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arXiv:1212.1620 · New Journal of Physics

Spectral description of the dynamics of ultracold interacting bosons in disordered lattices

Benoît Vermersch, Jean Claude Garreau

Published Apr 29, 2013• 4 citations
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Abstract

We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short-time dynamics, and are shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system's behaviour at longer times.

DOI
10.1088/1367-2630/15/4/045030

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We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short-time dynamics, and are shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system's behaviour at longer times.
We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system behaviour at longer times.
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We study the dynamics of an ultracold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from Kolmogorov-Arnold-Moser arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.
Spectral excitations of ultracold gases of bosonic atoms trapped in one-dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the Bose-Hubbard model. Qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap obtained from its formal definition and from the minimum peak distance, which is the quantity available from experiments.
We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential can exhibit chaotic dynamics due to the presence of a single impurity. The nonequilibrium dynamics is triggered by a quench of the impurity-Bose interaction and is illustrated via the evolution of the population imbalance for the bosons between the two wells. While the increase of the postquench interaction strength always facilitates the irregular motion for the bosonic population imbalance, it becomes regular again when the impurity is initially populated in the highly excited states. Such an integrability to chaos (ITC) transition is fully captured by the transient dynamics of the corresponding linear entanglement entropy, whose infinite-time-averaged value additionally characterizes the edge of the chaos and implies the existence of an effective Bose-Bose attraction induced by the impurity. To elucidate the physical origin for the observed ITC transition, we perform a detailed spectral analysis for the mixture with respect to both the energy spectrum as well as the eigenstates. Specifically, two distinguished spectral behaviors upon a variation of the interspecies interaction strength are observed. While the avoided level crossings take place in the low-energy spectrum, the energy levels in the high-energy spectrum possess a bandlike structure and are equidistant within each band. This leads to a significant delocalization of the low-lying eigenvectors, which, in turn, accounts for the chaotic nature of the bosonic dynamics. By contrast, those highly excited states bear a high resemblance to the noninteracting integrable basis, which explains the recovery of the integrability for the bosonic species. Finally, we discuss the induced Bose-Bose attraction as well as its impact on the bosonic dynamics.