dorsal/arxiv
View SchemaAtom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States
| Authors | H. M. Wiseman, John A. Vaccaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112145 |
| URL | https://arxiv.org/abs/quant-ph/0112145 |
| DOI | 10.1103/PhysRevA.65.043606 |
| Journal | Phys. Rev. A 65, 043606 (2002). |
Abstract
As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.
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"abstract": "As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state\nof an optical or atom laser far above threshold is a mixture of coherent field\nstates with random phase, or, equivalently, a Poissonian mixture of number\nstates. We are interested in which, if either, of these descriptions of\n$\\rho_{ss}$, is more natural. In the preceding paper we concentrated upon\nwhether descriptions such as these are physically realizable (PR). In this\npaper we investigate another relevant aspect of these ensembles, their\nrobustness. A robust ensemble is one for which the pure states that comprise it\nsurvive relatively unchanged for a long time under the system evolution. We\ndetermine numerically the most robust ensembles as a function of the parameters\nin the laser model: the self-energy $\\chi$ of the bosons in the laser mode, and\nthe excess phase noise $\\nu$. We find that these most robust ensembles are PR\nensembles, or similar to PR ensembles, for all values of these parameters. In\nthe ideal laser limit ($\\nu=\\chi=0$), the most robust states are coherent\nstates. As the phase noise $\\nu$ or phase dispersion $\\chi$ is increased, the\nmost robust states become increasingly amplitude-squeezed. We find scaling laws\nfor these states. As the phase diffusion or dispersion becomes so large that\nthe laser output is no longer quantum coherent, the most robust states become\nso squeezed that they cease to have a well-defined coherent amplitude. That is,\nthe quantum coherence of the laser output is manifest in the most robust PR\nstates having a well-defined coherent amplitude. This lends support to the idea\nthat robust PR ensembles are the most natural description of the state of the\nlaser mode. It also has interesting implications for atom lasers in particular,\nfor which phase dispersion due to self-interactions is expected to be large.",
"arxiv_id": "quant-ph/0112145",
"authors": [
"H. M. Wiseman",
"John A. Vaccaro"
],
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"doi": "10.1103/PhysRevA.65.043606",
"journal_ref": "Phys. Rev. A 65, 043606 (2002).",
"title": "Atom Lasers, Coherent States, and Coherence:II. Maximally Robust Ensembles of Pure States",
"url": "https://arxiv.org/abs/quant-ph/0112145"
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