Dipolar exchange induced transparency with Rydberg atoms

A three-level atomic medium can be made transparent to a resonant probe field in the presence of a strong control field acting on an adjacent atomic transition to a long-lived state, which can be represented by a highly excited Rydberg state. The long-range interactions between the Rydberg state atoms then translate into strong, non-local, dispersive or absorptive interactions between the probe photons, which can be used to achieve deterministic quantum logic gates and single photon sources. Here we show that long-range dipole-dipole exchange interaction with one or more spins -- two-level systems represented by atoms in suitable Rydberg states -- can play the role of control field for the optically-dense medium of atoms. This induces transparency of the medium for a number of probe photons $n_p$ not exceeding the number of spins $n_s$, while all the excess photons are resonantly absorbed upon propagation. In the most practical case of a single spin atom prepared in the Rydberg state, the medium is thus transparent only to a single input probe photon. For larger number of spins $n_s$, all $n_p \leq n_s$ photon components of the probe field would experience transparency but with an $n_p$-dependent group velocity.