Quantum state engineering and reconstruction in cavity QED: An analytical approach

The models of a strongly-driven micromaser and a one-atom laser are
developed. Their analytical solutions are obtained by means of
phase space techniques. It is shown how to exploit the model of a
one-atom laser for simultaneous generation and monitoring of the
decoherence of the atom-field "Schrödinger cat" states. The similar
machinery applied to the problem of the generation of the
maximally-entangled states of two atoms placed inside an optical
cavity permits its analytical solution. The steady-state solution
of the problem exhibits a structure in which the two-atom
maximally-entangled state correlates with the vacuum state of the
cavity. As a consequence, it is demonstrated that the atomic
maximally-entangled state, depending on a coupling regime, can be
produced via a single or a sequence of no-photon measurements. The
question of the implementation of a quantum memory device using a
dispersive interaction between the collective internal ground state
of an atomic ensemble and two orthogonal modes of a cavity is
addressed. The problem of quantum state reconstruction in the
context of cavity quantum electrodynamics is considered. The
optimal operational definition of the Wigner function of a cavity
field is worked out. It is based on the Fresnel transform of the
atomic invertion of a probe atom. The general integral
transformation for the Wigner function reconstruction of a particle
in an arbitrary symmetric potential is derived.