Degenerate Fermi gas in a combined harmonic-lattice potential

TL;DR

This paper derives an analytic density of states for atoms in a combined harmonic and lattice potential, compares it to numerical solutions, and explores implications for creating degenerate Fermi gases in optical lattices.

Contribution

It provides a new analytic approximation for the density of states considering higher bands, aiding in the analysis of quantum degenerate gases in combined potentials.

Findings

Analytic density of states matches numerical solutions within validity regime.

Occupation of excited bands improves conditions for degeneracy in Fermi gases.

Adiabatic loading affects the degeneracy temperature significantly.

Abstract

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices.