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arXiv:quant-ph/0702207 · Annals of Physics

Resonance theory of decoherence and thermalization

Marco Merkli, Israel Michael Sigal, G. P. Berman

Published Apr 15, 2007• 45 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2007.04.013

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A standard relaxation theory known as the BPP theory is of common use in magnetic resonance spectroscopy. A typical phenomenon that can be briefly elucidated by the theory is a broadening of peaks in Fourier spectra due to a transverse relaxation of a spin magnetization. There are, however, drawbacks: this theory is a classical phenomenological theory and often claimed to be insufficient to describe small relaxation time. In addition, it cannot describe a motional narrowing without introducing a phenomenological approach. We introduce a simple model in which a system spin ଵ ଶ is coupled with an environmental system localized around the system. The environmental system probabilistically dissipates into a thermal bath and a thermal environmental system migrates into the place instead. We show analytically that this model can describe a transverse relaxation and a motional narrowing simultaneously. We also show numerical simulations of decoherence in a spin system coupled with on-resonance bosonic modes. Our model will hopefully contribute to easier understanding of motional narrowing for a pedagogical purpose.