dorsal/arxiv
View SchemaApproximate Master Equations for Atom Optics
| Authors | D. J. Atkins, H. M. Wiseman, P. Warszawski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204074 |
| URL | https://arxiv.org/abs/quant-ph/0204074 |
| DOI | 10.1103/PhysRevA.67.023802 |
| Journal | Phys. Rev. A 67, 023802 (2003) |
Abstract
In the field of atom optics, the basis of many experiments is a two level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the spontaneous emission of photons from the atom. For many applications, it is necessary to minimize the effect of this irreversible evolution. This can be achieved by having a far detuned light field. The drawback of this regime is that making the detuning very large makes the timestep required to solve the master equation very small, much smaller than the timescale of any significant evolution. This makes the problem very numerically intensive. For this reason, approximations are used to simulate the master equation which are more numerically tractable to solve. This paper analyses four approximations: The standard adiabatic approximation; a more sophisticated adiabatic approximation (not used before); a secular approximation; and a fully quantum dressed-state approximation. The advantages and disadvantages of each are investigated with respect to accuracy, complexity and the resources required to simulate. In a parameter regime of particular experimental interest, only the sophisticated adiabatic and dressed-state approximations agree well with the exact evolution.
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"abstract": "In the field of atom optics, the basis of many experiments is a two level\natom coupled to a light field. The evolution of this system is governed by a\nmaster equation. The irreversible components of this master equation describe\nthe spontaneous emission of photons from the atom. For many applications, it is\nnecessary to minimize the effect of this irreversible evolution. This can be\nachieved by having a far detuned light field. The drawback of this regime is\nthat making the detuning very large makes the timestep required to solve the\nmaster equation very small, much smaller than the timescale of any significant\nevolution. This makes the problem very numerically intensive. For this reason,\napproximations are used to simulate the master equation which are more\nnumerically tractable to solve. This paper analyses four approximations: The\nstandard adiabatic approximation; a more sophisticated adiabatic approximation\n(not used before); a secular approximation; and a fully quantum dressed-state\napproximation. The advantages and disadvantages of each are investigated with\nrespect to accuracy, complexity and the resources required to simulate. In a\nparameter regime of particular experimental interest, only the sophisticated\nadiabatic and dressed-state approximations agree well with the exact evolution.",
"arxiv_id": "quant-ph/0204074",
"authors": [
"D. J. Atkins",
"H. M. Wiseman",
"P. Warszawski"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.67.023802",
"journal_ref": "Phys. Rev. A 67, 023802 (2003)",
"title": "Approximate Master Equations for Atom Optics",
"url": "https://arxiv.org/abs/quant-ph/0204074"
},
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