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Nonlinear Optics Using Intense Optical Coherent State Superpositions
Abstract
Superpositions of coherent light states are vital for quantum technologies. However, restrictions in existing state preparation and characterization schemes, in combination with decoherence effects, prevent their intensity enhancement and implementation in nonlinear optics. Here, by developing a decoherence-free approach, we generate intense femtosecond-duration infrared coherent state superpositions (CSSs) with a mean photon number orders of magnitude higher than the existing CSS sources. We utilize them in nonlinear optics to drive the second harmonic generation process in an optical crystal. We experimentally and theoretically show that the nonclassical nature of the intense infrared CSS is imprinted in the second-order autocorrelation traces. Additionally, theoretical analysis shows that the quantum features of the infrared CSS are also present in the generated second harmonic. The findings introduce the optical CSS into the realm of nonlinear quantum optics, opening up new paths in quantum information science and quantum light engineering by creating nonclassical light states in various spectral regions via nonlinear up-conversion processes.
... Recently, several breakthroughs have emerged in attosecond science [9][10][11][12][13][14], synchrotron radiation technique [15], and photonic quantum information technology [16], which pave the way for experimentally realizing large-scale optical cat states. These advances are opening new avenues for measuring, controlling, and engineering quantum materials through quantum light irradiation [17][18][19][20][21][22][23][24][25]. ...
We present an effective theory for describing electron dynamics driven by an optical external field in a Schr\"{o}dinger's cat state. We show that the electron density matrix evolves as an average over trajectories weighted by the Sudarshan--Glauber P distribution in the weak light--matter coupling regime. Each trajectory obeys an equation of motion, , where an effective Hamiltonian becomes non-Hermitian due to quantum interference of light. The optical quantum interference is transferred to electrons through the asymmetric action between the ket and bra state vectors in . This non-Hermitian dynamics differs from the conventional one observed in open quantum systems, described by , which has complex conjugation in the second term. We confirm that the results of the effective theory agree with those of full electron--photon system simulations for the few-electron Dicke model, demonstrating experimental accessibility to exotic non-Hermitian dynamics.
In the domain of quantum metrology, cat states have demonstrated their utility despite their inherent fragility with respect to losses. Here, we introduce noise robust optical cat states which exhibit a metrological robustness for phase estimation in the regime of high photon numbers. These cat states are obtained from the intense laser driven process of high harmonic generation (HHG), and show a resilience against photon losses. Focusing on a realistic scenario including experimental imperfections we opt for the case in which we can maximize the lower bound of the quantum Fisher information (QFI) instead of analyzing the best case scenario. We show that the decrease of the QFI in the lossy case is suppressed for the HHG-cat state compared to the even and odd counterparts. In the regime of small losses of just a single photon, the HHG-cat state remains almost pure while the even/odd cat state counterparts rapidly decohere to the maximally mixed state. More importantly, this translates to a significantly enhanced robustness for the HHG-cat against photon loss, demonstrating that high photon number optical cat states can indeed be used for metrological applications even in the presence of losses.
Strong--laser--field physics is a research direction that relies on the use of high-power lasers and has led to fascinating achievements ranging from relativistic particle acceleration to attosecond science. On the other hand, quantum optics has been built on the use of low photon number sources and has opened the way for groundbreaking discoveries in quantum technology, advancing investigations ranging from fundamental tests of quantum theory to quantum information processing. Despite the tremendous progress, until recently these directions have remained disconnected. This is because, the majority of the interactions in the strong-field limit have been successfully described by semi-classical approximations treating the electromagnetic field classically, as there was no need to include the quantum properties of the field to explain the observations. The link between strong--laser--field physics, quantum optics, and quantum information science has been developed in the recent past. Studies based on fully quantized and conditioning approaches have shown that intense laser--matter interactions can be used for the generation of controllable entangled and non-classical light states. These achievements open the way for a vast number of investigations stemming from the symbiosis of strong--laser--field physics, quantum optics, and quantum information science. Here, after an introduction to the fundamentals of these research directions, we report on the recent progress in the fully quantized description of intense laser--matter interaction and the methods that have been developed for the generation of non-classical light states and entangled states. Also, we discuss the future directions of non-classical light engineering using strong laser fields, and the potential applications in ultrafast and quantum information science.
