Information theoretic approach to effects of spin-orbit coupling in Bose-Einstein condensates

TL;DR

This paper uses Shannon entropy and Fisher information to analyze how spin-orbit coupling affects the density profiles of Bose-Einstein condensates, revealing localization, delocalization, and supersolid properties.

Contribution

It introduces an information theoretic approach to study the effects of spin-orbit coupling on BEC density profiles, highlighting phase distinctions and supersolid evidence.

Findings

Density becomes localized with increasing $\

Stripe phase shows similar information behavior to delocalized region

Enhanced Fisher information indicates supersolid properties

Abstract

We make use of Shannon entropy ($S$) and Fisher information ($I$) to study the response of atomic density profiles of a spin-orbit coupled Bose-Einstein condensate to changes in the wave number ($\kappa_L$) of the Raman laser that couples two hyperfine states of atoms in the condensate. The choice for values of $\kappa_L$, the so-called spin-orbit parameter, and Rabi frequency ($\Omega$) leads to two distinct regions in the system's energy spectrum with different order parameters and/or probability densities. In addition, we can have a spatially modulated density profile, reminiscent of the so called stripe phase. Our numbers for $S$ and $I$ demonstrate that for $\kappa_L^2<\Omega$ (region 1) the density profile becomes localized as $\kappa_L$ increases while we observe delocalization in the density distribution for $\kappa_L^2>\Omega$ (region 2) for increasing values of $\kappa_L$. In the stripe phase the nature of $S$ and $I$ to changes in $\kappa_L$ is similar to that found for the condensate in region 2. The results for information theoretic quantities in the stripe phase are, in general, augmented compared to those of region 2. In particular, the highly enhanced values of position-space Fisher information imply an extremely concentrated atomic density distribution to provide an evidence for supersolid properties of Bose-Einstein condensates in the presence of spin-orbit coupling.