Beliaev theory of spinor Bose-Einstein condensates

TL;DR

This paper extends Beliaev's Green's function method to analyze quantum depletion effects on the excitation spectra of spinor Bose-Einstein condensates, revealing increased magnon effective mass and proposing experimental measurement techniques.

Contribution

It generalizes Beliaev's approach to spinor BECs, showing quantum depletion impacts magnon effective mass and lifetime, with implications for precision magnetometry.

Findings

Quantum depletion increases magnon effective mass.

Magnon lifetime exceeds phonon lifetime.

Proposed experimental method to measure magnon effective mass.

Abstract

By generalizing the Green's function approach proposed by Beliaev [1, 2], we investigate the effect of quantum depletion on the energy spectra of elementary excitations in an F = 1 spinor Bose-Einstein condensate, in particular, of 87Rb atoms in an external magnetic field. We find that quantum depletion increases the effective mass of magnons in the spin-wave excitations with quadratic dispersion relations. The enhancement factor turns out to be the same for both ferromagnetic and polar phases, and also independent of the magnitude of the external magnetic field. The lifetime of these magnons in a 87Rb spinor BEC is shown to be much longer than that of phonons. We propose an experimental setup to measure the effective mass of these magnons in a spinor Bose gas by exploiting the effect of a nonlinear dispersion relation on the spatial expansion of a wave packet of transverse magnetization. This type of measurement has practical applications, for example, in precision magnetometry.