Squeezing in the weakly interacting uniform Bose condensate

TL;DR

This paper examines quantum squeezing phenomena in a weakly interacting Bose gas, showing that condensate squeezing is a finite-volume effect, while excitation squeezing persists in the thermodynamic limit, using variational and symmetry analysis.

Contribution

It introduces a detailed analysis of squeezing in Bose gases, highlighting the difference between condensate and excitation squeezing and their dependence on system size and symmetry considerations.

Findings

Condensate squeezing is absent at mean field level and vanishes in the thermodynamic limit.

Excitation squeezing persists in the thermodynamic limit and relates to density-phase variables.

Squeezing is analyzed using variational formulations and symmetry principles.

Abstract

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstone's theorem in the context of a squeezed coherent variational wavefunction, and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.