Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

Graefe, Eva-Maria; Korsch, Hans Jürgen; Niederle, Astrid Elisa

doi:10.1103/physreva.82.013629

Cited by 143 publications

(218 citation statements)

References 97 publications

(160 reference statements)

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“…This theme has also been considered in the BEC literature and in the context of the so-called leaky Bose-Hubbard dimers (allowing, e.g., the tunneling escape of atoms from one of the wells of a doublewell potential). There, a variant of the model considered below has been self-consistently derived in the mean-field approximation [15] and the correspondence of its classical with the full quantum behavior has been explored [16].…”

Section: Introductionmentioning

confidence: 99%

PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics

2011

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In the present work we focus on the case of (few-site) configurations respecting the parity-time (PT ) symmetry, i.e., with a spatially odd gain-loss profile. We examine the case of such "oligomers" with not only two sites, as in earlier works, but also the cases of three and four sites. While in the former case of recent experimental interest the picture of existing stationary solutions and their stability is fairly straightforward, the latter cases reveal a considerable additional complexity of solutions, including ones that exist past the linear PT -symmetry breaking point in the case of the trimer, and symmetry-breaking bifurcations, as well as more complex, even asymmetric solutions in the case of the quadrimer with nontrivial properties in their linear stability and in their nonlinear dynamics. The linearization around the obtained solutions and their dynamical evolution, when unstable, are discussed.

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Section: Introductionmentioning

confidence: 99%

PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics

2011

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“…Spectral singularities in PT -symmetric potentials [16] turned out to be connected with the amplification of waves [17] and the lasing threshold [18]. Nonlinear PT -symmetric quantum systems have been discussed for BECs described in a two-mode approximation [19][20][21] and in model potentials [22]. The first experimental realization was achieved * Holger.Cartarius@itp1.uni-stuttgart.de in 2009/2010, when two groups observed the expected properties in optical systems [23,24].…”

Section: Introductionmentioning

confidence: 99%

Coupling approach for the realization of aPT-symmetric potential for a Bose-Einstein condensate in a double well

et al. 2014

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We show how non-Hermitian potentials used to describe probability gain and loss in effective theories of open quantum systems can be achieved by a coupling of the system to an environment. We do this by coupling a Bose-Einstein condensate (BEC) trapped in an attractive double-δ potential to a condensate fraction outside the double well. We investigate which requirements have to be imposed on possible environments with a linear coupling to the system. This information is used to determine an environment required for stationary states of the BEC. To investigate the stability of the system we use fully numerical simulations of the dynamics. It turns out that the approach is viable and possible setups for the realization of a PT -symmetric potential for a BEC are accessible. Vulnerabilities of the whole system to small perturbations can be attributed to the singular character of the simplified δ-shaped potential used in our model.

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“…We consider an initial density written as a mixing of several states, The corresponding Husimi function is obtained as 27) and is shown in Fig. 9a.…”

Section: Smf With An Initial Mixed Densitymentioning

confidence: 99%

“…The mean-field approximation of the LMG model can be obtained by using the SU(2) spin coherent states [25][26][27][28]. The spin (Bloch) coherent states are defined by…”

Section: B the Mean-field Approximation With Su(2)mentioning

confidence: 99%

Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

2014

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In the stochastic mean-field (SMF) approach, an ensemble of initial values for a selected set of one-body observables is formed by stochastic sampling from a phase-space distribution that reproduces the initial quantum fluctuations. Independent mean-field evolutions are performed with each set of initial values followed by averaging over the resulting ensemble. This approach has been recently shown to be rather versatile and accurate in describing the correlated dynamics beyond the independent particle picture. In the original formulation of SMF, it was proposed to use a Gaussian assumption for the phase-space distribution. This assumption turns out to be rather effective when the dynamics of an initially uncorrelated state is considered, which was the case in all applications of this approach up to now. Using the Lipkin-Meshkov-Glick (LMG) model, we show that such an assumption might not be adequate if the quantum system under interest is initially correlated and presents configuration mixing between several Slater determinants. In this case, a more realistic description of the initial phase-space is necessary. We show that the SMF approach can be advantageously combined with standard methods to describe phase-space in quantum mechanics. As an illustration, the Husimi distribution function is used here to obtain a realistic representation of the phase-space of a quantum many-body system. This method greatly improves the description of initially correlated fermionic many-body states. In the LMG model, while the Gaussian approximation failed to describe these systems in all interaction strength range, the novel approach gives a perfect agreement with the exact evolution in the weak coupling regime and significantly improves the description of correlated systems in the strong coupling regime.

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Quantum-classical correspondence for a non-Hermitian Bose-Hubbard dimer

Cited by 143 publications

References 97 publications

PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics

PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics

Coupling approach for the realization of aPT-symmetric potential for a Bose-Einstein condensate in a double well

Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

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