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

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.

15 pages, 2 figures, accepted by Phys. Rev. A

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Quantum liquid droplets in a mixture of Bose-Einstein condensates
• Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macro-droplet in a dipolar quantum fluid
• Striped states in a many-body system of tilted dipoles
• Observation of a Lee-Huang-Yang Fluid
• Mott-Hubbard Transition of Bosons in Optical Lattices with Three-body Interactions
• Compressibility and the Equation of State of an Optical Quantum Gas in a Box
• Non-Universal Equation of State of the Two-Dimensional Bose Gas
• Ferromagnetism in an extended coherently-coupled atomic superfluid
• Condensation and superfluidity of dilute Bose gases with finite-range interaction
• On-shell approximation for the s-wave scattering theory
• Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover
• Interaction-Induced Dimensional Crossover through Full 3D to 1D

Cited by in corpus (1)

• Probing $p$-wave effects in spin-density separation of Bose mixtures with the dynamic structure factor