Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability

TL;DR

This paper reviews how interactions affect superfluid Bose-Einstein condensates in optical lattices, highlighting phenomena like loop formation, Landau-Zener tunneling, and stability regions, with implications for experimental observations.

Contribution

It provides a comprehensive theoretical analysis of interaction effects on Bloch wave stability and tunneling in superfluid BECs within optical lattices, including new insights into Landau and dynamical instabilities.

Findings

Formation of a loop in the energy dispersion at strong interactions.

Finite Landau-Zener tunneling probability at the Brillouin zone edge.

Identification of stable and unstable regions in the Bloch wave spectrum.

Abstract

Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.