Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 56, Issue 24, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/acd231
Keywords
quantum decoherence; non-Markovian master equation; reduced density matrix; sub-Ohmic spectral density; super-Ohmic spectral density; charged Brownian particle; dissipative dynamics
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We derive a non-Markovian master equation to study decoherence in a magnetic field coupled to a bath. We analyze the decay of off-diagonal elements of the reduced density matrix and find that the coherent oscillations are suppressed due to coupling with the environment. We compare three different cutoff models for the spectral density of an Ohmic bath and observe convergence at higher frequencies.
We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterized by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.
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