NonEQuMat

The physics of out-of-equilibrium quantum many-particle systems underlies the behavior of important existing and emerging platforms for quantum simulation, ranging from ultra cold atoms in optical lattices, to Rydberg arrays to coupled circuit QED cavities. Better understanding and controlling of quantum dynamics under the effect of drive and dissipation both involves interesting foundational research, and is likely to have a key role in the development of future generations of quantum technologies. The aim of this project is to address theoretical questions and models relevant for current and upcoming experiments in quantum simulation of non equilibrium quantum matter, focusing on platforms involving driven strongly interacting Fermi and Bose systems as well as quantum spin chains. The project will take advantage of the unique expertise in quantum many body dynamics of the Principal Investigator who has obtained important preliminary results in this field as described in the proposal, as well as of the excellent research environment provided by the Institute of Physics of College de France, where there is a tremendous activity ongoing with various platforms for quantum simulation. Key conceptual aspects of the project that set it apart include: (i) the proposal for quantum simulation of drive-induced eta-pairing in Fermi Hubbard model, an exotic phase of matter which cannot be realised in thermal equilibrium (ii) the investigation of dissipative quantum phase transitions and quantum time-crystals phases with CircuitQED arrays, (iii) The establishment of a theoretical activity on Quantum Dynamics in Rydberg Quantum Simulators which can be strategic given the current emerging position of France in this field on the experimental side. On the methodological side, the project will make use of a number of state of the art techniques developed in the recent years by the Principal Investigator (including Nonequilibrium Dynamical Mean Field Theory, Time-Dependent Variational Method for Quantum Dynamics, Flow Equation Method) and that will be further extended in different directions as elaborated in the proposal.