dorsal/arxiv
View SchemaStochastic wave function approach to the calculation of multitime correlation functions of open quantum systems
| Authors | Heinz-Peter Breuer, Bernd Kappler, Francesco Petruccione |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9807079 |
| URL | https://arxiv.org/abs/quant-ph/9807079 |
| DOI | 10.1103/PhysRevA.56.2334 |
| Journal | Phys.Rev. A56 (1997) 2334-2351 |
Abstract
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open quantum system coupled to an environment consisting of an ensemble of harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix elements of reduced Heisenberg picture operators and general time-ordered correlation functions can be expressed by time-symmetric expectation values of extended operators in a doubled Hilbert space. This representation allows the construction of a stochastic process in the doubled Hilbert space which enables the determination of arbitrary matrix elements and correlation functions. The numerical efficiency of the resulting stochastic simulation algorithm is investigated and compared with an alternative Monte Carlo wave function method proposed first by Dalibard et al. [Phys. Rev. Lett. {\bf 68}, 580 (1992)]. By means of a standard example the suggested algorithm is shown to be more efficient numerically and to converge faster. Finally, some specific examples from quantum optics are presented in order to illustrate the proposed method, such as the coupling of a system to a vacuum, a squeezed vacuum within a finite solid angle, and a thermal mixture of coherent states.
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"abstract": "Within the framework of probability distributions on projective Hilbert space\na scheme for the calculation of multitime correlation functions is developed.\nThe starting point is the Markovian stochastic wave function description of an\nopen quantum system coupled to an environment consisting of an ensemble of\nharmonic oscillators in arbitrary pure or mixed states. It is shown that matrix\nelements of reduced Heisenberg picture operators and general time-ordered\ncorrelation functions can be expressed by time-symmetric expectation values of\nextended operators in a doubled Hilbert space. This representation allows the\nconstruction of a stochastic process in the doubled Hilbert space which enables\nthe determination of arbitrary matrix elements and correlation functions. The\nnumerical efficiency of the resulting stochastic simulation algorithm is\ninvestigated and compared with an alternative Monte Carlo wave function method\nproposed first by Dalibard et al. [Phys. Rev. Lett. {\\bf 68}, 580 (1992)]. By\nmeans of a standard example the suggested algorithm is shown to be more\nefficient numerically and to converge faster. Finally, some specific examples\nfrom quantum optics are presented in order to illustrate the proposed method,\nsuch as the coupling of a system to a vacuum, a squeezed vacuum within a finite\nsolid angle, and a thermal mixture of coherent states.",
"arxiv_id": "quant-ph/9807079",
"authors": [
"Heinz-Peter Breuer",
"Bernd Kappler",
"Francesco Petruccione"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.56.2334",
"journal_ref": "Phys.Rev. A56 (1997) 2334-2351",
"title": "Stochastic wave function approach to the calculation of multitime correlation functions of open quantum systems",
"url": "https://arxiv.org/abs/quant-ph/9807079"
},
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