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

TL;DR

This paper derives a non-Markovian master equation for a charged particle in a magnetic field, analyzing how different environmental spectral densities and temperature regimes affect decoherence and coherence loss.

Contribution

It introduces a detailed non-Markovian framework for decoherence in charged particles, comparing various spectral cutoff models and extending beyond Ohmic baths.

Findings

Decoherence suppresses cyclotron oscillations over time.

Low-temperature quantum fluctuations slow decoherence significantly.

Different spectral cutoff models converge at high frequencies.

Abstract

We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analysing 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.