dorsal/arxiv
View SchemaLong-time dynamics of spontaneous parametric down-conversion and quantum limitations of conversion efficiency
| Authors | Michael Fleischhauer, Oliver Veits |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809089 |
| URL | https://arxiv.org/abs/quant-ph/9809089 |
| DOI | 10.1515/zna-1999-0108 |
Abstract
We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schr"odinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.
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"abstract": "We analyze the long-time quantum dynamics of degenerate parametric\ndown-conversion from an initial sub-harmonic vacuum (spontaenous\ndown-conversion). Standard linearization of the Heisenberg equations of motions\nfails in this case, since it is based on an expansion around an unstable\nclassical solution and neglects pump depletion. Introducing a mean-field\napproximation we find a periodic exchange of energy between the pump and\nsubharmonic mode goverened by an anharmonic pendulum equation. From this\nequation the optimum interaction time or crystal length for maximum conversion\ncan be determined. A numerical integration of the 2-mode Schr\"odinger equation\nusing a dynamically optimized basis of displaced and squeezed number states\nverifies the characteristic times predicted by the mean-field approximation. In\ncontrast to semiclassical and mean-field predictions it is found that quantum\nfluctuations of the pump mode lead to a substantial limitation of the\nefficiency of parametric down-conversion.",
"arxiv_id": "quant-ph/9809089",
"authors": [
"Michael Fleischhauer",
"Oliver Veits"
],
"categories": [
"quant-ph"
],
"doi": "10.1515/zna-1999-0108",
"title": "Long-time dynamics of spontaneous parametric down-conversion and quantum limitations of conversion efficiency",
"url": "https://arxiv.org/abs/quant-ph/9809089"
},
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