Particle creation in Bose--Einstein condensates: Theoretical formulation based on conserving gapless mean field theory

TL;DR

This paper develops a theoretical framework for particle creation in Bose-Einstein condensates using conserving gapless mean field theory, linking it to quantum field theory in curved spacetime and accounting for quantum backreaction effects.

Contribution

It introduces a method to calculate particle creation spectra in Bose-Einstein condensates via BdG Hamiltonian diagonalization, incorporating quantum backreaction within a conserving mean field approach.

Findings

Particle creation spectrum matches QFT in curved spacetime predictions.

Quantum backreaction modifies the effective metric in condensates.

The formulation ensures particle number conservation in the mean field theory.

Abstract

We formulate particle creation phenomena in Bose--Einstein condensates in terms of conserving gapless mean field theory for weakly interacting Bose gases. The particle creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean field theory. The conservation implies that quasiparticle creation is accompanied by quantum backreaction to the condensates. Particle creation in this mean field theory is found to be equivalent to that in quantum field theory (QFT) in curved spacetime. An expression is obtained for an effective metric affected by quantum backreaction. The formula for the particle creation spectrum obtained in terms of QFT in curved spacetime is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.