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arXiv:0801.4490 · Physical Review Letters

Fidelity Decay in Trapped Bose-Einstein Condensates

Giovanni Manfredi, Paul-Antoine Hervieux

Published Feb 8, 2008• 18 citations
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Abstract

The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.

DOI
10.1103/physrevlett.100.050405

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The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes of two condensates evolving in slightly different potentials.
The Fermi-decay law of Bose—Einstein condensate, which is trapped by a cigar-shaped anharmonic trap and subjected to a weak random perturbation, is investigated by numerically calculating quantum fidelity (Loschmidt echo), to reveal the coherence loss of the condensate. We find that there are three indispensable factors, anharmonic trap, weak random perturbation and nonlinear interaction, in charging of the Fermi-decay law. The anharmonic trap creates anharmonic oscillations, and the weak random perturbation causes coherence loss by disturbing their coherent oscillations, while the nonlinear interaction enhances the loss to the Fermi-decay law. Based on the Fermi-decay law, some suggestions are presented to prolong the coherent time during coherently manipulating condensates.
We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field-driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to 0.750.750.75 at the evolution time of 1.51.51.5 s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of 2.82.82.8 s for a trapped condensate of $5.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ interacting atoms.
We study the quantum Loschmidt echo (LE) in a Bose-Einstein condensate (BEC) in a double-well potential. The BEC may undergo a dynamical phase transition between two phases: a tunneling phase and a self-trapping phase. For sufficiently weak perturbation, the LE has Gaussian decay in both phases. While, for relatively strong perturbation, the LE has a Gaussian decay in the self-trapping phase and has a stretched exponential decay in the tunneling phase. This qualitative difference in the decaying law of the LE in the two phases provides a characterization of the dynamical phase transition of the BEC. The semiclassical theory is used to explain the numerically observed behaviors of the LE decay.
We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power law, depending on the initial location, the perturbation strength, as well as the underlying mean-field classical dynamics. In this case we find a clear correspondence between the fast quantum fidelity decay and the dynamical instability of the mean-field system. With the initial state prepared as a maximally entangled state, we find that the behavior of fidelity has no classical correspondence and observe an interesting behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.
The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate trapped in a symmetric double well potential is studied. The (nonexponential) decoherence induced on the oscillator by the measuring device is analyzed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: an initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expressions are obtained in the full quantum case where algebraic time decay of decoherence is observed.
We explore Loschmidt echo in two regimes of one-dimensional interacting Bose gases: the strongly interacting Tonks-Girardeau (TG) regime, and the weakly interacting mean-field regime. We find that the Loschmidt echo of a TG gas decays as a Gaussian when small (random and time independent) perturbations are added to the Hamiltonian. The exponent is proportional to the number of particles and the magnitude of a small perturbation squared. In the mean-field regime the Loschmidt echo shows richer behavior: it decays faster for larger nonlinearity, and the decay becomes more abrupt as the nonlinearity increases; it can be very sensitive to the particular realization of the noise potential, especially for relatively small nonlinearities.