  Recent experiments have realized an all-optical photon transistor using a
cold atomic gas. This approach relies on electromagnetically induced
transparency (EIT) in conjunction with the strong interaction among atoms
excited to high-lying Rydberg states. The transistor is gated via a so-called
Rydberg spinwave, in which a single Rydberg excitation is coherently shared by
the whole ensemble. In its absence the incoming photon passes through the
atomic ensemble by virtue of EIT while in its presence the photon is scattered
rendering the atomic gas opaque. An important current challenge is to preserve
the coherence of the Rydberg spinwave during the operation of the transistor,
which would enable for example its coherent optical read-out and its further
processing in quantum circuits. With a combined field theoretical and quantum
jump approach and by employing a simple model description we investigate
systematically and comprehensively how the coherence of the Rydberg spinwave is
affected by photon scattering. With large-scale numerical calculations we show
how coherence becomes increasingly protected with growing interatomic
interaction strength. For the strongly interacting limit we derive analytical
expressions for the spinwave fidelity as a function of the optical depth and
bandwidth of the incoming photon.
