dorsal/arxiv
View SchemaRelaxation of a two-level system strongly coupled to a reservoir: Anomalously slow decoherence
| Authors | A. G. Kofman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106015 |
| URL | https://arxiv.org/abs/quant-ph/0106015 |
| DOI | 10.1103/PhysRevA.64.033809 |
| Journal | Phys. Rev. A 64, 033809 (2001) |
Abstract
Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-$Q$ cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, $\Omega_0\gg\nu$, where $\Omega_0$ is the rms coupling amplitude (Rabi frequency) and $\nu$ is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: the most part of the decay occurs at $t\sim\Omega_0^{-1}$, the relaxation being reversible for $t\ll(\Omega_0^2\nu)^{-1/3}$, whereas for $t\gg(\Omega_0^2\nu)^{-1/3}$ the relaxation becomes irreversible and is practically over. The other half of the coherence decays with the rate on the order of $\nu$, which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at $t\ll\nu^{-1}$ the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states are correlated with the reservoir, being dependent on the reservoir phase.
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"abstract": "Relaxation of a two-level system (TLS) into a resonant infinite-temperature\nreservoir with a Lorentzian spectrum is studied. The reservoir is described by\na complex Gaussian-Markovian field coupled to the nondiagonal elements of the\nTLS Hamiltonian. The theory can be relevant for electromagnetic interactions in\nmicrowave high-$Q$ cavities and muon spin depolarization. Analytical results\nare obtained for the strong-coupling regime, $\\Omega_0\\gg\\nu$, where $\\Omega_0$\nis the rms coupling amplitude (Rabi frequency) and $\\nu$ is the width of the\nreservoir spectrum. In this regime, the population difference and half of the\ninitial coherence decay with two characteristic rates: the most part of the\ndecay occurs at $t\\sim\\Omega_0^{-1}$, the relaxation being reversible for\n$t\\ll(\\Omega_0^2\\nu)^{-1/3}$, whereas for $t\\gg(\\Omega_0^2\\nu)^{-1/3}$ the\nrelaxation becomes irreversible and is practically over. The other half of the\ncoherence decays with the rate on the order of $\\nu$, which may be slower by\norders of magnitude than the time scale of the population relaxation. The above\nfeatures are explained by the fact that at $t\\ll\\nu^{-1}$ the reservoir\ntemporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we\nidentify the pointer basis, in which the reduction of the state vector occurs.\nThe pointer states are correlated with the reservoir, being dependent on the\nreservoir phase.",
"arxiv_id": "quant-ph/0106015",
"authors": [
"A. G. Kofman"
],
"categories": [
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"doi": "10.1103/PhysRevA.64.033809",
"journal_ref": "Phys. Rev. A 64, 033809 (2001)",
"title": "Relaxation of a two-level system strongly coupled to a reservoir: Anomalously slow decoherence",
"url": "https://arxiv.org/abs/quant-ph/0106015"
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