dorsal/arxiv
View SchemaAdiabatic Elimination in Compound Quantum Systems with Feedback
| Authors | P. Warszawski, H. M. Wiseman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005127 |
| URL | https://arxiv.org/abs/quant-ph/0005127 |
| DOI | 10.1103/PhysRevA.63.013803 |
Abstract
Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the ancilla responds to fluctuations on a much shorter time scale than does the system, we show that it can be adiabatically eliminated, yielding a master equation for the system alone. This is very significant as it decreases the necessary basis size for numerical simulation and allows the effect of the ancilla to be understood more easily. We consider two types of ancilla: a two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g. an optical mode). For each, we consider two forms of feedback: coherent (for which a quantum mechanical description of the feedback loop is required) and incoherent (for which a classical description is sufficient). We test the master equations we obtain using numerical simulation of the full dynamics of the compound system. For the system (a parametric oscillator) and feedback (intensity-dependent detuning) we choose, good agreement is found in the limit of heavy damping of the ancilla. We discuss the relation of our work to previous work on feedback in compound quantum systems, and also to previous work on adiabatic elimination in general.
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"abstract": "Feedback in compound quantum systems is effected by using the output from one\nsub-system (``the system\u0027\u0027) to control the evolution of a second sub-system\n(``the ancilla\u0027\u0027) which is reversibly coupled to the system. In the limit where\nthe ancilla responds to fluctuations on a much shorter time scale than does the\nsystem, we show that it can be adiabatically eliminated, yielding a master\nequation for the system alone. This is very significant as it decreases the\nnecessary basis size for numerical simulation and allows the effect of the\nancilla to be understood more easily. We consider two types of ancilla: a\ntwo-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g.\nan optical mode). For each, we consider two forms of feedback: coherent (for\nwhich a quantum mechanical description of the feedback loop is required) and\nincoherent (for which a classical description is sufficient). We test the\nmaster equations we obtain using numerical simulation of the full dynamics of\nthe compound system. For the system (a parametric oscillator) and feedback\n(intensity-dependent detuning) we choose, good agreement is found in the limit\nof heavy damping of the ancilla. We discuss the relation of our work to\nprevious work on feedback in compound quantum systems, and also to previous\nwork on adiabatic elimination in general.",
"arxiv_id": "quant-ph/0005127",
"authors": [
"P. Warszawski",
"H. M. Wiseman"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.63.013803",
"title": "Adiabatic Elimination in Compound Quantum Systems with Feedback",
"url": "https://arxiv.org/abs/quant-ph/0005127"
},
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