Scale-invariant thermodynamics of a toroidally trapped Bose gas

Abstract

We consider a system of bosonic atoms in an axially symmetric harmonic trap augmented with a two dimensional repulsive Gaussian optical potential. We find an expression for the grand free energy of the system for configurations ranging from the harmonic trap to the toroidal regime. For large tori we identify an accessible regime where the ideal gas thermodynamics of the system are found to be independent of toroidal radius. This property is a consequence of an invariant extensive volume of the system that we identify analytically in the regime where the toroidal potential is radially harmonic. In considering corrections to the scale invariant transition temperature, we find that the first order interaction shift is the dominant effect in the thermodynamic limit, and is also scale invariant. We also consider adiabatic loading from the harmonic to toroidal trap configuration, which we show to have only a small effect on the condensate fraction of the ideal gas, indicating that loading into the scale invariant regime may be experimentally practical.

Reservoir interactions during Bose-Einstein condensation: Modified critical scaling in the Kibble-Zurek mechanism of defect formation

“…ζ(z) the Riemann zeta function, and N the number of particles [31]. To determine T c we have used the Thomas-Fermi value of the particle number N = µL/g 1 corresponding to the post-quench parameters, giving a value of N ≈ 14400.…”

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

“…Introducing the optical potential is a relatively simple extra step, allowing recent experiments to use this configuration to great effect [3,7]. This form of harmonic Gaussian trap has an advantage over other realizations of toroids: changes in the toroid size can be easily explored by altering the laser intensity while keeping the harmonic trap and beam width parameters constant, thus accessing the scale invariant regime [23].…”

“…The ideal gas thermodynamics of a Bose gas in a three dimensional toroidal potential was first considered in [23]. The specific form of toroidal potential examined in that work was the harmonic-Gaussian potential that has been produced using combined magneto-optical traps [3].…”

“…In Ref. [23] certain additional effects for the Bose gas were considered: The first order interaction shift to the critical temperature was found to be scale invariant, which motivates a more complete treatment of the interacting system to assess the robustness of the scale invariant predictions, and to critically assess the viability of this system for experimental studies.…”

“…In this work we present a general study of the properties of an ultra-cold gas in the harmonic-Gaussian toroid. We generalize the ideal thermodynamics of [23] to a single component fermionic system, and develop a meanfield treatment of the Bose gas to account for interaction effects. The scale invariant property is further investigated analytically by studying the density of states of the system, revealing the robust nature and fundamental origin of scale invariance in this trap, for both bosons and fermions.…”