Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Abstract

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
characterised 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.