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An easily scalable toroidal geometry presents an opportunity for creatinglarge scale persistent currents in Bose-Einstein condensates, for studies ofthe Kibble-Zurek mechanism, and for investigations of toroidally trappeddegenerate Fermi gases. We consider in detail the process of isentropic loadingof a Bose or Fermi gas from a harmonic trap into the scale invariant toroidalregime that exhibits a high degree of system invariance when increasing theradius of the toroid. The heating involved in loading a Bose gas is evaluatedanalytically and numerically, both above and below the critical temperature.Our numerical calculations treat interactions within theHartree-Fock-Bogoliubov-Popov theory. Minimal change in degeneracy is observedover a wide range of initial temperatures, and a regime of cooling isidentified. The scale invariant property is further investigated analyticallyby studying the density of states of the system, revealing the robust nature ofscale invariance in this trap, for both bosons and fermions. We give analyticalresults for a Thomas-Fermi treatment. We calculate the heating due to loading aspin-polarized Fermi gas and compare with analytical results for high and lowtemperature regimes. The Fermi gas is subjected to irreducible heating duringloading, caused by the loss of one degree of freedom for thermalization.

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