Atom lasers, coherent states, and coherence: I. physically realizable ensembles of pure states
Abstract
A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons. Far above threshold, the stationary state $\rho_{ss}$ of the laser mode is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of $\rho_{ss}$ as a stationary ensemble of pure states, be physically realized? An ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the purestate members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite selfenergy $\chi$ of the bosons in the laser mode, the coherent state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the selfenergy arising from elastic collisions is expected to be large. By contrast, the number state ensemble is always PR. As $\chi$ increases, the states in the PR ensemble closest to the coherent state ensemble become increasingly squeezed. Nevertheless, there are values of $\chi$ for which states with welldefined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bosedegenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (conditional Bose degeneracy).
 Publication:

arXiv eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:quantph/9906125
 Bibcode:
 1999quant.ph..6125W
 Keywords:

 Quantum Physics
 EPrint:
 20 pages, 7 figures. To be published in Phys. Rev. A, as part I of a twopart paper. This paper is considerably changed from the original version, and an error has been corrected. Some material from the original version is in quantph/0112145, which is part II of the twopart paper