Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

TL;DR

This paper explores how indistinguishable atoms with quantized motional states exhibit superradiance and subradiance, revealing conditions for their existence and the impact of decay rates on cooperative emission.

Contribution

It provides an exact and numerical analysis of cooperative emission in atoms with motional states, identifying conditions for superradiance, subradiance, and dark states.

Findings

Superradiance depends on decay rates $\, ext{and}\,\, ext{a parameter}\,\, ext{related to dipole-dipole shifts.

Dark states exist only when decay rates are equal, and are subradiant if decay rates differ.

A mean-field approach describes large-$N$ behavior, revealing a critical difference in decay rates for superradiance loss.

Abstract

We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\gamma$ and $\gamma_0$ and a single parameter $\Delta_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically for up to 30 atoms, and obtain the large-$N$-limit by amean-field approach. We find that there is a critical difference $\gamma_0-\gamma$ that depends on $N$ beyond which superradiance is lost. We show that exact non-trivial dark states (i.e. states other than the ground state with vanishing spontaneous emission) only exist for $\gamma=\gamma_0$, and that those states (dark when $\gamma=\gamma_0$) are subradiant when $\gamma<\gamma_0$.