Wave mixing of hybrid Bogoliubov modes in a Bose-Einstein condensate

TL;DR

This paper models mode-mixing in a Bose-Einstein condensate using the Bogoliubov approximation, revealing hybrid modes and a dark state, with calculations on second-harmonic generation showing strong excitation near resonance.

Contribution

It introduces a detailed Bogoliubov-based model of mode hybridization and second-harmonic generation in BECs, highlighting the formation of a dark state and quantifying coupling strengths.

Findings

Hybridization leads to a Bogoliubov dark state.

Strong excitation of hybrid modes near second-harmonic resonance.

Coupling strength is half of hydrodynamic estimate.

Abstract

Mode-mixing of coherent excitations of a trapped Bose-Einstein condensate is modelled using the Bogoliubov approximation. Hybridization of the modes of the breather ($l=0$) and surface ($l=4$) states leads to the formation of a Bogoliubov dark state. Calculations are presented for second-harmonic generation between the two lowest-lying even-parity $m=0$ modes in an oblate spheroidal trap. Two hybrid modes are strongly excited near second-harmonic resonance, and the coupling strength, and hence conversion rate, to the breather mode is half that given by an equivalent hydrodynamic estimate.