Routes towards the experimental observation of the large fluctuations due to chaos assisted tunneling effects with cold atoms

TL;DR

This paper explores how cold atom experiments can observe large fluctuations in quantum tunneling caused by chaos-assisted tunneling, focusing on practical experimental routes and the challenges involved.

Contribution

It proposes feasible experimental setups with cold atoms to observe chaos-assisted tunneling effects and analyzes the most promising configurations for detection.

Findings

Chaos-assisted tunneling causes large tunneling rate fluctuations.

Symmetry fragility between positive and negative momenta complicates observations.

Position-space symmetric islands are more promising for experimental observation.

Abstract

In the presence of a complex classical dynamics associated with a mixed phase space, a quantum wave function can tunnel between two stable islands through the chaotic sea, an effect that has no classical counterpart. This phenomenon, referred to as chaos assisted tunneling, is characterized by large fluctuations of the tunneling rate when a parameter is varied. To date the full extent of this effect as well as the associated statistical distribution have never been observed in a quantum system. Here we analyze the possibility of characterizing these effects accurately in a cold atom experiment. Using realistic values of the parameters of an experimental setup, we examine through analytical estimates and extensive numerical simulations a specific system that can be implemented with cold atoms, the atomic modulated pendulum. We assess the efficiency of three possible routes to observe in detail chaos assisted tunneling properties. Our main conclusion is that due to the fragility of the symmetry between positive and negative momenta as a function of quasimomentum, it is very challenging to use tunneling between classical islands centered on fixed points with opposite momentum. We show that it is more promising to use islands symmetric in position space, and characterize the regime where it could be done. The proposed experiment could be realized with current state-of-the-art technology.