Intense laser-matter interactions are at the center of interest in research and technology since the development of high-power lasers. They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast optoelectronics. Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superpositions. In this tutorial, we provide a comprehensive fully quantized description of intense laser-atom interactions. We elaborate on the processes of high-harmonic generation, above-threshold ionization, and we discuss new phenomena that cannot be revealed within the context of semiclassical theories. We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light. Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed of the symbiosis of attosecond physics and quantum information science.
We implement an iterative scheme for the generation of coherent states superpositions, using a quantum memory to take advantage of the iterative nature of the protocol. The generation rate has thus been increased by one order of magnitude, reaching 100 (Hz). Furthermore, the generated states were stored in the quantum memory during 184 (ns) before their characterization, paving the way toward the implementation of more complex iterative protocols.
The physics of intense laser–matter interactions1,2 is described by treating the light pulses classically, anticipating no need to access optical measurements beyond the classical limit. However, the quantum nature of the electromagnetic fields is always present³. Here we demonstrate that intense laser–atom interactions may lead to the generation of highly non-classical light states. This was achieved by using the process of high-harmonic generation in atoms4,5, in which the photons of a driving laser pulse of infrared frequency are upconverted into photons of higher frequencies in the extreme ultraviolet spectral range. The quantum state of the fundamental mode after the interaction, when conditioned on the high-harmonic generation, is a so-called Schrödinger cat state, which corresponds to a superposition of two distinct coherent states: the initial state of the laser and the coherent state reduced in amplitude that results from the interaction with atoms. The results open the path for investigations towards the control of the non-classical states, exploiting conditioning approaches on physical processes relevant to high-harmonic generation.
A cat state is a superposition of two coherent states with amplitudes α0 and −α0. Recent experiments create cat states in a microwave cavity field using superconducting circuits. As with degenerate parametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the states are formed in a signal cavity mode via a two-photon dissipative process induced by the down conversion of a pump field to generate pairs of signal photons. The damping of the signal and the presence of thermal fluctuations rapidly decoheres the state, and the effect on the dynamics is to either destroy the possibility of a cat state or else to sharply reduce the lifetime and size of the cat states that can be formed. In this paper, we study the effect on both the DPO and microwave systems of a squeezed reservoir coupled to the cavity. While the threshold nonlinearity is not altered, we show that the use of squeezed states significantly lengthens the lifetime of the cat states. This improves the feasibility of generating cat states of large amplitudes and with a greater degree of quantum macroscopic coherence, which is necessary for many quantum technology applications. Using current experimental parameters for the microwave setup, which requires a modified Hamiltonian, we further demonstrate how squeezed states enhance the quality of the cat states that could be formed in this regime. Squeezing also combats the significant decoherence due to thermal noise, which is relevant for microwave fields at finite temperature. By modeling a thermal squeezed reservoir, we show that the thermal decoherence of the dynamical cat states can be inhibited by a careful control of the squeezing of the reservoir. To signify the quality of the cat state, we consider different signatures including fringes and negativity, and the Cl1 measure of quantum coherence.
This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the "simple man's models" which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include High-Harmonic Generation (HHG), Above-Threshold Ionization (ATI), and Non-Sequential Multielectron Ionization (NSMI). "Simple man's models"provide, both an intuitive basis for understanding the numerical solutions of the time-dependent Schr\"odinger equation, and the motivation for the powerful analytic approximations generally known as the Strong Field Approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between Electron Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization (RESI); (ii) time-dependent treatment in the single active electron (SAE) approximation of "large" molecules and targets which are themselves undergoing dynamics during the HHG or ATI process. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields.
We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age o.
Using quantum states of light for imaging both reveals quantum phenomena and enables new protocols that result in images that surpass classical limitations. Such systems require both quantum light sources and often the ingenious use of detector technologies.
Superpositions of macroscopically distinct quantum states, introduced in Schrödinger's famous Gedankenexperiment, are an epitome of quantum ‘strangeness’ and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schrödinger's cat (SC)—the superposition of two opposite-amplitude coherent states—is also the backbone of continuous-variable quantum information processing. However, the existing preparation methods limit the amplitudes of the component coherent states, which curtails the state's usefulness for fundamental and practical applications. Here, we convert a pair of negative squeezed SC states of amplitude 1.15 to a single positive SC state of amplitude 1.85 with a success probability of ∼0.2. The protocol consists in bringing the initial states into interference on a beamsplitter and a subsequent heralding quadrature measurement in one of the output channels. Our technique can be realized iteratively, so arbitrarily high amplitudes can, in principle, be reached.
