Coherent time‐delayed feedback allows the control of a quantum system and its partial stabilization against noise and decoherence. The crucial and externally accessible parameters in such control setups are the round‐trip‐induced delay time τ and the frequencies ω of the involved optical transitions which are typically controllable via global parameters like temperature, bias, or strain. They influence the dynamics via the amplitude and the phase ϕ=ωτ of the feedback signal. These quantities are, however, not independent. Here, the aim is to control the feedback phase via a microwave pump field. Using the example of a Λ‐type three‐level system, it is shown that the Rabi frequency of the pump field induces phase shifts on demand and therefore increases the applicability of coherent quantum feedback control protocols.

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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