Quantum Optics Seminar: Kseniia Vodenkova

Continuous Coherent Quantum Feedback with Time Delays: Tensor Network Approach

Coherent quantum feedback refers to the situation when both the system and its controller are quantum in nature. An exciting scientific frontier in this field is the exploration of phenomena that emerge in a regime when the controller can store and process the quantum state of multiple degrees of freedom. This is the case when time delay in the feedback loop is large, i.e., when the time required for excitations to propagate through the feedback loop is large compared to the time required to emit an excitation. We developed a novel method to solve problems involving quantum optical systems coupled to coherent quantum feedback loops featuring time delays. Our method is based on exact mappings of such non-Markovian problems to equivalent Markovian driven dissipative quantum many-body problems. We show that the resulting Markovian quantum many-body problems can be solved (numerically) exactly and efficiently using tensor network methods. In particular, we show that our method allows solving problems in so far inaccessible regimes, including problems with arbitrary long time delays and arbitrary numbers of excitations in the delay lines. We obtain solutions for the full real-time dynamics as well as the steady state in all these regimes. Finally, motivated by our results, we develop a novel mean-field approach, which allows us to find the solution semi-analytically, and we identify parameter regimes where this approximation is in excellent agreement with our tensor network results.