High-order harmonics in the extreme-ultraviolet spectral range, resulting from the strong-field laser-atom interaction, have been used in a broad range of fascinating applications in all states of matter. In the majority of these studies the harmonic generation process is described using semi-classical theories which treat the electromagnetic field of the driving laser pulse classically without taking into account its quantum nature. In addition, for the measurement of the generated harmonics, all the experiments require diagnostics in the extreme-ultraviolet spectral region. Here by treating the driving laser field quantum mechanically we reveal the quantum-optical nature of the high-order harmonic generation process by measuring the photon number distribution of the infrared light exiting the harmonic generation medium. It is found that the high-order harmonics are imprinted in the photon number distribution of the infrared light and can be recorded without the need of a spectrometer in the extreme-ultraviolet.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50–50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties - known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators. These are different from Glauber's g- functions for photon counting which use normally ordered products of ordinary operators. Entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.
We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrödinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.
Photon beams exhibit temporal correlations that are characteristics of their emission mechanism. For instance, photons issued from incoherent sources tend to be detected in bunches. This striking 'bunching' behaviour has been observed in the seminal experiment by Hanbury-Brown and Twiss (HBT) in the fifties, who measured the time of arrival of partially coherent photons on two separate photon-counting modules1. Since then, HBT Interferometry has become a widespread technique to study photon correlations down to only the nanosecond range, because of the detector-limited bandwidth, preventing the observation of bunching for real thermal sources. It has been suggested later that two-photon absorption (TPA) could measure the photon temporal correlations at a much shorter timescale2,3, as it involves an almost simultaneous absorption of two photons, within a maximum delay given by the Heisenberg principle. Here, for the first time, this prediction is experimentally demonstrated using TPA in a GaAs photon-counting module. We have observed photon bunching in the femtosecond range for real blackbody sources (an enhancement of six orders of magnitude in the time resolution of present techniques), opening the way to monitor optical quantum statistics at the ultrashort timescale.
We present an improved phase estimation scheme employing entangled coherent states and demonstrate that these states give the smallest variance in the phase parameter in comparison to NOON, "bat," and "optimal" states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.
For many years twin beams originating from parametric down-converted light beams have aroused great interest and attention in the photonics community. One particular aspect of the twin beams is their peculiar intensity correlation functions, which are related to the coincidence rate of photon pairs. Here we take advantage of the huge bandwidth offered by two-photon absorption in a semiconductor to quantitatively determine correlation functions of twin beams generated by spontaneous parametric down-conversion. Compared with classical incoherent sources, photon extrabunching is unambiguously and precisely measured, originating from exact coincidence between down-converted pairs of photons, travelling in unison. These results strongly establish that two-photon counting in semiconductors is a powerful tool for the absolute measurement of light beam photon correlations at ultrashort timescales.
In classical estimation theory, the central limit theorem implies that the
statistical error in a measurement outcome can be reduced by an amount
proportional to n^(-1/2) by repeating the measures n times and then averaging.
Using quantum effects, such as entanglement, it is often possible to do better,
decreasing the error by an amount proportional to 1/n. Quantum metrology is the
study of those quantum techniques that allow one to gain advantages over purely
classical approaches. In this review, we analyze some of the most promising
recent developments in this research field. Specifically, we deal with the
developments of the theory and point out some of the new experiments. Then we
look at one of the main new trends of the field, the analysis of how the theory
must take into account the presence of noise and experimental imperfections.
We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called root binning, that is used to transform the continuous variables measurements into binary results needed for the tests of quantum mechanics versus local realistic theories. A physical process in order to produce such states is also suggested. The use of high-efficiency spacelike separated homodyne detections with these states and this binning process would result in a conclusive loophole-free test of quantum mechanics.
A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50–50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.
Single-photon-added coherent states are the result of the most elementary amplification process of classical light fields by a single quantum of excitation. Being intermediate between a single-photon Fock state (fully quantum-mechanical) and a coherent (classical) one, these states offer the opportunity to closely follow the smooth transition between the particle-like and the wavelike behavior of light. We report the experimental generation of single-photon-added coherent states and their complete characterization by quantum tomography. Besides visualizing the evolution of the quantum-to-classical transition, these states allow one to witness the gradual change from the spontaneous to the stimulated regimes of light emission.
We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-Gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6 dB squeezed light and a homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent experimental generation of single-mode non-Gaussian states, suggests that this method opens a promising avenue towards a complete experimental Bell test.
Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional
measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as
the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using
quantum strategies that employ “quantum tricks” such as squeezing and entanglement.
