Cavity-field distribution in multiphoton Jaynes-Cummings resonances

Th K Mavrogordatos

doi:10.1103/physreva.104.063717

Abstract

We calculate the cavity-field distribution in the Wigner representation for the two-photon resonance of the weakly driven Jaynes-Cummings (JC) oscillator in its strong-coupling limit. Using an effective four-level system, we analytically demonstrate the presence of steady-state and transient bimodality which breaks azimuthal symmetry in phase space. The two steady-state peaks are located at opposite positions and do not correspond to the two-photon amplitude of the driven transition. The developing bimodality is portrayed in parallel with the evolution of the intensity correlation function for the forwards-scattered photons, before being finally contrasted to the few-photon steady-state and transient phase-space profiles for the cavity mode in the JC model driven on resonance.

Highlights

The two-level behavior of an optical cavity mode strongly coupled to a single atom and excited near a vacuum Rabi resonance has been demonstrated abou√t three decades ago as a paradigmatic system relying on the n nonlinearity of the Jaynes-Cummings (JC) model and exhibiting photon blockade [1]
In this article we have revealed the distinct character of multimodality accompanying a multiphoton resonance in a regime where quantum dynamics produces a visible departure from the mean-field predictions
For the special case of the driven two-photon resonance, we have shown that the two peaks of the bimodal distribution are bound by the unit circle for every drive amplitude for which the perturbative treatment remains valid and are not in correspondence with the two-photon amplitude, i.e., a peak of√the distribution at a position vector of magnitude equal to 2

Summary

INTRODUCTION

The two-level behavior of an optical cavity mode strongly coupled to a single atom and excited near a vacuum Rabi resonance has been demonstrated abou√t three decades ago as a paradigmatic system relying on the n nonlinearity of the Jaynes-Cummings (JC) model and exhibiting photon blockade [1]. This effect was reported a few years after single-atom absorptive optical bistability had been ascertained in a regime lying at the “at interface between the quantum limit, in which quantum-mechanical noise invalidates the semiclassical prediction of bistability, and the classical limit, in which quantum noise is a negligible perturbation on semiclassical results” [2]. In the last part of our discussion, reserved for the Conclusions, we point to a possible experimental observation of the change occurring in the multiphoton quantum nonlinearity when we transition from the photon-blockade regime to resonant excitation

FORMULATING THE EFFECTIVE MASTER EQUATION

JAYNES-CUMMINGS INTERACTION DRIVEN ON RESONANCE

CONCLUDING REMARKS