Cavity QED with tunneling: an application of adiabatic elimination in quantum trajectory theory

TL;DR

This paper models a single atom in a cavity with tunneling, analyzing photon statistics and tunneling effects, and extends the approach to Bose-Einstein Condensates in Josephson junction regimes using adiabatic elimination in quantum trajectory theory.

Contribution

It introduces a method to analyze photon correlations in cavity QED with tunneling and extends the framework to Bose-Einstein Condensates in Josephson regimes using adiabatic elimination.

Findings

Photon correlation $g^{(2)}(\tau)$ depends on tunneling rate.

Oscillations in $g^{(2)}(\tau)$ are proportional to tunneling coefficient.

Method demonstrated in the bad-cavity limit.

Abstract

We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom. The atom may tunnel between sites in the lattice. We find the photon counting statistic $g^{(2)}(\tau)$ depends on the tunneling rate. Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation, in ther Josephson junction regime. It is shown that oscillations in $g^{(2)}(\tau)$ are directly proportional to the tunneling coefficient. We work in the bad-cavity limit and give an example of the use of adiabatic elimination in quantum trajectory theory