dorsal/arxiv
View SchemaFormation and Dynamics of a Schr\"odinger-Cat State in Continuous Quantum Measurement
| Authors | G. P. Berman, F. Borgonovi, G. Chapline, S. A. Gurvitz, P. C. Hammel, D. V. Pelekhov, A. Suter, V. I. Tsifrinovich |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101035 |
| URL | https://arxiv.org/abs/quant-ph/0101035 |
Abstract
We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) as an example of a truly continuous measurement in quantum mechanics. This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a quasi-classical cantilever, modeled by a quantum oscillator in a coherent state in a quasi-classical region of parameters. The entire system is treated rigorously within the framework of the Schr\"odinger equation, without any artificial assumptions. Computer simulations of the spin-cantilever dynamics, where the spin is continuously rotated by means of cyclic adiabatic inversion, show that the cantilever evolves into a Schr\"odinger-cat state: the probability distribution for the cantilever position develops two asymmetric peaks that quasi-periodically appear and vanish. For a many-spin system our equations reduce to the classical equations of motion, and we accurately describe conventional MRFM experiments involving cyclic adiabatic inversion of the spin system. We surmise that the interaction of the cantilever with the environment would lead to a collapse of the wave function; however, we show that in such a case the spin does not jump into a spin eigenstate.
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"abstract": "We consider the process of a single-spin measurement using magnetic resonance\nforce microscopy (MRFM) as an example of a truly continuous measurement in\nquantum mechanics. This technique is also important for different applications,\nincluding a measurement of a qubit state in quantum computation. The\nmeasurement takes place through the interaction of a single spin with a\nquasi-classical cantilever, modeled by a quantum oscillator in a coherent state\nin a quasi-classical region of parameters. The entire system is treated\nrigorously within the framework of the Schr\\\"odinger equation, without any\nartificial assumptions. Computer simulations of the spin-cantilever dynamics,\nwhere the spin is continuously rotated by means of cyclic adiabatic inversion,\nshow that the cantilever evolves into a Schr\\\"odinger-cat state: the\nprobability distribution for the cantilever position develops two asymmetric\npeaks that quasi-periodically appear and vanish. For a many-spin system our\nequations reduce to the classical equations of motion, and we accurately\ndescribe conventional MRFM experiments involving cyclic adiabatic inversion of\nthe spin system. We surmise that the interaction of the cantilever with the\nenvironment would lead to a collapse of the wave function; however, we show\nthat in such a case the spin does not jump into a spin eigenstate.",
"arxiv_id": "quant-ph/0101035",
"authors": [
"G. P. Berman",
"F. Borgonovi",
"G. Chapline",
"S. A. Gurvitz",
"P. C. Hammel",
"D. V. Pelekhov",
"A. Suter",
"V. I. Tsifrinovich"
],
"categories": [
"quant-ph"
],
"title": "Formation and Dynamics of a Schr\\\"odinger-Cat State in Continuous Quantum Measurement",
"url": "https://arxiv.org/abs/quant-ph/0101035"
},
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