Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems

TL;DR

This paper introduces a modified Bloch-Redfield master equation that accurately models the dynamics of multilevel quantum systems under incoherent light, distinguishing between quantum coherent and incoherent regimes and capturing population-coherence interactions.

Contribution

The work develops a new theoretical method combining Bloch-Redfield theory with a partial secular approximation to explicitly account for transition dipole orientations in multilevel systems.

Findings

The method distinguishes between quantum coherent and incoherent energy transfer regimes.

Incoherent regime characterized by orthogonal transition dipoles leading to a Pauli-type master equation.

Coherent regime involves non-orthogonal dipoles, enabling quantum coherence generation.

Abstract

We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis, and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state, and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.