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arXiv:1209.4426 · Physical Review E

Coherence dynamics of kicked Bose-Hubbard dimers: Interferometric signatures of chaos

Christine Khripkov, Doron Cohen, Amichay Vardi

Published Jan 18, 2013• 20 citations
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Abstract

We study the coherence dynamics of a kicked two-mode Bose-Hubbard model starting with an arbitrary coherent spin preparation. For preparations in the chaotic regions of phase space we find a generic behavior with Floquet participation numbers that scale as the entire N-particle Hilbert space, leading to a rapid loss of single-particle coherence. However, the chaotic behavior is not uniform throughout the chaotic sea and unique statistics is found for preparations at the vicinity of hyperbolic points that are embedded in it. This is contrasted with the low log(N) participation that is responsible for the revivals in the vicinity of isolated hyperbolic instabilities.

DOI
10.1103/physreve.87.012910

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We study the coherence dynamics of a kicked two-mode Bose-Hubbard model starting with an arbitrary coherent spin preparation. For preparations in the chaotic regions of phase space we find a generic behavior with Floquet participation numbers that scale as the entire N-particle Hilbert space, leading to a rapid loss of single-particle coherence. However, the chaotic behavior is not uniform throughout the chaotic sea and unique statistics is found for preparations at the vicinity of hyperbolic points that are embedded in it. This is contrasted with the low log(N) participation that is responsible for the revivals in the vicinity of isolated hyperbolic instabilities.
Systems of interacting bosons in double-well potentials, modeled by two-site Bose-Hubbard models, are of significant theoretical and experimental interest and attracted intensive studies in contexts ranging from many-body physics and quantum dynamics to the onset of quantum chaos. In this work we systematically study a kicked two-site Bose-Hubbard model (Bose-Hubbard dimer) with the on-site potential difference being periodically modulated. Our model can be equivalently represented as a kicked Lipkin-Meshkov-Glick model and thus displays different dynamical behaviors from the kicked-top model. By analyzing spectral statistics of Floquet operator, we unveil that the system undergoes a transition from regularity to chaos with increasing the interaction strength. Then based on semiclassical approximation and the analysis of R\'enyi entropy of coherent states in the basis of Floquet operator eigenstates, we reveal the local chaotic features of our model, which indicate the existence of integrable islands even in the deep chaotic regime. The semiclassical analysis also suggests that the system in chaotic regime may display different dynamical behavior depending on the choice of initial states. Finally, we demonstrate that dynamical signatures of chaos can be manifested by studying dynamical evolution of local operators and out-of-time-order correlation function as well as the entanglement entropy. Our numerical results exhibit the richness of dynamics of the kicked Bose-Hubbard dimer in both regular and chaotic regimes as the initial states are chosen as coherent spin states located in different locations of phase space.
We study the quantum signatures of chaos by using the concept of bipartite fluctuations in the kicked two-site Bose-Hubbard model, which can be mapped to the well-studied kicked top model. We find that the evolution of bipartite fluctuations is quasiperiodic when the initial state centered in the regular regions, while it becomes irregular as the initial state centered in the chaotic regions. As a result, the quantum signatures of chaos can be identified in both the dynamical bipartite fluctuations and the long time averaged bipartite fluctuations. We further demonstrate that the regular versus irregular behaviors of bipartite fluctuations are induced by the different localization properties of the evolved state in regular and chaotic regimes. Finally, we discuss how to identify the signature of global chaos via bipartite fluctuations; and point out the relationship between bipartite fluctuations and the classical Lyapunov exponent.
We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.
We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.
Abstract We investigate the chaotic phase of the Bose–Hubbard model (Pausch et al 2021 Phys. Rev. Lett. 126 150601) in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose–Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.
In the large-NNN, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunneling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behavior in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond-mean-field dynamics.