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform `quantum floating point' computations. Problems of noise, finite precision, and error correction are discussed. Comment: 9 pages, TeX
We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements and "small" coherent superposition resource states.
When a superposition of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of , as was recently discovered by O. Hirota and M. Sasaki. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat states Comment: 11 pages LaTeX, 3 eps figures. Submitted to Phys. Rev. A
Squeezed optical fields are a powerful resource for a variety of investigations in basic research and technology. However, the generation of intense squeezed light is challenging. Here, we show that intense squeezed light can be produced using strongly laser driven atoms and the so far unrelated process of high harmonic generation. We demonstrate that when the intensity of the driving field significantly depletes the ground state of the atoms, leading to dipole moment correlations, the quantum state of the driving field and the generated high harmonics are entangled and squeezed. Furthermore, we analyze how the resulting quadrature squeezing of the fundamental laser mode after the interaction can be controlled. The findings open the way for the generation of high intensity squeezed light states for a wide range of applications.
The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically—and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.
High-harmonic generation (HHG) has emerged as a pivotal process in strong-field physics, yielding extreme ultraviolet radiation and attosecond pulses for a wide range of applications. Furthermore, its emergent connection with the field of quantum optics has revealed its potential for generating nonclassical states of light. Here, we investigate the process of high-harmonic generation in semiconductors under a quantum optical perspective while using a Bloch-based solid-state description. Through the implementation of quantum operations based on the measurement of high-order harmonics, we demonstrate the generation of nonclassical light states similar to those found when driving atomic systems. These states are characterized using diverse quantum optical observables and quantum information measures, showing the influence of electron dynamics on their properties. Additionally, we analyze the dependence of their features on solid characteristics such as the dephasing time and crystal orientation, while also assessing their sensitivity to changes in driving field strength. This paper provides insights into HHG in semiconductors and its potential for generating nonclassical light sources.
Quantum information science and intense laser-matter interaction are two apparently unrelated fields. Here, we introduce the notion of quantum information theory to intense laser-driven processes by providing the quantum mechanical description of measurement protocols for high-order harmonic generation in atoms. This allows one to conceive new protocols for quantum state engineering of light. We explicitly evaluate conditioning experiments on individual optical field modes and provide the corresponding quantum operation for coherent states. The associated positive-operator-valued measures are obtained and give rise to the quantum theory of measurement for the generation of high-dimensional entangled states and coherent-state superposition with controllable nonclassical features on the attosecond timescale. This establishes the use of intense laser-driven processes as an alternative platform for quantum information processing.
We present a theoretical demonstration on the generation of entangled coherent states and of coherent state superpositions, with photon numbers and frequencies orders of magnitude higher than those provided by the current technology. This is achieved by utilizing a quantum mechanical multimode description of the single- and two-color intense laser field driven process of high harmonic generation in atoms. It is found that all field modes involved in the high harmonic generation process are entangled, and upon performing a quantum operation, lead to the generation of high photon number optical cat states spanning from the far infrared to the extreme ultraviolet spectral region. This provides direct insights into the quantum mechanical properties of the optical field in the intense laser matter interaction. Finally, these states can be considered as a new resource for fundamental tests of quantum theory, quantum information processing, or sensing with nonclassical states of light.
Recently, intensely driven laser-matter interactions have been used to connect the fields of strong laser field physics with quantum optics by generating nonclassical states of light. Here, we take a further key step and show the potential of strong laser fields for generating controllable high-photon-number coherent-state superpositions. This has been achieved by using two of the most prominent strong-laser induced processes: high-harmonic generation and above-threshold ionization. We show how the obtained coherent-state superpositions change from an optical Schrödinger “cat” state to a “kitten” state by changing the atomic density in the laser-atom interaction region, and we demonstrate the generation of a nine-photon shifted optical “cat” state, which, to our knowledge, is the highest photon number optical “cat” state experimentally reported. Our findings anticipate the development of new methods that naturally lead to the creation of high-photon-number controllable coherent-state superpositions, advancing investigations in quantum technology.
The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l 1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.
We find that Bell’s inequality can be significantly violated (up to Tsirelson’s bound) with two-mode entangled coherent states using only homodyne measurements. This requires Kerr nonlinear interactions for local operations on the entangled coherent states. Our example is a demonstration of Bell-inequality violations using classical measurements. We conclude that entangled coherent states with coherent amplitudes as small as 0.842 are sufficient to produce such violations.
An entangled two-mode coherent state is studied within the framework of 2×2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.
