Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the last decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering, pairing and superfluidity, and the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength DW order is stabilized in the system, which we identify via its superradiant light scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the BCS-BEC crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.Comment: 11 pages, 7 figure

Quantum Phases of Ultra-Cold Fermi Gases in Optical Cavities

Main aim of the present thesis is to investigate the quantum phases arising from the interaction of an ultra-cold Fermi gas with the quantized electromagnetic field of a single-mode optical cavity. Both numerical and analytical methods are used. In particular, we suggest that the same microscopic mechanism, originated by exchange of photons inside the optical cavity, induces interactions between the spins of the fermionic atoms and, indirectly, a superfluid pairing. As a result, a phase diagram can be established, where different order parameters emerge, related to spin and density degrees of freedom, which evolve into each other after tuning the sign and strength of the interactions across the cavity resonance