Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

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(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 a mean-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 nontrivial 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).