Decoherence factor as a convolution: an interplay between a Gaussian and an exponential coherence loss

We identify and investigate the origin and nature of the transition between Gaussian and exponential forms of decoherence: the decoherence factor (that controls the time dependence of the off-diagonal terms of the density matrix expressed in the pointer basis representation) is the convolution of th...

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Bibliographic Details
Published in:New journal of physics 2022-11, Vol.24 (11), p.113029
Main Authors: Yan, Bin, Zurek, Wojciech H
Format: Article
Language:English
Subjects:
Brownian motion
Coherence
Convolution
Couplings
Decay
decoherence
Density
Eigenvalues
Eigenvectors
Energy
Fourier transforms
Laboratories
Phase transitions
Physics
spin-bath model
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Summary:We identify and investigate the origin and nature of the transition between Gaussian and exponential forms of decoherence: the decoherence factor (that controls the time dependence of the off-diagonal terms of the density matrix expressed in the pointer basis representation) is the convolution of the Fourier transforms of the spectral density and of the overlap (between the eigenstates the environment with and without couplings to the system). Spectral density alone tends to lead to the (approximately) Gaussian decay of coherence while the overlap alone results in a (largely) exponential decay. We show that these two contributions combine as a convolution, their relative importance controlled by the strength of the system-environment coupling. The resulting decoherence factor in the strong and weak coupling limits leads to predominantly Gaussian or exponential decay, respectively, as is demonstrated with two paradigmatic examples of decoherence—a spin-bath model and the quantum Brownian motion.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ac9fe8