  An all-optical transistor is a device in which a gate light pulse switches
the transmission of a target light pulse with a gain above unity. The gain
quantifies the change of the transmitted target photon number per incoming gate
photon. We study the quantum limit of one incoming gate photon and observe a
gain of 20. The gate pulse is stored as a Rydberg excitation in an ultracold
gas. The transmission of the subsequent target pulse is suppressed by Rydberg
blockade which is enhanced by a F\"orster resonance. The detected target
photons reveal in a single shot with a fidelity above 0.86 whether a Rydberg
excitation was created during the gate pulse. The gain offers the possibility
to distribute the transistor output to the inputs of many transistors, thus
making complex computational tasks possible.

Quantum Physics