Master equation for collective spontaneous emission with quantized atomic motion

TL;DR

This paper derives a comprehensive Markovian master equation that incorporates atomic motion quantization, revealing how recoil and indistinguishability influence collective emission and dipole interactions in atomic ensembles.

Contribution

It introduces a unified theoretical framework for internal atomic dynamics considering quantized motion, extending beyond the Lamb-Dicke regime and applicable to various atomic states.

Findings

Derived general expressions for decay rates and dipole shifts.

Provided closed-form formulas for Gaussian, Fock, and thermal states.

Showed external motion modulates dipole interactions and cooperative emission.

Abstract

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.