dorsal/arxiv
View SchemaConstructing the Davies process of Resonance Fluorescence with Quantum Stochastic Calculus
| Authors | Luc Bouten, Hans Maassen, Burkhard Kuemmerer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207164 |
| URL | https://arxiv.org/abs/quant-ph/0207164 |
| DOI | 10.1134/1.1586743 |
| Journal | Optics and Spectroscopy, 94:911-919, 2003 |
Abstract
Starting point is a given semigroup of completely positive maps on the 2 times 2 matrices. This semigroup describes the irreversible evolution of a decaying 2-level atom. Using the integral-sum kernel approach to quantum stochastic calculus we couple the 2-level atom to an environment, which in our case will be interpreted as the electromagnetic field. The irreversible time evolution of the 2-level atom then stems from the reversible time evolution of atom and field together. Mathematically speaking, we have constructed a Markov dilation of the semigroup. The next step is to drive the atom by a laser and to count the photons emitted into the field by the decaying 2-level atom. For every possible sequence of photon counts we construct a map that gives the time evolution of the 2-level atom inferred by that sequence. The family of maps that we obtain in this way forms a so-called Davies process. In his book Davies describes the structure of these processes, which brings us into the field of quantum trajectories. Within our model we calculate the jump operators and we briefly describe the resulting counting process.
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"abstract": "Starting point is a given semigroup of completely positive maps on the 2\ntimes 2 matrices. This semigroup describes the irreversible evolution of a\ndecaying 2-level atom. Using the integral-sum kernel approach to quantum\nstochastic calculus we couple the 2-level atom to an environment, which in our\ncase will be interpreted as the electromagnetic field. The irreversible time\nevolution of the 2-level atom then stems from the reversible time evolution of\natom and field together. Mathematically speaking, we have constructed a Markov\ndilation of the semigroup. The next step is to drive the atom by a laser and to\ncount the photons emitted into the field by the decaying 2-level atom. For\nevery possible sequence of photon counts we construct a map that gives the time\nevolution of the 2-level atom inferred by that sequence. The family of maps\nthat we obtain in this way forms a so-called Davies process. In his book Davies\ndescribes the structure of these processes, which brings us into the field of\nquantum trajectories. Within our model we calculate the jump operators and we\nbriefly describe the resulting counting process.",
"arxiv_id": "quant-ph/0207164",
"authors": [
"Luc Bouten",
"Hans Maassen",
"Burkhard Kuemmerer"
],
"categories": [
"quant-ph"
],
"doi": "10.1134/1.1586743",
"journal_ref": "Optics and Spectroscopy, 94:911-919, 2003",
"title": "Constructing the Davies process of Resonance Fluorescence with Quantum Stochastic Calculus",
"url": "https://arxiv.org/abs/quant-ph/0207164"
},
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