Avalanches of Bose-Einstein Condensates in Leaking Optical Lattices

TL;DR

This paper investigates the decay dynamics of Bose-Einstein Condensates in leaking optical lattices, revealing avalanche-like atom loss with power-law distributions indicative of phase transition behavior, using a mean-field DNLSE approach.

Contribution

It demonstrates that atom population decay in leaking optical lattices follows avalanche dynamics with power-law distributions, linking complex decay patterns to phase transition phenomena.

Findings

Atom populations decay in avalanches of size J.

Distribution of avalanche sizes follows a power law ${ m P}(J) \\sim 1/J^{\alpha}$.

Scale-free behavior indicates complex phase space structure.

Abstract

One of the most fascinating experimental achievements of the last decade was the realization of Bose-Einstein Condensation (BEC) of ultra-cold atoms in optical lattices (OL's). The extraordinary level of control over these structures allows us to investigate complex solid state phenomena and the emerging field of ``atomtronics'' promises a new generation of nanoscale devices. It is therefore of fundamental and technological importance to understand their dynamical properties. Here we study the outgoing atomic flux of BECs loaded in an one-dimensional OL with leaking edges, using a mean field description provided by the Discrete Non-Linear Schrodinger Equation (DNLSE). We demonstrate that the atom population inside the OL decays in avalanches of size $J$. For intermediate values of the interatomic interaction strength their distribution ${\cal P}(J)$ follows a power law i.e. ${\cal P}(J)\sim1/J^{\alpha}$ characterizing systems at phase transition. This scale free behaviour of ${\cal P}(J)$ reflects the complexity and the hierarchical structure of the underlying classical mixed phase space. Our results are relevant in a variety of contexts (whenever DNLSE is adequate), most prominently the light emmitance from coupled non-linear optics waveguides.