Interplay of the dipole blockade and interaction-induced dephasing in Rydberg single-photon sources

Interactions between Rydberg atoms can result in a dipole blockade for which the probability ${P}_{n}$ to have $n$ atomic excitations is reduced significantly when $n\ensuremath{\ge}2$. Ideally, this allows one to create a single collective Rydberg excitation in an atomic ensemble with ${P}_{1}=1$. A single-photon source is realized by mapping this atomic excitation into a propagating light field. Even if ${P}_{n}\ensuremath{\ne}0$ for $n\ensuremath{\ge}2$, a single-photon source can be approximated if interaction-induced dephasing damps the contributions from multiply excited collective states into the preferred spatial field mode. Two quantities that can be used as figures of merit for these single-photon sources are the second-order correlation function ${g}^{(2)}$ associated with the phase-matched field emitted by the sample and the second-order correlation function ${g}^{(A)}$ associated with the atoms. Here we demonstrate that interaction-induced dephasing can lead to significant differences between ${g}^{(2)}$ and ${g}^{(A)}$ even if ${P}_{2}\ensuremath{\ll}{P}_{1}\ensuremath{\approx}1$. Theoretical expressions are derived for these quantities and it is shown that ${g}^{(2)}\ensuremath{\le}{g}^{(A)}$. It is also shown that there is a distinct advantage for minimizing ${g}^{(2)}\phantom{\rule{4pt}{0ex}}$ and ${g}^{(A)}$ by using adiabatic pulsed fields rather than constant amplitude fields to excite the ensemble. These results maybe useful for optimizing Rydberg single-photon sources.