Resonant Matter Wave Amplification in Mean Field Theory

TL;DR

This paper introduces a Green's function mean-field theory for matter-light wave mixing, demonstrating faster resonant amplification in a Raman matter-wave amplifier and analyzing spatial dynamics and suppression effects.

Contribution

It develops a novel Green's function based mean-field approach and applies it to analyze resonant matter-wave amplification, highlighting advantages over off-resonance methods.

Findings

Resonant driving yields faster amplification.

The matter-wave gain to atom loss ratio depends on optical depth.

Short-time single-mode approximation matches full dynamics.

Abstract

We develop a Green's function based mean-field theory for coherent mixing of matter- and light-waves. To demonstrate the utility of this approach, we analyse a co-propagating Raman matter-wave amplifier. We find that for a given laser intensity, a significantly faster amplification process can be achieved employing resonant rather than off-resonance driving. The ratio of the matter-wave gain to atom loss-rate due to spontaneous emission is given by the optical depth of the sample, and is the same both on- and off-resonance. Furthermore, we show that for short-times, the single-mode approximation for the matter-waves gives exact agreement with the full spatial dynamics. For long times, the off-resonant case shows suppressed amplification due to a spatially inhomogenous AC Stark shift associated with laser depletion. This suppression is absent on-resonance, where the AC Stark shift is absent.