Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas

TL;DR

This paper extends the effective field theory approach to ultracold Bose gases, deriving beyond-LHY corrections to the equation of state using the Cornwall-Jackiw-Tomboulis method, with implications for quantum simulation experiments.

Contribution

It introduces a two-loop CJT effective field theory to calculate next-to-LHY corrections for the EOS of ultracold Bose gases with finite-range interactions.

Findings

Derived analytical expressions for quantum depletion and chemical potential beyond LHY.

Proposed an experimental protocol to observe nonuniversal corrections via breathing mode frequency shifts.

Extended the EOS to include next-leading order effects characterized by 

Abstract

The equation of state (EOS) serves as a cornerstone in elucidating the properties of quantum many-body systems. A recent highlight along this research line consists of the derivation of the nonuniversal Lee-Huang-Yang (LHY) EOS for an ultracold quantum bosonic gas with finite-range interatomic interactions using one-loop effective path-integral field theory. The purpose of this work is to extend Salasnich's pioneering work to uncover beyond-LHY corrections to the EOS by employing the Cornwall-Jackiw-Tomboulis (CJT) effective field theory, leveraging its two-loop approximation. In this end, we expand Salasnich's remarkable findings of EOS to the next leading order characterized by $\left(\rho a_{\text{s}}^{3}\right)^{2}$, with $\rho$ and $a_{\text{s}}$ being the density and the $s$-wave scattering length. Notably, we derive analytical expressions for quantum depletion and chemical potential, representing the next-to-LHY corrections to nonuniversal EOS induced by finite-range effects. Moreover, we propose an experimental protocol of observing the nonuniversal next-to-LHY corrections to the EOS by calculating fractional frequency shifts in the breathing modes. The nonuniversal beyond-LHY EOS in this work paves the way of using LHY effects in quantum simulation experiments and for investigations beyond the LHY regime.