involving three levels and a subsequent fast relaxation channel, which is activated by tuning the qubits-reservoir couplings, a maximally entangled state can be populated. This mechanism does not require the fine tuning of multiphoton resonances but depends on the sign of the qubit-qubit coupling. In particular, we find that by a proper design of the system parameters and the driving protocol, the two-qubit steady-state concurrence can attain values close to 1 in a wide range of driving amplitudes. Our results may be useful to gain further insight into entanglement control and manipulation in dissipative quantum systems exposed to strong driving.
A protocol for remote state preparation is proposed for spin ensembles, where the aim is to prepare a state with a given set of spin expectation values on a remote spin ensemble using entanglement, local spin rotations, and measurements in the Fock basis. The spin ensembles could be realized by thermal atomic ensembles or spinor Bose-Einstein condensates. The protocol works beyond the Holstein-Primakoff approximation, such that spin expectation values for the full Bloch sphere can be prepared. The main practical obstacle is the preparation of the maximally entangled state between the spin ensembles. To overcome this, we examine the protocol using states based on the two-axis two-spin (2A2S) Hamiltonian in place of the maximally entangled state and examine its performance. We find that the version of the protocol with 2A2S squeezing well approximates the maximally entangled state, such that spin averages can be remotely prepared. We evaluate the errors that are introduced by using 2A2S squeezed states, and find that it decreases with the ensemble size. With postselection, errors can be systematically decreased further.
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In Secs. 7 and 8, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in Sec. 9, the comparison of results is provided with reference to other existing research.
Optimal generation of entangled states is of significance to quantum information processing. Here an efficient scheme is proposed for performing controllable and accelerated generation of entangled states between two superconducting qubits. Two three-level artificial atoms of Cooper-pair box circuits, coupling to a quantized field of transmission-line resonator, are individually driven by classical microwaves. In the two-photon resonance with a large detuning, each atom is reduced to an effective two-level qubit. Within a composite qubit-photon-qubit system, two types of entangled state can be controllably created using the technique of invariant-based shortcuts to adiabaticity. Compared with an adiabatic case, the entanglement generations in the shortcut manner need much shorter times. Numerical simulations show that the operations are robust against decoherence effects, and the interatomic cross resonance is safely negligible. The proposed scheme could pave a promising avenue towards optimized preparation of entangled states with superconducting qubits in circuit QED.
We theoretically reveal the unusual features of the Josephson effect in a strained zigzag graphene nanoribbon with a small length relative to the superconducting coherence length and an arbitrary width. We find a step-wise variation of the critical supercurrent with the width of the nanoribbon, showing additional small width plateaus placed between the broad steps of a unstrained structure. We further demonstrate the peculiar quantization of the critical supercurrent in terms of the strain, resulted from the coupling of the pseudospin of Dirac fermions with the strain-induced gauge potential, where the height of the steps decreases with growing the strength of the fictitious gauge potential. Moreover, our results determine the potential of the proposed superconducting quantum point contact for the realization of the supercurrent switch under an applied strain. Besides, we find the local density of states of the strained zigzag nanoribbon displays a crossover between the decaying and oscillating behavior with the distance from the edges, by tuning the width and Fermi wavelength of the nanoribbon.
In this paper, we propose a scheme for quantum information transfer by a gap-tunable bridge qubit between two superconducting (SC) qubits, which are initially prepared in separable quantum states. As is observed, enough high-fidelity and maximally entanglement between the two superconducting resonators, as well as between the two of qubits, can be achieved. It is shown that by implementing driven magnetic field to high detuned superconducting qubits, we are able to induce sidebands in the qubit–resonator and also qubit–qubit couplings. The influence of decay rates of qubits and resonator modes on the dynamics of quantum fidelity and entanglement is also investigated, either individually or simultaneously, by numerical analysis. Our numerical results show that the decay rate parameters have destructive, constructive, and no critical effect on the fidelity, depending on the chosen decay parameters. Moreover, they have destructive effects on the generated entangled state in the outlined quantum information transfer process.
The dynamics of the fluxon in the Josephson junction is studied. The dielectric layer of the junction has a variable thickness. It is shown that the modified area of the junction acts on the fluxon as a potential barrier. The relation between the critical bias current and the thickness of the dielectric layer is analytically and numerically determined.
