Influence of spontaneous emission on atomic solitons

We numerically solve an effective single-atom Hartree-Fock master equation in order to investigate the effects of spontaneous emission on atomic Thirring solitons and atomic gap solitons. We show that spontaneous emission detrimentally effects the existence of Thirring solitons, as expected from the fact that they only occur on resonance. In contrast, gap solitons, which can also exist off resonance, survive in the presence of spontaneous emission in weakly allowed transitions, albeit at high atomic densities. This result is illustrated in the case of the [2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_0$⇆2 ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$]- intercombination line of magnesium.