Geometric scale invariance as a route to macroscopic degeneracy: loading a toroidal trap with a Bose or Fermi gas

TL;DR

This paper investigates the process of loading Bose and Fermi gases into a scale-invariant toroidal trap, analyzing heating effects, degeneracy preservation, and the robustness of scale invariance for potential applications in quantum systems.

Contribution

It provides a detailed analysis of isentropic loading into a toroidal trap, including analytical and numerical evaluations of heating, degeneracy, and the density of states for both bosons and fermions.

Findings

Minimal change in degeneracy over a wide temperature range

Identification of a cooling regime during loading

Robust scale invariance in the density of states for both gases

Abstract

An easily scalable toroidal geometry presents an opportunity for creating large scale persistent currents in Bose-Einstein condensates, for studies of the Kibble-Zurek mechanism, and for investigations of toroidally trapped degenerate Fermi gases. We consider in detail the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. The heating involved in loading a Bose gas is evaluated analytically and numerically, both above and below the critical temperature. Our numerical calculations treat interactions within the Hartree-Fock-Bogoliubov-Popov theory. Minimal change in degeneracy is observed over a wide range of initial temperatures, and a regime of cooling is identified. The scale invariant property is further investigated analytically by studying the density of states of the system, revealing the robust nature of scale invariance in this trap, for both bosons and fermions. We give analytical results for a Thomas-Fermi treatment. We calculate the heating due to loading a spin-polarized Fermi gas and compare with analytical results for high and low temperature regimes. The Fermi gas is subjected to irreducible heating during loading, caused by the loss of one degree of freedom for thermalization.