We present a design for effectively isolating low-dissipation
superconducting tunnel junctions without causing excessive heating. In
order to obtain a long decoherence time in macroscopic quantum coherence
experiments, it will be essential to make high impedance connections to
the junction. In our design, the connections are made by thin-film
resistors. To prevent excessive heating, we divide the resistors into
many short sections, each of which is heat-sunk to small metal banks. We
rely on electron diffusion to carry the heat out of the resistors and
into the banks. We calculate the resulting temperature profile in the
resistors and discuss the effect on the decoherence time of the junction
Replication protein A (RPA) is a single-stranded DNA-binding protein identified as an essential factor for SV40 DNA replication in vitro. To understand the in vivo functions of RPA, we mutagenized the Saccharomyces cerevisiae RFA1 gene and identified 19 ultraviolet light (UV) irradiation- and methyl methane sulfonate (MMS)-sensitive mutants and 5 temperature-sensitive mutants. The UV- and MMS-sensitive mutants showed up to 10(4) to 10(5) times increased sensitivity to these agents. Some of the UV- and MMS-sensitive mutants were killed by an HO-induced double-strand break at MAT. Physical analysis of recombination in one UV- and MMS-sensitive rfa1 mutant demonstrated that it was defective for mating type switching and single-strand annealing recombination. Two temperature-sensitive mutants were characterized in detail, and at the restrictive temperature were found to have an arrest phenotype and DNA content indicative of incomplete DNA replication. DNA sequence analysis indicated that most of the mutations altered amino acids that were conserved between yeast, human, and Xenopus RPA1. Taken together, we conclude that RPA1 has multiple roles in vivo and functions in DNA replication, repair, and recombination, like the single-stranded DNA-binding proteins of bacteria and phages.
Microwave spectroscopy experiments have been performed on two quantum levels of a macroscopic superconducting loop with three
Josephson junctions. Level repulsion of the ground state and first excited state is found where two classical persistent-current
states with opposite polarity are degenerate, indicating symmetric and antisymmetric quantum superpositions of macroscopic
states. The two classical states have persistent currents of 0.5 microampere and correspond to the center-of-mass motion of
millions of Cooper pairs.
In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.
Be they prokaryotic or eukaryotic, organisms are exposed to a multitude of deoxyribonucleic acid (DNA) damaging agents ranging from ultraviolet (UV) light to fungal metabolites, like Aflatoxin B1. Furthermore, DNA damaging agents, such as reactive oxygen species, can be produced by cells themselves as metabolic byproducts and intermediates. Together, these agents pose a constant threat to an organism's genome. As a result, organisms have evolved a number of vitally important mechanisms to repair DNA damage in a high fidelity manner. They have also evolved systems (cell cycle checkpoints) that delay the resumption of the cell cycle after DNA damage to allow more time for these accurate processes to occur. If a cell cannot repair DNA damage accurately, a mutagenic event may occur. Most bacteria, including Escherichia coli, have evolved a coordinated response to these challenges to the integrity of their genomes. In E. coli, this inducible system is termed the SOS response, and it controls both accurate and potentially mutagenic DNA repair functions [reviewed comprehensively in () and also in ()]. Recent advances have focused attention on the umuD(+)C(+)-dependent, translesion DNA synthesis (TLS) process that is responsible for SOS mutagenesis (). Here we discuss the SOS response of E. coli and concentrate in particular on the roles of the umuD(+)C(+) gene products in promoting cell survival after DNA damage via TLS and a primitive DNA damage checkpoint.
In eukaryotes, the ATM and ATR family proteins play a critical role in the DNA damage and replication checkpoint controls.
These proteins are characterized by a kinase domain related to the phosphatidylinositol 3-kinase, but they have the ability
to phosphorylate proteins. In budding yeast, the ATR family protein Mec1/Esr1 is essential for checkpoint responses and cell
growth. We have isolated the PIE1 gene in a two-hybrid screen for proteins that interact with Mec1, and we show that Pie1 interacts physically with Mec1 in
vivo. Like MEC1, PIE1is essential for cell growth, and deletion of the PIE1 gene causes defects in the DNA damage and replication block checkpoints similar to those observed in mec1Δ mutants. Rad53 hyperphosphorylation following DNA damage and replication block is also decreased in pie1Δ cells, as in mec1Δcells. Pie1 has a limited homology to fission yeast Rad26, which forms a complex with the ATR family protein Rad3. Mutation
of the region in Pie1 homologous to Rad26 results in a phenotype similar to that of thepie1Δ mutation. Mec1 protein kinase activity appears to be essential for checkpoint responses and cell growth. However, Mec1 kinase
activity is unaffected by the pie1Δ mutation, suggesting that Pie1 regulates some essential function other than Mec1 kinase activity. Thus, Pie1 is structurally
and functionally related to Rad26 and interacts with Mec1 to control checkpoints and cell proliferation.
