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Many-body resonant tunneling in the Wannier-Stark system

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

Published Jul 19, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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 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.
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.
Stimulated by the experimental realization of spin-dependent tunneling via a gradient magnetic field [C. J. Kennedy et al., Phys. Rev. Lett. 111, 225301 (2013); M. Aidelsburger et al., Phys. Rev. Lett. 111, 185301 (2013)], we investigate the dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anticrossing if the two spin states are coupled by external fields. For a wave packet away from the spatial anticrossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intraband Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the interspin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for nonstrong interspin couplings, the system undergoes nonadiabatic Bloch-Landau-Zener dynamics.