Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices

TL;DR

This paper investigates the thermodynamic behavior of the 3D Hubbard model relevant to cold atomic gases in optical lattices, analyzing cooling strategies through theoretical methods and their implications for experimental cooling techniques.

Contribution

It provides a comparative analysis of dynamical mean-field theory and high-temperature series for the 3D Hubbard model and explores their implications for cooling cold atomic gases.

Findings

Benchmarking of theoretical methods delineates their validity ranges.

Analysis of adiabatic processes clarifies atom redistribution effects.

Application of cooling procedures to idealized models offers practical insights.

Abstract

We present a comprehensive study of the thermodynamic properties of the three-dimensional fermionic Hubbard model, with application to cold fermionic atoms subject to an optical lattice and a trapping potential. Our study is focused on the temperature range of current experimental interest. We employ two theoretical methods - dynamical mean-field theory and high-temperature series - and perform comparative benchmarks to delimitate their respective range of validity. Special attention is devoted to understand the implications that thermodynamic properties of this system have on cooling. Considering the distribution function of local occupancies in the inhomogeneous lattice, we show that, under adiabatic evolution, the variation of any observable (e.g., temperature) can be conveniently disentangled into two distinct contributions. The first contribution is due to the redistribution of atoms in the trap during the evolution, while the second one comes from the intrinsic change of the observable. Finally, we provide a simplified picture of the cooling procedure recently proposed in J.-S. Bernier et al., Phys. Rev. A 79, 061601 (2009) by applying this method to an idealized model.