Macroscopic self-trapping in the dynamical tunneling of a Bose-Einstein condensate

TL;DR

This paper investigates how nonlinear interactions in a Bose-Einstein condensate affect dynamical tunneling in a modulated anharmonic potential, revealing conditions for self-trapping and stability of Floquet states.

Contribution

It introduces a two-mode model based on nonlinear Floquet states to analyze dynamical tunneling and identifies the critical nonlinearity for tunneling suppression.

Findings

Dynamical tunneling ceases beyond a critical nonlinearity.

Derived an expression for the critical nonlinearity for tunneling suppression.

Demonstrated the dynamical instability of certain nonlinear Floquet states.

Abstract

A Bose-Einstein condensate in a modulated, one-dimensional, anharmonic potential can exhibit dynamical tunneling between islands of regular motion in phase space. With increasingly repulsive atomic interactions, dynamical tunneling is predicted to cease due to self-trapping [S. W\"uster et al. Phys. Rev. Lett. 109 080401 (2012)]. This suppression of tunneling oscillations is related to the same phenomenon that occurs in the two-mode dynamics of a repulsively interacting Bose-Einstein condensate in a double-well potential. Here we present a two-mode model for dynamical tunnelling based on nonlinear Floquet states and examine the range of validity of the approximation. We characterise nonlinear dynamical tunneling for different trap strengths, modulation amplitudes, and effective Planck constants. Using the linear Floquet states we derive an expression for the critical nonlinearity beyond which tunneling ceases. Finally we demonstrate the dynamical instability of selected nonlinear Floquet states and show how to initialise some Floquet states in experiments. Our detailed survey will enable experiments to target accessible parameter regimes for the study of nonlinear dynamical tunneling.