Information theoretic approach to effects of spin–orbit coupling in quasi-one-dimensional Bose–Einstein condensates

Abstract

Abstract We consider a spin-orbit coupled (SOC) one dimensional Bose–Einstein condensate (BEC) with attractive atom-atom interaction and make use of Shannon entropy (S), and Fisher information (I) to study the response of atomic density profiles to changes in κ L , the strength of the spin–orbit coupling for fixed values of Rabi frequency (Ω). Density profiles of our interest are characterized by (i) κ L 2 < Ω (region 1) and (ii) κ L 2 > Ω (region 2). We also pay attention to a spatially modulated density profile representing stripe phase of the condensate. Our numbers for S and I show that in region 1 the profile becomes localized as κ L increases while in region 2 we observe delocalization. Values of I in the stripe phase provide an evidence for the supersolid properties of the SOC BEC and indicate that supersolidity is a purely quantum phenomenon.