dorsal/arxiv
View SchemaPhysical interpretation of stochastic Schroedinger equations in cavity QED
| Authors | Tarso B. L. Kist, M. Orszag, T. A. Brun, L. Davidovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805027 |
| URL | https://arxiv.org/abs/quant-ph/9805027 |
| DOI | 10.1088/1464-4266/1/2/009 |
| Journal | J. Optics B 1, 251-263 (1999) |
Abstract
We propose physical interpretations for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr\"odinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger equation, depending on the system configuration. We also show that the Monte Carlo Wave-Function approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states.
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"abstract": "We propose physical interpretations for stochastic methods which have been\ndeveloped recently to describe the evolution of a quantum system interacting\nwith a reservoir. As opposed to the usual reduced density operator approach,\nwhich refers to ensemble averages, these methods deal with the dynamics of\nsingle realizations, and involve the solution of stochastic Schr\\\"odinger\nequations. These procedures have been shown to be completely equivalent to the\nmaster equation approach when ensemble averages are taken over many\nrealizations. We show that these techniques are not only convenient\nmathematical tools for dissipative systems, but may actually correspond to\nconcrete physical processes, for any temperature of the reservoir. We consider\na mode of the electromagnetic field in a cavity interacting with a beam of two-\nor three-level atoms, the field mode playing the role of a small system and the\natomic beam standing for a reservoir at finite temperature, the interaction\nbetween them being given by the Jaynes-Cummings model. We show that the\nevolution of the field states, under continuous monitoring of the state of the\natoms which leave the cavity, can be described in terms of either the Monte\nCarlo Wave-Function (quantum jump) method or a stochastic Schr\\\"odinger\nequation, depending on the system configuration. We also show that the Monte\nCarlo Wave-Function approach leads, for finite temperatures, to localization\ninto jumping Fock states, while the diffusion equation method leads to\nlocalization into states with a diffusing average photon number, which for\nsufficiently small temperatures are close approximations to mildly squeezed\nstates.",
"arxiv_id": "quant-ph/9805027",
"authors": [
"Tarso B. L. Kist",
"M. Orszag",
"T. A. Brun",
"L. Davidovich"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/1/2/009",
"journal_ref": "J. Optics B 1, 251-263 (1999)",
"title": "Physical interpretation of stochastic Schroedinger equations in cavity QED",
"url": "https://arxiv.org/abs/quant-ph/9805027"
},
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