Nonlinear tunneling in two-dimensional lattices

TL;DR

This paper analyzes nonlinear tunneling of Bose-Einstein condensates in two-dimensional lattices, deriving models and performing simulations to understand the effects of instabilities, acceleration, and initial states on tunneling phenomena.

Contribution

It introduces several few-mode models for nonlinear tunneling in 2D lattices and evaluates their accuracy through numerical simulations, highlighting the role of instabilities and acceleration effects.

Findings

Two-mode models accurately describe tunneling between stable states.

Instabilities lead to population of higher bands, affecting tunneling.

Acceleration direction influences tunneling rates and band involvement.

Abstract

We present thorough analysis of the nonlinear tunneling of Bose-Einstein condensates in static and accelerating two-dimensional lattices within the framework of the mean-field approximation. We deal with nonseparable lattices considering different initial atomic distributions in the highly symmetric states. For analytical description of the condensate before instabilities are developed, we derive several few-mode models, analyzing both essentially nonlinear and quasi-linear regimes of tunneling. By direct numerical simulations, we show that two-mode models provide accurate description of the tunneling when either initially two states are populated or tunneling occurs between two stable states. Otherwise a two-mode model may give only useful qualitative hints for understanding tunneling but does not reproduce many features of the phenomenon. This reflects crucial role of the instabilities developed due to two-body interactions resulting in non-negligible population of the higher bands. This effect becomes even more pronounced in the case of accelerating lattices. In the latter case we show that the direction of the acceleration is a relevant physical parameter which affects the tunneling by changing the atomic rates at different symmetric states and by changing the numbers of bands involved in the atomic transfer.