Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling

TL;DR

This study explores how two-dimensional fermionic systems with spin-orbit coupling and interactions exhibit quantum chaos signatures, using mean-field solutions and statistical analysis to understand the effects of interactions and external fields.

Contribution

It provides a comprehensive analysis of the interplay between spin-orbit coupling, interactions, and chaos in a 2D fermionic system with a deformed trap, highlighting the conditions that promote or suppress chaos.

Findings

Quantum chaos signatures depend on system parameters.

Two-body repulsion can both promote and suppress chaos.

Cold atoms can serve as platforms to study quantum chaos.

Abstract

We investigate a two-dimensional system of with two values of the internal (spin) degree of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body short range repulsion. We obtain self-consistent mean-field $N$-body solutions as functions of the interaction parameters. Single-particle Spectra and total energies are computed and compared to the results without interaction. We perform a statistical analysis for the distributions of nearest neighbor energy level spacings and show that quantum signatures of chaos are seen in certain parameters regimes. Furthermore, the effects of two-body repulsion on the nearest neighbor distributions are investigated. This repulsion can either promote or destroy the signatures of potential chaotic behavior depending on relative strengths of parameters. Our findings support the suggestion that cold atoms may be used to study quantum chaos both in the presence and absence of interactions.