We report the generation and observation of coherent temporal oscillations between the macroscopic quantum states of a Josephson tunnel junction by applying microwaves with frequencies close to the level separation. Coherent temporal oscillations of excited state populations were observed by monitoring the junction's tunneling probability as a function of time. From the data, the lower limit of phase decoherence time was estimated to be about 5 microseconds.
We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the “quantronium.”
An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement
of the state can be performed by a pulsed readout subcircuit. The measured quality factor of quantum coherenceQ
ϕ ≅ 25,000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
Using a nucleus-free DNA replication system we have investigated the roles of Xenopus ATR (XATR) and Hus1 (Xhus1) as the DNA replication checkpoint sensors. Like XATR, Xhus1 is required for the checkpoint-dependent
phosphorylation of Xchk1 and associates with chromatin in an initiation-dependent manner. While removal of replication protein
A inhibits chromatin association of both XATR and Xhus1, removal of polymerase α only disrupts chromatin association of Xhus1.
In addition, chromatin association of XATR and Xhus1 are independent of each other. Finally, like XATR, Xhus1 associates with
chromatin in unperturbed S phase and dissociates from chromatin following completion of DNA replication.
We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.
The escape of a current-biased Josephson tunnel junction from the zero-voltage state in the presence of weak microwave radiation is investigated experimentally at low temperatures. The measurements of the junction switching current distribution indicate the macroscopic quantum tunneling of the phase below a crossover temperature of T small star, filled approximately 280 mK. At temperatures below T small star, filled we observe both single-photon and multiphoton transitions between the junction energy levels by applying microwave radiation in the frequency range between 10 and 38 GHz to the junction. These observations reflect the anharmonicity of the junction potential containing only a small number of levels.
We study an LC circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge-phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.
We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits. Comment: 4 pages, 6 figures. Slightly Revised and final accepted version
The probability distributions for switching out of the superconducting state of low-cur-rent-density 1-μm Nb Josephson junctions with capacitance ≈ 0.1 pF have been measured as a function of temperature T down to 3 mK. Below 100 mK the distribution widths become independent of T. The results are in excellent agreement with predictions for the quantum tunneling of the (macroscopic) junction phase that include the reduction of tunneling rates due to dissipation.
This paper discusses the question: How far do experiments on the so-called “macroscopic quantum systems” such as superfluids
and superconductors test the hypothesis that the linear Schrödinger equation may be extrapolated to arbitrarily complex systems?
It is shown that the familiar “macroscopic quantum phenomena” such as flux quantization and the Josephson effect are irrelevant
in this context, because they correspond to states having a very small value of a certain critical property (christened “disconnectivity”)
while the states important for a discussion of the quantum theory of measurement have a very high value of this property.
Various possibilities for verifying experimentally the existence of such states are discussed, with the conclusion that the
most promising is probably the observation of quantum tunnelling between states with macroscopically different properties.
It is shown that because of their very high “quantum purity” and consequent very low dissipation at low temperatures, superconducting
systems (in particular SQUID rings) offer good prospects for such an observation.
Yeast strains were constructed in which a single telomere could be eliminated from the end of a dispensable chromosome. In wild-type cells, elimination of a telomere caused a RAD9-mediated cell cycle arrest, indicating that telomeres help cells to distinguish intact chromosomes from damaged DNA. However, many cells recovered from the arrest without repairing the damaged chromosome, replicating and segregating it for as many as ten cell divisions prior to its eventual loss. Telomere elimination caused a dramatic increase in loss of the chromosome in all strains examined, demonstrating that yeast telomeres are also essential for maintaining chromosome stability. Thus, in spite of checkpoint and DNA damage repair systems, many chromosomes that lose a telomere are themselves destined for loss.
Replication protein A [RPA; also known as replication factor A (RFA) and human single-stranded DNA-binding protein] is a single-stranded DNA-binding protein that is required for multiple processes in eukaryotic DNA metabolism, including DNA replication, DNA repair, and recombination. RPA homologues have been identified in all eukaryotic organisms examined and are all abundant heterotrimeric proteins composed of subunits of approximately 70, 30, and 14 kDa. Members of this family bind nonspecifically to single-stranded DNA and interact with and/or modify the activities of multiple proteins. In cells, RPA is phosphorylated by DNA-dependent protein kinase when RPA is bound to single-stranded DNA (during S phase and after DNA damage). Phosphorylation of RPA may play a role in coordinating DNA metabolism in the cell. RPA may also have a role in modulating gene expression.
