dorsal/arxiv
View SchemaAtom lasers, coherent states, and coherence: I. physically realizable ensembles of pure states
| Authors | H. M. Wiseman, John A. Vaccaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906125 |
| URL | https://arxiv.org/abs/quant-ph/9906125 |
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 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).
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"abstract": "A laser, be it an optical laser or an atom laser, is an open quantum system\nthat produces a coherent beam of bosons. Far above threshold, the stationary\nstate $\\rho_{ss}$ of the laser mode is a mixture of coherent field states with\nrandom phase, or, equivalently, a Poissonian mixture of number states. This\npaper answers the question: can descriptions such as these, of $\\rho_{ss}$ as a\nstationary ensemble of pure states, be physically realized? An ensemble of pure\nstates for a particular system can be physically realized if, without changing\nthe dynamics of the system, an experimenter can (in principle) know at any time\nthat the system is in one of the pure-state members of the ensemble. Such\nknowledge can be obtained by monitoring the baths to which the system is\ncoupled, provided that coupling is describable by a Markovian master equation.\nUsing a family of master equations for the (atom) laser, we solve for the\nphysically realizable (PR) ensembles. We find that for any finite self-energy\n$\\chi$ of the bosons in the laser mode, the coherent state ensemble is not PR;\nthe closest one can come to it is an ensemble of squeezed states. This is\nparticularly relevant for atom lasers, where the self-energy arising from\nelastic collisions is expected to be large. By contrast, the number state\nensemble is always PR. As $\\chi$ increases, the states in the PR ensemble\nclosest to the coherent state ensemble become increasingly squeezed.\nNevertheless, there are values of $\\chi$ for which states with well-defined\ncoherent amplitudes are PR, even though the atom laser is not coherent (in the\nsense of having a Bose-degenerate output). We discuss the physical significance\nof this anomaly in terms of conditional coherence (conditional Bose\ndegeneracy).",
"arxiv_id": "quant-ph/9906125",
"authors": [
"H. M. Wiseman",
"John A. Vaccaro"
],
"categories": [
"quant-ph"
],
"title": "Atom lasers, coherent states, and coherence: I. physically realizable ensembles of pure states",
"url": "https://arxiv.org/abs/quant-ph/9906125"
},
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