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arXiv:1410.7577 · Physical Review A

Quantum decoherence of an anharmonic oscillator monitored by a Bose-Einstein condensate

Daniel Alonso, S. Brouard, D. Sokolovski

Published Sep 11, 2014• 4 citations
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Abstract

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.

DOI
10.1103/physreva.90.032106

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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 investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double-well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a ``coherent'' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power-law) or rapid (Gaussian) decoherence of the mean values themselves.
The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.
We study the dynamics of Bose-Einstein condensates in symmetric double-well potentials following a sudden change of the potential from the Mott-insulator to the superfluid regime. We introduce a continuum approximation that maps that problem onto the wave-packet dynamics of a particle in an anharmonic effective potential. For repulsive two-body interactions the visibility of interference fringes that result from the superposition of the two condensates following a stage of ballistic expansion exhibits a collapse of coherent oscillations onto a background value whose magnitude depends on the amount of squeezing of the initial state. Strong attractive interactions are found to stabilize the relative number dynamics. We visualize the dynamics of the system in phase space using a quasiprobability distribution that allows for an intuitive interpretation of the various types of dynamics.
The dynamical properties of partially coherent Bose-Einstein condensates in double wells are investigated in three typical regimes. In the extreme Fock regime, the time evolution of the degree of coherence is shown to decay rapidly. In the Rabi regime, a relation between the amplitude of Rabi oscillation and the degree of coherence is obtained, which is expected to determine the degree of coherence by measuring the amplitude of Rabi oscillation. The study on the self-trapping phenomena in the Josephson regime exhibits that both the degree of coherence and the initial relative phase can affect the final particle distribution.
We consider an electrostatic qubit located near a Bose-Einstein condensate (BEC) of noninteracting bosons in a double-well potential, which is used for qubit measurements. Tracing out the BEC variables we obtain a simple analytical expression for the qubit's density matrix. The qubit's evolution exhibits a slow $(\ensuremath{\propto}1/\sqrt{t})$ damping of the qubit's coherence term, which however turns to be a Gaussian one in the case of static qubit. This is in contrast to the exponential damping produced by most classical detectors. The decoherence is, in general, incomplete and strongly depends on the initial state of the qubit.