Many-body dynamics of non-Markovian open quantum systems

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Over the past years, many experimental platforms in atomic and solid state physics have developed exceptional control over strongly interacting many-particle systems. These platforms are interesting both for exploring fundamental elements of quantum physics, and for potential applications across a range of quantum technologies. As this control has improved, one key open question has become how to describe and control open many-body quantum systems, i.e., many-body quantum systems coupled to their environment. This can give rise both to unwanted effects (e.g., decoherence), and to new tools (e.g., new ways to cool and prepare quantum states). Many techniques from quantum optics and other fields have been employed to describe Markovian open quantum systems (where the environment effectively has no memory of the past evolution of the system), non-Markovian systems where an environment has non-trivial memory effects have only recently started to be explored. These are important both because they occur naturally in many solid-state systems (e.g., decoherence in quantum computers based on superconducting qubits), and also because they can give rise to new opportunities to engineer novel phenomena in many-body systems, or generate new levels of control for future quantum technologies. In this project we aim to further develop and apply state of the art numerical techniques, including Time-Evolving Matrix Product Operators (TEMPO) and quantum state diffusion techniques based on a Hierarchy of Pure States (HOPS). We will extend these techniques in order to explore how non-Markovian dissipation interacts with the quantum coherent dynamics of many-body systems. These effects appear both in solid-state quantum technologies and in highly controlled systems of cold atoms in optical cavities. The primary objectives will be: 1) to gain an understanding of the fundamental physics which results from the interplay between coherent processes and non-Markovian dissipation in strongly interacting many-particle systems, 2) to extend recently developed numerical methods to provide new tools for studying non-Markovian dissipation in a broad range of systems, and 3) to identify areas where non-Markovian dissipative dynamics can provide tools for applications of many-body systems in future quantum technologies.