Efficiency for preforming molecules from mixtures of light Fermi and heavy Bose atoms in optical lattices: the strong-coupling-expansion method

TL;DR

This paper demonstrates that the strong-coupling expansion method efficiently and accurately studies molecule formation, entropy, and thermal fluctuations in light-Fermi-heavy-Bose mixtures in optical lattices, even at low temperatures.

Contribution

The paper introduces the application of the strong-coupling expansion to analyze molecule pre-formation and thermometry in Fermi-Bose mixtures, enabling large system simulations with minimal computational effort.

Findings

Strong-coupling expansion accurately predicts molecule formation efficiency.

The method remains valid down to low temperatures.

Thermometry based on fluctuation-dissipation is effective at low temperatures.

Abstract

We discuss the application of a strong-coupling expansion (perturbation theory in the hopping) for studying light-Fermi-heavy-Bose (like $^{40}$K-$^{87}$Rb) mixtures in optical lattices. We use the strong-coupling method to evaluate the efficiency for pre-forming molecules, the entropy per particle and the thermal fluctuations. We show that within the strong interaction regime (and at high temperature), the strong-coupling expansion is an economical way to study this problem. In some cases, it remains valid even down to low temperatures. Because the computational effort is minimal, the strong-coupling approach allows us to work with much larger system sizes, where boundary effects can be eliminated, which is particularly important at higher temperatures. Since the strong-coupling approach is so efficient and accurate, it allows one to rapidly scan through parameter space in order to optimize the pre-forming of molecules on a lattice (by choosing the lattice depth and interspecies attraction). Based on the strong-coupling calculations, we test the thermometry scheme based on the fluctuation-dissipation theorem and find the scheme gives accurate temperature estimation even at very low temperature. We believe this approach and the calculation results will be useful in the design of the next generation of experiments, and will hopefully lead to the ability to form dipolar matter in the quantum degenerate regime.