dorsal/arxiv
View SchemaTheory of non-Markovian decay of a cascade atom in high-Q cavities and photonic band-gap materials
| Authors | B. M. Garraway, B. J. Dalton |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602102 |
| URL | https://arxiv.org/abs/quant-ph/0602102 |
| DOI | 10.1088/0953-4075/39/15/S21 |
| Journal | J. Phys. B 39, S767 (2006) |
Abstract
The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In all cases non-Markovian behaviour for the atomic system can be found, such as oscillatory decay for the high-Q cavity case and population trapping for the photonic band-gap case. In the master equation approaches, the atomic system is augmented by a small number of pseudomodes or quasimodes, which in the quasimode approach themselves undergo Markovian relaxation into a flat reservoir of continuum quasimodes. Results from these methods are found to be identical to those from the Laplace transform method including two-photon excitation of the reservoir with both emitting sequences. This shows that complicated non-Markovian decays of an atomic system into structured EM field reservoirs can be described by Markovian models for the atomic system coupled to a small number of pseudomodes or quasimodes.
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"abstract": "The dynamics of a three-level atom in a cascade configuration with both\ntransitions coupled to a single structured reservoir of quantized field modes\nis treated using Laplace transform methods applied to the coupled amplitude\nequations. Results are also obtained from master equations by two different\napproaches, that is, involving either pseudomodes or quasimodes. Two different\ntypes of reservoir are considered, namely a high-Q cavity and a photonic\nband-gap system, in which the respective reservoir structure functions involve\nLorentzians. Non-resonant transitions are included in the model. In all cases\nnon-Markovian behaviour for the atomic system can be found, such as oscillatory\ndecay for the high-Q cavity case and population trapping for the photonic\nband-gap case. In the master equation approaches, the atomic system is\naugmented by a small number of pseudomodes or quasimodes, which in the\nquasimode approach themselves undergo Markovian relaxation into a flat\nreservoir of continuum quasimodes. Results from these methods are found to be\nidentical to those from the Laplace transform method including two-photon\nexcitation of the reservoir with both emitting sequences. This shows that\ncomplicated non-Markovian decays of an atomic system into structured EM field\nreservoirs can be described by Markovian models for the atomic system coupled\nto a small number of pseudomodes or quasimodes.",
"arxiv_id": "quant-ph/0602102",
"authors": [
"B. M. Garraway",
"B. J. Dalton"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0953-4075/39/15/S21",
"journal_ref": "J. Phys. B 39, S767 (2006)",
"title": "Theory of non-Markovian decay of a cascade atom in high-Q cavities and photonic band-gap materials",
"url": "https://arxiv.org/abs/quant-ph/0602102"
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