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ABSTRACT: We numerically demonstrate the control of motional degrees of freedom of an ensemble of neutral atoms in an optical lattice with a shallow trapping potential. Taking into account the range of quasimomenta across different Brillouin zones results in an ensemble whose members effectively have inhomogeneous control fields as well as spectrally distinct control Hamiltonians. We present an ensemble-averaged optimal control technique that yields high-fidelity control pulses, irrespective of quasimomentum, with average fidelities above 98%. The resulting controls show a broadband spectrum with gate times in the order of several free oscillations to optimize gates with up to 13.2% dispersion in the energies from the band structure. This can be seen as a model system for the prospects of robust quantum control. This result explores the limits of discretizing a continuous ensemble for control theory.
Phys. Rev. A. 02/2012; 85(2).
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ABSTRACT: We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown-Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.
Physical Review Letters 11/2011; 107(21):217401. · 7.37 Impact Factor
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ABSTRACT: In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.
Phys. Rev. A. 08/2011; 84(2).
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ABSTRACT: In this article, we develop a numerical method to find optimal control pulses
that accounts for the separation of timescales between the variation of the
input control fields and the applied Hamiltonian. In traditional numerical
optimization methods, these timescales are treated as being the same. While
this approximation has had much success, in applications where the input
controls are filtered substantially or mixed with a fast carrier, the resulting
optimized pulses have little relation to the applied physical fields. Our
technique remains numerically efficient in that the dimension of our search
space is only dependent on the variation of the input control fields, while our
simulation of the quantum evolution is accurate on the timescale of the fast
variation in the applied Hamiltonian.
02/2011;
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ABSTRACT: In qubits made from a weakly anharmonic oscillator the leading source of
error at short gate times is leakage of population out of the two dimensional
Hilbert space that forms the qubit. In this paper we develop a general scheme
based on an adiabatic expansion to find pulse shapes that correct this type of
error. We find a family of solutions that allows tailoring to what is practical
to implement for a specific application. Our result contains and improves the
previously developed DRAG technique [F. Motzoi, et. al., Phys. Rev. Lett. 103,
110501 (2009)] and allows a generalization to other non-linear oscillators with
more than one leakage transition.
11/2010;
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ABSTRACT: We investigate three superconducting flux qubits coupled in a loop. In this setup, tripartite entanglement can be created in a natural, controllable, and stable way. Both generic kinds of tripartite entanglement--the W type as well as the GHZ type entanglement--can be identified among the eigenstates. We also discuss the violation of Bell inequalities in this system and show the impact of a limited measurement fidelity on the detection of entanglement and quantum nonlocality.
Nanotechnology 07/2010; 21(27):274015. · 3.98 Impact Factor
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ABSTRACT: The question as to whether or not quantum mechanics is applicable to the macroscopic scale has motivated efforts to generate superposition states of macroscopic numbers of particles and to determine their effective size. Superpositions of circulating current states in flux qubits constitute candidate states that have been argued to be at least mesoscopic. We present a microscopic analysis that reveals the number of electrons participating in these superpositions to be surprisingly but not trivially small, even though differences in macroscopic observables are large. Comment: 7 pages, no figures
03/2010;
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ABSTRACT: Flux qubits, small superconducting loops interrupted by Josephson junctions, are successful realizations of quantum coherence for macroscopic variables. Superconductivity in these loops is carried by $\sim 10^6$ -- $10^{10}$ electrons, which has been interpreted as suggesting that coherent superpositions of such current states are macroscopic superpositions analogous to Schr\"odinger's cat. We provide a full microscopic analysis of such qubits, from which the macroscopic quantum description can be derived. This reveals that the number of microscopic constituents participating in superposition states for experimentally accessible flux qubits is surprisingly but not trivially small. The combination of this relatively small size with large differences between macroscopic observables in the two branches is seen to result from the Fermi statistics of the electrons and the large disparity between the values of superfluid and Fermi velocity in these systems. Comment: Minor cosmetic changes. Published version.
10/2009;
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ABSTRACT: We apply optimal control theory to determine the shortest time in which an
energy eigenstate of a weakly anharmonic oscillator can be created under the
practical constraint of linear driving. We show that the optimal pulses are
beatings of mostly the transition frequencies for the transitions up to the
desired state and the next leakage level. The time of a shortest possible pulse
for a given nonlinearity scale with the nonlinearity parameter delta as a power
law of alpha with alpha=-0.73 +/-0.029. This is a qualitative improvement
relative to the value alpha=1 suggested by a simple Landau-Zener argument.
09/2009;
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ABSTRACT: In realizations of quantum computing, a two-level system (qubit) is often singled out from the many levels of an anharmonic oscillator. In these cases, simple qubit control fails on short time scales because of coupling to leakage levels. We provide an easy to implement analytic formula that inhibits this leakage from any single-control analog or pixelated pulse. It is based on adding a second control that is proportional to the time derivative of the first. For realistic parameters of superconducting qubits, this strategy reduces the error by an order of magnitude relative to the state of the art, all based on smooth and feasible pulse shapes. These results show that even weak anharmonicity is sufficient and in general not a limiting factor for implementing quantum gates.
