Cross-Phase Modulation Enhancement Via a Resonating Cavity: Semiclassical Description

TL;DR

This paper demonstrates that coupling a ladder atomic system to an optical resonator significantly enhances cross-phase modulation, with the enhancement proportional to the resonator's finesse, and provides a semiclassical theoretical framework for this effect.

Contribution

It introduces a semiclassical model showing how a resonator enhances XPM in a far-off-resonance atomic system, optimizing the nonlinear phase shift.

Findings

XPM enhancement scales with resonator finesse as F/4π

Optimal XPM occurs when off-resonance effective cooperativity equals one

Resonator coupling improves phase shift at the few-photon level

Abstract

We evaluate the advantages of performing cross-phase modulation (XPM) on a very-far-off-resonance atomic system. We consider a ladder system with a weak (few-photon level) control coherent field imparting a conditional nonlinear phase shift on a probe beam. We find that by coupling to an optical resonator the optimal XPM is enhanced proportional to the finesse of the resonator by a factor of $F/4\pi$. We present a semi-classical description of the system and show that the phenomenon is optimal in the self-defined condition of off-resonance-effective-cooperativity equal to one.