Pump-coupled high-Q micromasers with conditional measurements of atoms: Transient and steady-state entanglement of nonlocal fields.

Abstract

Two lossless micromasers are coupled in a series by the common pumping beam of two-level atoms the states of which are measured conditionally after the second cavity. Pure evolutions of the two fields are studied starting from uncorrelated coherent states for the four measurement schemes denoted by a-M'M''-a, b-M'M''-b, a-M'M''-b, and b-M'M''-a indicating the state of each atom, \ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉, before and after the two maser cavities, M' and M''. It is shown that energy-preserving schemes (first two above) produce a two-dimensional set of distinct Fock states at a steady state under the envelope of the initial amplitude distribution of the fields. Since the initial fields were uncorrelated the generated ones will be uncorrelated, too. In the case of energy-transferring schemes (second two) the system makes transitions between correlated and uncorrelated regimes. Nonlocal superpositions reminiscent of the form of \ensuremath{\Vert}N,N+M〉+\ensuremath{\Vert}N+M,N〉 can be generated at an optimum number of atoms as a result of two coexisting trapping mechanisms. This is a transient entanglement since it is destroyed by the atoms to follow due to the trapping effects themselves. However, we also show that by switching from any of the two energy-transferring schemes to any of the two preserving ones the transient correlation produced by the former scheme can be frozen into a steady state by the latter one. In the absence of dissipations this combination of schemes can generate steady-state coherent superpositions of arbitrary number states of two nonlocal fields (nonlocal Schr\"odinger cats) at reasonably high detection probabilities of the conditioned atomic states.