dorsal/arxiv
View SchemaThe transition to classical chaos in a coupled quantum system through continuous measurement
| Authors | Shohini Ghose, Paul Alsing, Ivan Deutsch, Tanmoy Bhattacharya, Salman Habib, Kurt Jacobs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309093 |
| URL | https://arxiv.org/abs/quant-ph/0309093 |
| DOI | 10.1103/PhysRevA.69.052116 |
| Journal | Phys. Rev. A69 (2004) 052116 |
Abstract
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough that quantum backaction noise is negligible. We investigate the conditions under which classical dynamics emerges, via continuous position measurement, for a particle moving in a harmonic well with its position coupled to internal spin. As a consequence of this coupling we find that classical dynamics emerges only when the position and spin actions are both large compared to $\hbar$. These conditions are quantified by placing bounds on the size of the covariance matrix which describes the delocalized quantum coherence over extended regions of phase space. From this result it follows that a mixed quantum-classical regime (where one subsystem can be treated classically and the other not) does not exist for a continuously observed spin 1/2 particle. When the conditions for classicallity are satisfied (in the large-spin limit), the quantum trajectories reproduce both the classical periodic orbits as well as the classically chaotic phase space regions. As a quantitative test of this convergence we compute the largest Lyapunov exponent directly from the measured quantum trajectories and show that it agrees with the classical value.
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"abstract": "Continuous observation of a quantum system yields a measurement record that\nfaithfully reproduces the classically predicted trajectory provided that the\nmeasurement is sufficiently strong to localize the state in phase space but\nweak enough that quantum backaction noise is negligible. We investigate the\nconditions under which classical dynamics emerges, via continuous position\nmeasurement, for a particle moving in a harmonic well with its position coupled\nto internal spin. As a consequence of this coupling we find that classical\ndynamics emerges only when the position and spin actions are both large\ncompared to $\\hbar$. These conditions are quantified by placing bounds on the\nsize of the covariance matrix which describes the delocalized quantum coherence\nover extended regions of phase space. From this result it follows that a mixed\nquantum-classical regime (where one subsystem can be treated classically and\nthe other not) does not exist for a continuously observed spin 1/2 particle.\nWhen the conditions for classicallity are satisfied (in the large-spin limit),\nthe quantum trajectories reproduce both the classical periodic orbits as well\nas the classically chaotic phase space regions. As a quantitative test of this\nconvergence we compute the largest Lyapunov exponent directly from the measured\nquantum trajectories and show that it agrees with the classical value.",
"arxiv_id": "quant-ph/0309093",
"authors": [
"Shohini Ghose",
"Paul Alsing",
"Ivan Deutsch",
"Tanmoy Bhattacharya",
"Salman Habib",
"Kurt Jacobs"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.69.052116",
"journal_ref": "Phys. Rev. A69 (2004) 052116",
"title": "The transition to classical chaos in a coupled quantum system through continuous measurement",
"url": "https://arxiv.org/abs/quant-ph/0309093"
},
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