Exact description of non-Markovian effect in open quantum system: the discretized environment method

TL;DR

The paper introduces the discretized environment method, an exact approach to model non-Markovian effects in open quantum systems by discretizing the environment, validated on qubit and qutrit systems with strong memory effects.

Contribution

It presents a novel discretized environment method that accurately captures non-Markovian dynamics in open quantum systems, especially at low temperatures.

Findings

Perfect agreement with quantum Langevin approach for qubits.

Effective modeling of strong memory effects in qutrit systems.

Method is particularly accurate in low temperature, strongly non-Markovian regimes.

Abstract

An approach, called discretized environment method, is introduced to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment method is validated on a two-level system (qubit) coupled to a bosonic or fermionic heat bath. A perfect agreement with the quantum Langevin approach is found. Further illustrations are made on a three-level system (qutrit) coupled to a bosonic heat-bath. Emerging processes due to strong memory effects are discussed.