dorsal/arxiv
View SchemaBayesian feedback versus Markovian feedback in a two-level atom
| Authors | H. M. Wiseman, Stefano Mancini, Jin Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201145 |
| URL | https://arxiv.org/abs/quant-ph/0201145 |
| DOI | 10.1103/PhysRevA.66.013807 |
| Journal | PRA 66, 013807 (2002) |
Abstract
We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. {\bf 70}, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty {\em et al.} [Phys. Rev. A {\bf 62}, 012105 (2000)]. Here we choose to call it, for brevity, {\em Bayesian feedback}. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtain without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.
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"abstract": "We compare two different approaches to the control of the dynamics of a\ncontinuously monitored open quantum system. The first is Markovian feedback as\nintroduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. {\\bf 70},\n548 (1993)]. The second is feedback based on an estimate of the system state,\ndeveloped recently by Doherty {\\em et al.} [Phys. Rev. A {\\bf 62}, 012105\n(2000)]. Here we choose to call it, for brevity, {\\em Bayesian feedback}. For\nsystems with nonlinear dynamics, we expect these two methods of feedback\ncontrol to give markedly different results. The simplest possible nonlinear\nsystem is a driven and damped two-level atom, so we choose this as our model\nsystem. The monitoring is taken to be homodyne detection of the atomic\nfluorescence, and the control is by modulating the driving. The aim of the\nfeedback in both cases is to stabilize the internal state of the atom as close\nas possible to an arbitrarily chosen pure state, in the presence of inefficient\ndetection and other forms of decoherence. Our results (obtain without recourse\nto stochastic simulations) prove that Bayesian feedback is never inferior, and\nis usually superior, to Markovian feedback. However it would be far more\ndifficult to implement than Markovian feedback and it loses its superiority\nwhen obvious simplifying approximations are made. It is thus not clear which\nform of feedback would be better in the face of inevitable experimental\nimperfections.",
"arxiv_id": "quant-ph/0201145",
"authors": [
"H. M. Wiseman",
"Stefano Mancini",
"Jin Wang"
],
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],
"doi": "10.1103/PhysRevA.66.013807",
"journal_ref": "PRA 66, 013807 (2002)",
"title": "Bayesian feedback versus Markovian feedback in a two-level atom",
"url": "https://arxiv.org/abs/quant-ph/0201145"
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