Analytical pair correlations in ideal quantum gases: Temperature-dependent bunching and antibunching

TL;DR

This paper derives exact analytical expressions for the temperature-dependent pair distribution function in ideal quantum gases, revealing temperature-driven bunching and antibunching behaviors similar to experimental observations in ultracold gases.

Contribution

It introduces a new analytical approach to calculate the static structure factor and pair distribution functions in ideal quantum gases, highlighting temperature-dependent quantum correlations.

Findings

Bosonic g(r) shows Bose pile and long-range correlations near T_c.

Fermionic g(r) exhibits Fermi hole with featureless behavior.

Correlation decreases with temperature below T_c.

Abstract

The fluctuation-dissipation theorem together with the exact density response spectrum for ideal quantum gases has been utilized to yield a new expression for the static structure factor, which we use to derive exact analytical expressions for the temperature{dependent pair distribution function g(r) of the ideal gases. The plots of bosonic and fermionic g(r) display "Bose pile" and "Fermi hole" typically akin to bunching and antibunching as observed experimentally for ultracold atomic gases. The behavior of spin-scaled pair correlation for fermions is almost featureless but bosons show a rich structure including long-range correlations near T_c. The coherent state at T=0 shows no correlation at all, just like single-mode lasers. The depicted decreasing trend in correlation with decrease in temperature for T < T_c should be observable in accurate experiments.