Probing information theoretic measures of nonlinear ultracold quantum gases using phase-space distributions

Summary

arXiv:2606.02656v1 Announce Type: new Abstract: We use phase space distributions, specifically the Wigner and Husimi quasi probability distributions, to study harmonically trapped Bose--Einstein condensate described by the Gross Pitaevskii equation. From the mean field ground state wavefunction we construct both distributions and their position and momentum space marginals and we use these to compute a comprehensive set of information theoretic measures: Shannon, Wehrl, and R\'enyi entropies; Fisher information; cumulative and cross cumulative residual entropies; mutual information; and Kullback--Leibler, Jeffreys, Cauchy Schwarz, and R\'enyi divergences. Studying these quantities as a function of the $s$-wave scattering length for a representative Rb-85 condensate, we find that stronger repulsive interactions drive increased phase space delocalization, seen by a monotonic growth of Shannon and Wehrl entropies, while the Fisher information shows the complementary trend -- increasing in position space and decreasing in momentum space in a manner consistent with the global Fisher uncertainty bound.