Factorization rule for multitime correlations in non-Markovian open quantum systems

Abstract: Experiments performed on quantum systems often measure multitime correlation functions. When quantum systems are weakly coupled to their environment, the time evolution of such correlation functions can be reduced to that of the reduced density matrix by the quantum regression theorem (QRT). While no QRT is available for general non-Markovian open quantum systems, we show that for time-independent Hamiltonians and finite memory times $τ_c$, an exact factorization rule exists that relates higher-order multitime correlations to products of lower-order correlations. Consequently, all information needed to reconstruct $n$-time correlations is contained in a temporal volume of $\mathcal{O}(τ_c^n)$. On the example of quantum dots coupled to phonons, we demonstrate that this factorization makes numerical calculations of multitime correlations extremely efficient and even enables semianalytical solutions in systems where the standard QRT breaks down.