Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

Abstract

Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to analytical treatment for a number of timely problems like the system interaction with two-photon wavepackets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.

Collisional-model quantum trajectories for entangled qubit environments

“…Collisional models typically employ single-qubit baths, where a single, uncorrelated qubit interacts with the system at each time, with recent investigations pushing beyond this in various ways. Temporally correlated singlequbit baths can be used to model non-classical environments such as n-photon states [24][25][26], which drive non-Markovian evolution due to the temporal entanglement in the input bath [27]. Another way to to go beyond single-qubit baths is to increase the number of qubits per interaction time.…”