dorsal/arxiv
View SchemaContinuous Fuzzy Measurement of Energy for a Two-Level System
| Authors | Jürgen Audretsch, Michael Mensky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9703049 |
| URL | https://arxiv.org/abs/quant-ph/9703049 |
| DOI | 10.1103/PhysRevA.56.44 |
| Journal | Phys.Rev. A56 (1997) 44 |
Abstract
A continuous measurement of energy which is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy, continuous monitoring gives a readout E(t) from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes in absence of measurement Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: 1) the Zeno regime where the measurement results in a freezing of the transitions between the levels and 2) the Rabi regime when the transitions maintain. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.
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"abstract": "A continuous measurement of energy which is sharp (perfect) leads to the\nquantum Zeno effect (freezing of the state). Only if the quantum measurement is\nfuzzy, continuous monitoring gives a readout E(t) from which information about\nthe dynamical development of the state vector of the system may be obtained in\ncertain cases. This is studied in detail. Fuzziness is thereby introduced with\nthe help of restricted path integrals equivalent to non-Hermitian Hamiltonians.\nFor an otherwise undisturbed multilevel system it is shown that this\nmeasurement represents a model of decoherence. If it lasts long enough, the\nmeasurement readout discriminates between the energy levels and the von Neumann\nstate reduction is obtained. For a two-level system under resonance influence\n(which undergoes in absence of measurement Rabi oscillations between the\nlevels) different regimes of measurement are specified depending on its\nduration and fuzziness: 1) the Zeno regime where the measurement results in a\nfreezing of the transitions between the levels and 2) the Rabi regime when the\ntransitions maintain. It is shown that in the Rabi regime at the border to the\nZeno regime a correlation exists between the time dependent measurement readout\nand the modified Rabi oscillations of the state of the measured system.\nPossible realizations of continuous fuzzy measurements of energy are sketched.",
"arxiv_id": "quant-ph/9703049",
"authors": [
"J\u00fcrgen Audretsch",
"Michael Mensky"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.56.44",
"journal_ref": "Phys.Rev. A56 (1997) 44",
"title": "Continuous Fuzzy Measurement of Energy for a Two-Level System",
"url": "https://arxiv.org/abs/quant-ph/9703049"
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