Lifetime of Excitations in Atomic and Molecular Bose-Einstein Condensates

TL;DR

This paper analyzes the quasiparticle spectrum and lifetimes in atomic and molecular Bose-Einstein condensates, revealing how symmetry breaking influences decay rates and spectral features relevant for experiments.

Contribution

It provides a theoretical computation of quasiparticle lifetimes in atomic and molecular BEC phases, highlighting the effects of symmetry breaking and decay mechanisms.

Findings

Goldstone mode decay rate matches Belyaev result

Gapped mode sharpness varies with momentum and phase

Decay rates influence spectral responses in experiments

Abstract

Recent experimental progress has produced Molecular Superfluids (MSF) in thermal equilibrium; this opens the door to a new class of experiments investigating the associated thermodynamic and dynamical responses. We review the theoretical picture of the phase diagram and quasiparticle spectrum in the Atomic Superfluid (ASF) and MSF phases. We further compute the parametric dependence of the quasiparticle lifetimes at one-loop order. In the MSF phase, the $U(1)$ particle number symmetry breaks to $\mathbb{Z}_2$ and the spectrum exhibits a gapless Goldstone mode in addition to a gapped $\mathbb{Z}_2$-protected atom-like mode. In the ASF phase, the $U(1)$ symmetry breaks completely, leaving behind a Goldstone mode and an unprotected gapped mode. In both phases, the Goldstone mode decays with a rate given by the celebrated Belyaev result, as in a single component condensate. In the MSF phase, the gapped mode is sharp up to a critical Cherenkov momentum beyond which it emits phonons. In the ASF phase, the gapped mode decays with a constant rate even at small momenta. These decay rates govern the spectral response in microtrap tunneling experiments and lead to sharp features in the transmission spectrum of atoms fired through molecular clouds.