The escape rate of an underdamped (Q≈30), current-biased Josephson junction from the zero-voltage state has been measured. The relevant parameters of the junction were determined in situ in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves. At low temperatures, the escape rate became independent of temperature with a value that, with no adjustable parameters, was in excellent agreement with the zero-temperature prediction for macroscopic quantum tunneling.
We report the first observation of quantized energy levels for a macroscopic variable, namely the phase difference across a current-biased Josephson junction in its zero-voltage state. The position of these energy levels is in quantitative agreement with a quantum mechanical calculation based on parameters of the junction that are measured in the classical regime.
We identified YDR499W as a Saccharomyces cerevisiae open reading frame with homology to several checkpoint proteins, including S. cerevisiae Rfc5p and Schizosaccharomyces pombe Rad26. Disruption of YDR499W (termed LCD1) results in lethality that is rescued by increasing cellular deoxyribonucleotide levels. Cells lacking LCD1 are very sensitive to a range of DNA-damaging agents, including UV irradiation, and to the inhibition of DNA replication. LCD1 is necessary for the phosphorylation and activation of Rad53p in response to DNA damage or DNA replication blocks, and for Chk1p activation in response to DNA damage. LCD1 is also required for efficient DNA damage-induced phosphorylation of Rad9p and for the association of Rad9p with the FHA2 domain of Rad53p after DNA damage. In addition, cells lacking LCD1 are completely defective in the G(1)/S and G(2)/M DNA damage checkpoints. Finally, we reveal that endogenous Mec1p co-immunoprecipitates with Lcd1p both before and after treatment with DNA-damaging agents. These results indicate that Lcd1p is a pivotal checkpoint regulator, involved in both the essential and checkpoint functions of the Mec1p pathway.
The large subunit of replication protein A (Rpa1) consists of three single-stranded DNA binding domains and an N-terminal
domain (Rpa1N) of unknown function. To determine the essential role of this domain we searched for mutations that require
wild-type Rpa1N for viability in yeast. A mutation in RFC4, encoding a small subunit of replication factor C (RFC), was found to display allele-specific interactions with mutations
in the gene encoding Rpa1 (RFA1). Mutations that map to Rpa1N and confer sensitivity to the DNA synthesis inhibitor hydroxyurea, such asrfa1-t11, are lethal in combination withrfc4-2. The rfc4-2 mutant itself is sensitive to hydroxyurea, and like rfc2 and rfc5 strains, it exhibits defects in the DNA replication block and intra-S checkpoints. RFC4 and the DNA damage checkpoint geneRAD24 were found to be epistatic with respect to DNA damage sensitivity. We show that the rfc4-2 mutant is defective in the G1/S DNA damage checkpoint response and that both therfc4-2 and rfa1-t11 strains are defective in the G2/M DNA damage checkpoint. Thus, in addition to its essential role as part of the clamp loader in DNA replication, Rfc4 plays
a role as a sensor in multiple DNA checkpoint pathways. Our results suggest that a physical interaction between Rfc4 and Rpa1N
is required for both roles.
A practical quantum computer, if built, would consist of a set of coupled two-level quantum systems (qubits). Among the variety of qubits implemented, solid-state qubits are of particular interest because of their potential suitability for integrated devices. A variety of qubits based on Josephson junctions have been implemented; these exploit the coherence of Cooper-pair tunnelling in the superconducting state. Despite apparent progress in the implementation of individual solid-state qubits, there have been no experimental reports of multiple qubit gates--a basic requirement for building a real quantum computer. Here we demonstrate a Josephson circuit consisting of two coupled charge qubits. Using a pulse technique, we coherently mix quantum states and observe quantum oscillations, the spectrum of which reflects interaction between the qubits. Our results demonstrate the feasibility of coupling multiple solid-state qubits, and indicate the existence of entangled two-qubit states.
A small superconducting electrode (a single-Cooper-pair box) connected to a reservoir via a Josephson junction constitutes an artificial two-level system, in which two charge states that differ by 2e are coupled by tunneling of Cooper pairs. Despite its macroscopic nature involving a large number of electrons, the two-level system shows coherent superposition of the two charge states, and has been suggested as a candidate for a qubit, i.e. a basic component of a quantum computer. Here we report on time-domain observation of the coherent quantum-state evolution in the two-level system by applying a short voltage pulse that modifies the energies of the two levels nonadiabatically to control the coherent evolution. The resulting state was probed by a tunneling current through an additional probe junction. Our results demonstrate coherent operation and measurement of a quantum state of a single two-level system, i.e. a qubit, in a solid-state electronic device. Comment: 4 pages, 4 figures; to be published in Nature
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