Non-Markovian Quantum Brownian Motion

Decoherence is a phenomenon investigated in many different contexts and is usually considered as the fingerprint of the transition of a system's dynamics from the quantum to the classical. Typically, decoherence times are computed by using the framework of Markovian open quantum systems, often following the approach of Caldeira and Leggett. In this Letter we develop a non-Markovian extension to the standard Caldeira-Leggett model and investigate its implications for decoherence times. By using the influence functional formalism, we expand the dynamics of the reduced system in inverse powers of the cut-off frequency of the spectral density of the environment. This procedure allows us to derive a novel non-Markovian Master Equation for the reduced density matrix of the quantum system of interest, whose numerical solution shows a strong deviation from Markovian behaviour. We compute the $l_1$-norm of coherence in the system, which exhibits a gradual transition from exponential decay over time in the Markovian case to an inverse-power law in the fully non-Markovian case, with intermediate dynamics characterised by stretched exponential relaxation. We find that decoherence times are increased significantly when non-Markovian corrections are included, and we identify the corresponding mechanisms in dynamical terms, a result that may have important implications in quantum computing.