Abstract

We study the time evolution of the quantum field inside a cavity coupled to a beam of two-level atoms of temperature T, given that each atom, after having crossed the cavity, interacts with a classical field ? and finally with a detector measuring its state. It is found that, if the coupling between the atoms and the quantum field is weak and ? is not too small, for any given realization of the measurements, an arbitrary initial state of the field localizes after some time into squeezed states. The centre ? of the squeezed state moves randomly in time in the complex plane, but the squeezing amplitude r and phase ? show very small fluctuations. Their mean values r? and ?? are independent of the random results of the measurements, of the initial state and of the atom-field coupling constant ?. The time evolution of r and ? is determined analytically by deriving and solving the quantum state diffusion equation describing the field dynamics in the limit of small ?, keeping ? finite. It is shown that r? increases with T, i.e., the squeezing is enhanced by increasing the temperature of the atomic beam.