Selective Amplification of a Quantum State

We predict a novel effect in a quantum two-level system (TLS) coupled to a resonant cavity. By bringing the TLS in and out of resonance with the cavity by a series of $N$ rectangular bias pulses (the length of the $m$th pulse scaling as $1/\sqrt{m}$), we will coherently excite the $N$-photon state, $|N,$ of the cavity only if the TLS was initially in an appropriate quantum state ("go" state). Otherwise the number of photons in the cavity will remain small compared to $N$ ({\em selective amplification}). If the TLS was in a coherent superposition of the "go" and "no go" states, the cavity will be in a superposition of states, in which the state $|N$ will enter with the same weight as the initial "go" component. The effect is due to $\sqrt{N+1}$-dependence of the Rabi oscillation frequency on the number $N$ of photons in the cavity. It is stable with respect to noise, pulse shape, finite temperature, TLS decoherence and TLS detuning from resonance with the cavity. The effect can be used as a means to read out a quantum state of a qubit coupled to a resonator.