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arXiv:1607.04301 · Physical Review A

Mott-insulator state of cold atoms in tilted optical lattices: Doublon dynamics and multilevel Landau-Zener tunneling

Andrey R. Kolovsky, Дмитрий Н. Максимов

Published Oct 14, 2016• 11 citations
arXivHTMLPDF

Abstract

We discuss the dynamical response of strongly interacting Bose atoms in an adiabatically tilted optical lattice. The analysis is performed in terms of the multilevel Landau-Zener tunneling. Different regimes of tunneling are identified and analytical expressions for the doublon number, which is the quantity measured in laboratory experiments, are derived.

DOI
10.1103/physreva.94.043630

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We discuss the dynamical response of strongly interacting Bose atoms in an adiabatically tilted optical lattice. The analysis is performed in terms of the multilevel Landau-Zener tunneling. Different regimes of tunneling are identified and analytical expressions for the doublon number, which is the quantity measured in laboratory experiments, are derived.
A comprehensive study of the tunneling dynamics of a Bose-Einstein condensate in a tilted periodic potential is presented. We report numerical and experimental results on time-resolved measurements of the Landau-Zener tunneling of ultracold atoms introduced by the tilt, which experimentally is realized by accelerating the lattice. The use of different protocols enables us to access the tunneling probability, numerically as well as experimentally, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our numerical and experimental results are compared with existing two-state Landau-Zener models.
A comprehensive study of the time-resolved Landau–Zener tunneling of a Bose– Einstein condensate in a tilted periodic potential is presented in this thesis. Several ways are discussed how to control the tunneling. In the first collection of our results, the tunneling from the ground band to the continuum is shown to depend crucially on the initial condition and system parameters, and also on the strength of atom-atom interactions. The use of different protocols enables us to access the tunneling probability in two different bases, namely, the adiabatic basis (eigenstates of the Hamiltonian with the potential) and the diabatic basis (free-particle momentum eigenstates). The structure of the survival probability and the measure of the tunneling time depend on the chosen basis. All these possibilities have been checked and proved in experiments. We go also beyond and propose a possibility to manipulate the tunneling probability of ultracold atoms in the tilted time-dependent stochastic potentials. Our theoretical and numerical results show that the tunneling in such a potential can be controlled by adding different types of colored noise. A scaling law is introduced for these results, which effectively reduces the parameter-dependence of the tunneling and leads to a better understanding of dynamics in the proposed noisy system.
We study the dynamics of Bose-Einstein condensates in tilted and driven optical superlattices. For a bichromatic lattice, each Bloch band splits up into two minibands such that the dynamics is governed by the interplay of Bloch oscillations and transitions between the bands. Thus, bichromatic potentials provide an excellent model system for the study of nonlinear Landau-Zener tunneling, and they allow for a variety of applications in matter-wave interferometry and quantum metrology. In the present paper, we investigate the coherent dynamics of an interacting Bose-Einstein condensate as well as its stability. Different mechanisms of instability are discussed, which lead to a rapid depletion of the condensate.
We study the dynamics of strongly repulsive Bose gas in tilted or driven bichromatic optical lattices. Using the Bose-Fermi mapping and exact numerical method, we calculate the reduced single-particle density matrices, and study the dynamics of the density profile, the momentum distribution, and the condensate fraction. We show the oscillating and breathing mode of the dynamics, and the depletion of condensate for short-time dynamics. For long-time dynamics, we clearly show the reconstruction of system at integer multiples of Bloch-Zener time. We also show how to achieve clear Bloch oscillation and Landau-Zener tunneling for many-particle systems.
Ultracold atoms in optical lattices provide an ideal platform for exploring many-body physics of a large system arising from the coupling among a series of small identical systems whose few-body dynamics is exactly solvable. Using Landau-Zener (LZ) transition of bosonic atoms in double-well optical lattices as an experimentally realizable model, we investigate such few- to many-body routes by exploring the relation and difference between the small few-body (in one double well) and the large many-body (in double-well lattice) nonequilibrium dynamics of cold atoms in optical lattices. We find the many-body coupling between double wells greatly enhances the LZ transition probability. The many-body dynamics in the double-well lattice shares both similarity and difference from the few-body dynamics in one and two double wells. The sign of the on-site interaction plays a significant role in the many-body LZ transition. Various experimental signatures of the many-body LZ transition, including atom density, momentum distribution, and density-density correlation, are obtained.