Geometry-induced modification of fluctuation spectrum in quasi-two-dimensional condensates

TL;DR

This study investigates how changing the trapping potential from harmonic to toroidal alters the spectral modes and fluctuation characteristics of quasi-two-dimensional condensates, revealing topology-dependent quantum and thermal fluctuation behaviors.

Contribution

It demonstrates the impact of geometry on spectral modes and fluctuation profiles in condensates using Hartree-Fock-Bogoliubov theory with the Popov approximation.

Findings

Quantum fluctuations increase with toroidal geometry at zero temperature.

Finite temperature density profiles show significant changes with trap modification.

Overlap of condensate and non-condensate maxima occurs in toroidal condensates.

Abstract

We report the structural transformation of the low-lying spectral modes, especially the Kohn mode, from radial to circular topology as harmonic confining potential is modified to a toroidal one, and this corresponds to a transition from simply to multiply connected geometry. For this we employ the Hartree-Fock-Bogoliubov theory to examine the evolution of low energy quasiparticles. We, then, use the Hartree-Fock-Bogoliubov theory with the Popov approximation to demonstrate the two striking features of quantum and thermal fluctuations. At $T=0$, the non-condensate density due to interaction induced quantum fluctuations increases with the transformation from pancake to toroidal geometry. The other feature is, there is a marked change in the density profile of the non-condensate density at finite temperatures with the modification of trapping potential. In particular, the condensate and non-condensate density distributions have overlapping maxima in the toroidal condensate, which is in stark contrast to the case of pancake geometry. The genesis of this difference lies in the nature of the thermal fluctuations.