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arXiv:1207.4699 · Physical Review A

Two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system

Carlos A. Parra-Murillo, Javier Madroñero, Sandro Wimberger

Published Sep 30, 2013• 31 citations
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Abstract

We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A crossover between regular and quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the nonequilibrium dynamics of our many-body system in different parameter regimes.

DOI
10.1103/physreva.88.032119

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We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A crossover between regular and quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the nonequilibrium dynamics of our many-body system in different parameter regimes.
We study an experimentally realizable paradigm of a complex many-body quantum system, a twoband Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A clean cross-over between regular to quantum chaotic spectra is found within the many-level avoided crossings at resonant tunneling conditions. The spectral properties determine the evolution of states across a cascade of Landau-Zener events, which can be used to study diffusion and to dynamically prepare target states interesting for experimental applications.
A two‐band Bose‐Hubbard model is presented which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many‐body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau‐Zener transitions from single‐particle to many‐body realizations. The temporal evolution of single‐ and two‐body observables along the sweeps is investigated in order to characterize the non‐equilibrium dynamics in our complex quantum system. image
We study a model for ultracold, spinless atoms in quasi-one-dimensional optical lattices and subjected to a tunable tilting force. Statistical tests are employed to quantitatively characterize the spectrum of the Floquet-Bloch operator of the system along the transition from the regular to the quantum chaotic regime. Moreover, we perturbatively include the coupling of the one-band model to the second energy band. This allows us to study the Landau-Zener interband tunneling within a truly many-body description of ultracold atoms. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition.
We study the resonant tunneling eect in a many-body WannierStark system, realized by ultracold bosonic atoms in an optical lattice subjected to an external Stark force.The properties of the many-body system are eectively described in terms of upper-band excitation manifolds, which allow for the study of the transition between regular and quantum chaotic spectral statistics.We show that our system makes it possible to control the spectral statistics locally in energy space by the competition of the force and the interparticle interaction.By a time-dependent sweep of the Stark force the dynamics is reduced to a LandauZener problem in the single-particle setting.