Many-body quantum state diffusion for non-Markovian dynamics in structured environments

Experimental systems in quantum optics offer a controllable way of probing the effects of dissipative processes on the dynamics of many-body systems, beyond the typical Born-Markov approximation. Developing numerical tools for theoretically analysing these systems is important for understanding such experiments, and is generally a challenging problem -- especially for strongly-interacting many-body systems. By combining non-Markovian quantum state diffusion techniques and tensor network methods, we study environments that have power law spectral densities (e.g. Ohmic) such as those that can be realised in many physical situations, including impurity atoms immersed in Bose-Einstein condensates. We benchmark these methods, applying them to a Hubbard-Holstein model with dissipative phonon modes, where we are now able to capture features in the spreading of correlation functions that go beyond what is simulable within standard open quantum system techniques.