dorsal/arxiv
View SchemaA model of deterministic detector with dynamical decoherence
| Authors | Jae Weon Lee, Dmitri V. Averin, Giuliano Benenti, Dima L. Shepelyansky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501153 |
| URL | https://arxiv.org/abs/quant-ph/0501153 |
| DOI | 10.1103/PhysRevA.72.012310 |
| Journal | Phys. Rev. A 72, 012310 (2005) |
Abstract
We discuss a deterministic model of detector coupled to a two-level system (a qubit). The detector is a quasi-classical object whose dynamics is described by the kicked rotator Hamiltonian. We show that in the regime of quantum chaos the detector acts as a chaotic bath and induces decoherence of the qubit. We discuss the dephasing and relaxation rates and demonstrate that several features of Ohmic baths can be reproduced by our fully deterministic model. Moreover, we show that, for strong enough qubit-detector coupling, the dephasing rate is given by the rate of exponential instability of the detector's dynamics, that is, by the Lyapunov exponent of classical motion. Finally, we discuss the measurement in the regimes of strong and weak qubit-detector coupling. For the case of strong coupling the detector performs a measurement of the up/down state of the qubit. In the case of weak coupling, due to chaos, the dynamical evolution of the detector is strongly sensitive to the state of the qubit. However, in this case it is unclear how to extract a signal from any measurement with a coarse-graining in the phase space on a size much larger than the Planck cell.
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"abstract": "We discuss a deterministic model of detector coupled to a two-level system (a\nqubit). The detector is a quasi-classical object whose dynamics is described by\nthe kicked rotator Hamiltonian. We show that in the regime of quantum chaos the\ndetector acts as a chaotic bath and induces decoherence of the qubit. We\ndiscuss the dephasing and relaxation rates and demonstrate that several\nfeatures of Ohmic baths can be reproduced by our fully deterministic model.\nMoreover, we show that, for strong enough qubit-detector coupling, the\ndephasing rate is given by the rate of exponential instability of the\ndetector\u0027s dynamics, that is, by the Lyapunov exponent of classical motion.\nFinally, we discuss the measurement in the regimes of strong and weak\nqubit-detector coupling. For the case of strong coupling the detector performs\na measurement of the up/down state of the qubit. In the case of weak coupling,\ndue to chaos, the dynamical evolution of the detector is strongly sensitive to\nthe state of the qubit. However, in this case it is unclear how to extract a\nsignal from any measurement with a coarse-graining in the phase space on a size\nmuch larger than the Planck cell.",
"arxiv_id": "quant-ph/0501153",
"authors": [
"Jae Weon Lee",
"Dmitri V. Averin",
"Giuliano Benenti",
"Dima L. Shepelyansky"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.012310",
"journal_ref": "Phys. Rev. A 72, 012310 (2005)",
"title": "A model of deterministic detector with dynamical decoherence",
"url": "https://arxiv.org/abs/quant-ph/0501153"
},
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