Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

Wiseman, H. M. and Vaccaro, J. A. (2002) Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states. Physical Review A, 65 4: 043605-1-043605-19. doi:10.1103/PhysRevA.65.043605

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Author Wiseman, H. M.
Vaccaro, J. A.
Title Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2002-04-01
Year available 2002
Sub-type Article (original research)
DOI 10.1103/PhysRevA.65.043605
Volume 65
Issue 4
Start page 043605-1
End page 043605-19
Total pages 19
Editor B. Crasemann
Place of publication United States
Publisher American Physical Society
Collection year 2002
Language eng
Subject C1
240201 Theoretical Physics
780102 Physical sciences
Abstract A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). 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? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: 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 the self-energy 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 (and hence conditional Bose degeneracy).
Keyword Optics
Physics, Atomic, Molecular & Chemical
Bose-einstein Condensation
Stochastic Differential-equations
Wave-function Approach
Dissipative Processes
Quantum Trajectories
Convenient Fiction
Optical Coherence
Master Equation
Output Coupler
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
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