dorsal/arxiv
View SchemaCoupled Classical and Quantum Oscillators
| Authors | Rachael M. McDermott, Ian H. Redmount |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403184 |
| URL | https://arxiv.org/abs/quant-ph/0403184 |
Abstract
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators provide a simple, exactly soluble model for exploring such interaction. Even the ground state of a pair of identical oscillators exhibits effects on the quantum nature of one oscillator, e.g., a diminution of position uncertainty, and an increase in momentum uncertainty and uncertainty product, from their unperturbed values. Interaction between quantum and classical oscillators is simulated by constructing a quantum state with one oscillator initially in its ground state, the other in a coherent or Glauber state. The subsequent wave function for this state is calculated exactly, both for identical and distinct oscillators. The reduced probability distribution for the quantum oscillator, and its position and momentum expectation values and uncertainties, are obtained from this wave function. The oscillator acquires an oscillation amplitude corresponding to a beating between the normal modes of the system; the behavior of the position and momentum uncertainties can become quite complicated. For oscillators with equal unperturbed frequencies, i.e., at resonance, the uncertainties exhibit a time-dependent quantum squeezing which can be extreme.
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"abstract": "Some of the most enduring questions in physics--including the quantum\nmeasurement problem and the quantization of gravity--involve the interaction of\na quantum system with a classical environment. Two linearly coupled harmonic\noscillators provide a simple, exactly soluble model for exploring such\ninteraction. Even the ground state of a pair of identical oscillators exhibits\neffects on the quantum nature of one oscillator, e.g., a diminution of position\nuncertainty, and an increase in momentum uncertainty and uncertainty product,\nfrom their unperturbed values. Interaction between quantum and classical\noscillators is simulated by constructing a quantum state with one oscillator\ninitially in its ground state, the other in a coherent or Glauber state. The\nsubsequent wave function for this state is calculated exactly, both for\nidentical and distinct oscillators. The reduced probability distribution for\nthe quantum oscillator, and its position and momentum expectation values and\nuncertainties, are obtained from this wave function. The oscillator acquires an\noscillation amplitude corresponding to a beating between the normal modes of\nthe system; the behavior of the position and momentum uncertainties can become\nquite complicated. For oscillators with equal unperturbed frequencies, i.e., at\nresonance, the uncertainties exhibit a time-dependent quantum squeezing which\ncan be extreme.",
"arxiv_id": "quant-ph/0403184",
"authors": [
"Rachael M. McDermott",
"Ian H. Redmount"
],
"categories": [
"quant-ph"
],
"title": "Coupled Classical and Quantum Oscillators",
"url": "https://arxiv.org/abs/quant-ph/0403184"
},
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