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Based on tensor network realizations of path integrals reducing exponentialmemory scaling to polynomial efficiency and a Liouville space implementation ofa time-discrete quantum memory, we investigate a quantum system simultaneouslyexposed to two structured reservoirs. For this purpose, we employ a numericallyexact quasi-2D tensor network combining both diagonal and off-diagonalsystem-reservoir interactions with a twofold memory for continuous and discreteretardation effects. As a possible example, we study the non-Markoviandynamical interplay between discrete photonic feedback and structured acousticphonon modes, resulting in emerging inter-reservoir correlations andlong-living population trapping within an initially-excited two-level system.

Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space