Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

TL;DR

This paper introduces a strong-coupling expansion method for modeling ultracold bosons in optical lattices at finite temperatures, accurately capturing density profiles and superfluid behavior, and aligning well with experimental and quantum Monte Carlo data.

Contribution

The paper develops a novel strong-coupling expansion technique applicable at finite temperatures, providing accurate density profiles and insights into superfluidity in trapped ultracold bosons.

Findings

Results agree with quantum Monte Carlo simulations.

Superfluid order parameter remains non-zero due to proximity effect.

Calculated entropy per particle matches experimental data.

Abstract

We develop a strong-coupling ($t \ll U$) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to proximity effect. Our calculations for the scaled density in the vacuum to superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.