The nonlinear Mach-Zehnder interferometer is presented as a device whereby a pair of coherent states can be transformed into an entangled superposition of coherent states for which the notion of entanglement is generalized to include nonorthogonal, but distinct, component states. Each mode is directed to a homodyne detector. We show that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism. In contradistinction to previous optical schemes which test local realism, the initial state used here possesses a positive Glauber-Sudarshan representation and is therefore a semiclassical state. The nonlinearity itself is responsible for generating the nonclassical state.
Distributing secret keys with information-theoretic security is arguably one
of the most important achievements of the field of quantum information
processing and communications. The rapid progress in this field has enabled
quantum key distribution (QKD) in real-world conditions and commercial devices
are now readily available. QKD systems based on continuous variables present
the major advantage that they only require standard telecommunication
technology, and in particular, that they do not use photon counters. However,
these systems were considered up till now unsuitable for long-distance
communication. Here, we overcome all previous limitations and demonstrate for
the first time continuous-variable quantum key distribution over 80 km of
optical fibre. The demonstration includes all aspects of a practical scenario,
with real-time generation of secret keys, stable operation in a regular
environment, and use of finite-size data blocks for secret information
computation and key distillation. Our results correspond to an implementation
guaranteeing the strongest level of security for QKD reported to date for such
long distances and pave the way to practical applications of secure quantum
communications.
We present an object-oriented open-source framework for solving the dynamics
of open quantum systems written in Python. Arbitrary Hamiltonians, including
time-dependent systems, may be built up from operators and states defined by a
quantum object class, and then passed on to a choice of master equation or
Monte-Carlo solvers. We give an overview of the basic structure for the
framework before detailing the numerical simulation of open system dynamics.
Several examples are given to illustrate the build up to a complete
calculation. Finally, we measure the performance of our library against that of
current implementations. The framework described here is particularly
well-suited to the fields of quantum optics, superconducting circuit devices,
nanomechanics, and trapped ions, while also being ideal for use in classroom
instruction.
We present a simple, analytic, and fully quantum theory of high-harmonic generation by low-frequency laser fields. The theory recovers the classical interpretation of Kulander et al. in Proceedings of the SILAP III Works hop, edited by B. Piraux (Plenum, New York, 1993) and Corkum [Phys. Rev. Lett. 71, 1994 (1993)] and clearly explains why the single-atom harmonic-generation spectra fall off at an energy approximately equal to the ionization energy plus about three times the oscillation energy of a free electron in the field. The theory is valid for arbitrary atomic potentials and can be generalized to describe laser fields of arbitrary ellipticity and spectrum. We discuss the role of atomic dipole matrix elements, electron rescattering processes, and of depletion of the ground state. We present the exact quantum-mechanical formula for the harmonic cutoff that differs from the phenomenological law Ip+3.17Up, where Ip is the atomic ionization potential and Up is the ponderomotive energy, due to the account for quantum tunneling and diffusion effects.
We present a detailed experimental analysis of a free-propagating light pulse prepared in a “Schrödinger kitten” state, which
is defined as a quantum superposition of “classical” coherent states with small amplitudes. This kitten state is generated
by subtracting one photon from a squeezed vacuum beam, and it clearly presents a negative Wigner function. The predicted influence
of the experimental parameters is in excellent agreement with the experimental results. The amplitude of the coherent states
can be amplified to transform our “Schrödinger kittens” into bigger Schrödinger cats, providing an essential tool for quantum
information processing.
Schrödinger's cat is a Gedankenexperiment in quantum physics, in which an atomic decay triggers the death of the cat. Because quantum physics allow atoms to remain in superpositions of states, the classical cat would then be simultaneously dead and alive. By analogy, a 'cat' state of freely propagating light can be defined as a quantum superposition of well separated quasi-classical states-it is a classical light wave that simultaneously possesses two opposite phases. Such states play an important role in fundamental tests of quantum theory and in many quantum information processing tasks, including quantum computation, quantum teleportation and precision measurements. Recently, optical Schrödinger 'kittens' were prepared; however, they are too small for most of the aforementioned applications and increasing their size is experimentally challenging. Here we demonstrate, theoretically and experimentally, a protocol that allows the generation of arbitrarily large squeezed Schrödinger cat states, using homodyne detection and photon number states as resources. We implemented this protocol with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly exhibits several quantum phase-space interference fringes between the 'dead' and 'alive' components, and is large enough to become useful for quantum information processing and experimental tests of quantum theory.