Pathway to chaos through hierarchical superfluidity in a cavity-BEC system

TL;DR

This paper investigates how atomic correlations in a cavity-BEC system lead to a transition from ordered states to chaos at high pump power, revealing a hierarchical self-organization process beyond mean-field theory.

Contribution

It introduces a many-body approach to analyze the transition to chaos in a cavity-BEC system, highlighting the role of hierarchical self-organization and correlations.

Findings

Path to chaos involves hierarchical self-organization from single to double-well lattices.

Correlated states exhibit local superfluid and Mott insulating phases.

Dynamical instability to chaos prevents local superfluid-Mott transitions.

Abstract

We explore the role of atomic correlations in a harmonically trapped Bose-Einstein condensate coupled to a dissipative cavity, where both the atoms and the cavity are blue detuned from the external pumping laser. Using a genuine many-body approach that goes beyond mean-field, we extract density distributions and many-body correlations to unveil a pathway to chaos at large pump power through a hierarchical self-organization of the atoms, where the atoms transition from a single-well optical lattice to a double-well optical lattice. Correlated states of the atoms emerge and are characterized by local superfluid correlations in phases which are globally superfluid or Mott insulating. Local superfluid-Mott transitions are precluded by a dynamical instability to chaos which occurs via quasiperiodic attractors. Our results explain the mechanism behind the dynamical instabilities observed in experiments.