Quantum-state extraction from high-$Q$ cavities

The problem of extraction of a single-mode quantum state from a high-$Q$ cavity is studied for the case in which the time of preparation of the quantum state of the cavity mode is short compared with its decay time. The temporal evolution of the quantum state of the field escaping from the cavity is calculated in terms of phase-space functions. A general condition is derived under which the quantum state of the pulse built up outside the cavity is a nearly perfect copy of the quantum state the cavity field was initially prepared in. The results show that unwanted losses prevent the realization of a nearly perfect extraction of nonclassical quantum states from high-$Q$ optical microcavities with presently available technology.

Figure 1

(Color online) Wigner function of the quantum state of the pulse that leaves the cavity, the mode of which is (initially) prepared in a single-photon state. (a) $\eta \left(t\right)=0.99$; (b) $\eta \left(t\right)=0.71$; (c) $\eta \left(t\right)=0.5$.

Figure 2

(Color online) Wigner function of the quantum state of the pulse that leaves the cavity, the mode of which is (initially) prepared in a Schrödinger catlike state given by Eq. (70) with ${\alpha }_0=3$ (a) $\eta \left(t\right)=0.998$; (b) $\eta \left(t\right)=0.952$; (c) $\eta \left(t\right)=0.84$.