Physical Review Letters 09/2009; 103(11):110501. · 7.37 Impact Factor
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ABSTRACT: We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven oscillator changes the effective temperature of the qubit. Comment: To appear in Phys. Rev. A (2010)
07/2009;
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ABSTRACT: We provide insight into the qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symmetry. Comment: 5 pages, 5 figures
05/2009;
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ABSTRACT: In this paper we derive an effective master equation and quantum trajectory
equation for multiple qubits in a single resonator and in the large resonator
decay limit. We show that homodyne measurement of the resonator transmission is
a weak measurement of the collective qubit inversion. As an example of this
result, we focus on the case of two qubits and show how this measurement can be
used to generate an entangled state from an initially separable state. This is
realized without relying on an entangling Hamiltonian. We show that, for {\em
current} experimental values of both the decoherence and measurement rates,
this approach can be used to generate highly entangled states. This scheme
takes advantage of the fact that one of the Bell states is decoherence-free
under Purcell decay.
12/2008;
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ABSTRACT: Physical implementations of quantum bits can contain coherent transitions to energetically close nonqubit states. In particular, for inharmonic-oscillator systems such as the superconducting phase qubit and the transmon, a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single weakly off-resonant leakage level. The gate error of a spin-flip (NOT) operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.
Phys. Rev. B. 08/2008; 79(6).
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ABSTRACT: We present a measurement protocol for a flux qubit coupled to a dc-Superconducting QUantum Interference Device (SQUID), representative of any two-state system with a controllable coupling to an harmonic oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.
04/2008;
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ABSTRACT: Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantum-mechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1/2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwave-spectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
Physics-Uspekhi 10/2007; 44(10S):117. · 2.15 Impact Factor
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ABSTRACT: We investigate macroscopic dynamical quantum tunneling (MDQT) in the driven Duffing oscillator, characteristic for Josephson junction physics and nanomechanics. Under resonant conditions between stable coexisting states of such systems we calculate the tunneling rate. In macroscopic systems coupled to a heat bath, MDQT can be masked by driving-induced activation. We compare both processes, identify conditions under which tunneling can be detected with present day experimental means and suggest a protocol for its observation.
Physical Review Letters 10/2007; 99(13):137001. · 7.37 Impact Factor
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ABSTRACT: Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.
03/2007;
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ABSTRACT: A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate the implementation of quantum gates for a paradigmatic model: A single qubit coupled to a two-level system exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open systems Gradient Ascent Pulse Engineering (GRAPE) algorithm. We show and explain that next to the known optimal bias point of this model, there are optimal shapes which refocus unwanted terms in the Hamiltonian. We study the limitations of control set by the decoherence properties, which go beyond a simple random telegraph noise model. This can lead to a significant improvement of quantum operations in hostile environments. A promising class of candidates for the practical re-alization of scalable quantum computers are solid state quantum devices based on superconductors [1, 2, 3, 4, 5] and lateral quantum dots [6]. A key challenge to over-come in this enterprise is the decoherence induced by the coupling to the macroscopic bath of degrees of free-dom not used for quantum computation (see e.g. ref. [7] for a recent review). Many of these decoherence sources can be engineered at the origin. In the case of intrinsic slow noise originating from two level fluctuators (TLFs) this is much harder [8, 9], albeit not impossible [10, 11]. Thus, in order to advance the limitations of coherent quantum manipulations in the solid state, it is imper-ative to find strategies which accomodate this kind of noise. A number of methods have been proposed by intu-ition and analogies to different areas, such as dynamical decoupling [12, 13], the optimum working point strategy [1, 5, 14], and NMR-like approaches [15]. Even in light of their success, it is by no means clear, whether even better strategies can be formulated and, on a more general level, where the limits of quantum control under hostile condi-tions are reached. Thus we resort to numerical methods of optimal control. The closed systems GRAPE (gradient ascent pulse engineering) algorithm [16] has proven useful in coupled Josephson devices already [17]. It was recently extended to open systems in the strictly Markovian do-main [18]. In this Letter, we generalize the method to in-clude a complex environment leading to non-Markovian qubit dynamics and non-Gaussian noise. We show that next to an optimal working point there is also an optimal pulse shape and optimal gate duration. Accelerating the fluctuations can improve the gate. We discuss the physics ultimately limiting the gate performance no longer cor-rectable by pulse shaping.
03/2007;
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ABSTRACT: We consider a superconducting charge qubit coupled to distinct orthogonal electromagnetic field modes belonging to a coplanar wave guide and a microstrip transmission line resonators. This architecture allows the simultaneous implementation of a Jaynes-Cummings and anti-Jaynes-Cummings dynamics, a resonant method for generating mesoscopic qubit-field superpositions and for field-state reconstruction. Furthermore, we utilize this setup to propose a field measurement technique that is, in principle, robust to qubit dephasing and field relaxation due to a fast pre-measurement.
01/2007;
