  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 pure-state 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 self-energy
$\chi$ 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 self-energy 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 well-defined
coherent amplitudes are PR, even though the atom laser is not coherent (in the
sense of having a Bose-degenerate output). We discuss the physical significance
of this anomaly in terms of conditional coherence (conditional Bose
degeneracy).
