Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability

TL;DR

This paper investigates the quantum dynamics of Bose-Einstein condensates in tilted optical lattices, revealing how dynamical instability leads to decoherence and different oscillation behaviors.

Contribution

It connects classical dynamical instability with quantum decoherence and identifies three distinct dynamical regimes in the quantum many-body system.

Findings

Dynamical instability causes Floquet-Bogoliubov state depletion.

Decoherence of the condensate is linked to chaotic mean-field dynamics.

Three types of Bloch oscillation behaviors are identified.

Abstract

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown, that these phenomena are related to a depletion of the Floquet-Bogoliubov states and a decoherence of the condensate in the many-particle description. Three different types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability, and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.