Strongly correlated Fermi gases in optical cavities

• Applicant: Professor Dr. Walter Hofstetter
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 557989325

Ultracold atoms in optical lattices are powerful quantum simulators of interacting many-body systems. They can be trapped in single-mode optical cavities, where the scattering of photons between the pump and the cavity by atoms leads to long-range interactions among the atoms, which can for example induce spontaneous formation of a density wave together with macroscopic occupation of the cavity mode (superradiance). This has recently been experimentally observed for ultracold fermions, and it was predicted that nesting of the Fermi surface can lead to superradiance even at infinitesimal pump strength. The competition between short-range- and cavity-mediated long-range interactions in these systems is expected to lead to an even richer phase diagram. It has been studied for bosons, where an interplay between the superfluid-Mott-insulator transition and the formation of a density wave or lattice supersolid was observed, but it is mostly unexplored for fermions. Similarly, while spin textures and dynamical spin-orbit coupling have already been observed for bosonic systems, the role of spin degrees of freedom is largely unexplored for fermions in a cavity. Due to the cavity loss these are intrinsically open quantum systems, where dissipation-stabilized phases and non-stationary phenomena can emerge. The present proposal intends to clarify the interplay of strong short- and long-range interactions in ultracold Fermi gases in an optical lattice, coupled to an optical cavity and pump lasers. We will calculate the effective temperature in the steady state and study formation of spontaneous density- or spin-order. Moreover, emerging types of pairing and superfluidity, for example pair-density-waves, will be investigated both for attractive and repulsive long-range interactions, and for the full crossover from weak to strong short-range attraction. These studies will be extended to multiflavor fermions, where we will search for “color” superfluidity or magnetism. Effects of spatial randomness or incommensurability on fermionic superradiance will be studied. Numerical simulations in this project are based on the nonperturbative dynamical mean-field theory (DMFT) and its extensions to inhomogeneous systems. A complementary field-theoretical approach will also be used to study paired phases in the presence of repulsive long-range interactions.

• DFG Programme: Research Grants
• Co-Investigator: Professor Francesco Piazza, Ph.D.