Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken-symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the
p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low-temperature phase diagram by numerically solving the functional renormalization-group flow equations and find a nontrivial density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.
High-energy scattering spectroscopy is a widely established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases, I investigate the general relationships existing between the density contrast, the superfluid fraction, and the response to a high-energy scattering probe of density-modulated states within a classical-field approach. I focus on the two extreme regimes of shallow and deep supersolids, which are of particular interest in describing the phase transitions of the supersolid to a uniform superfluid and an incoherent crystal state, respectively. Using relevant Ans\"atze for the fields of dipolar supersolid states in these regimes, I specify and illustrate the scaling laws relating the three observables. This work was first prompted to develop an intuitive understanding of a concomitant study based on experiments and mean-field numerical simulations. Beyond this specific application, this works provides a simple and general framework to describe density-modulated states and in particular the intriguing case of supersolids. It describes key properties characterizing the supersolid order and highlights possibilities for probing such properties based on high-energy scattering response.
High-energy scattering spectroscopy is a widely-established technique for probing the characteristic properties of complex physical systems. Motivated by the recent observation of long-sought supersolid states in dipolar quantum Bose gases, I investigate the general relationships existing between the density contrast, the superfluid fraction, and the response to a high-energy scattering probe of such exotic states within a simple model. I focus on the scaling laws relating these three observables in the two extreme regimes of shallow and deep supersolids, which are of particular interest in describing the phase transitions of the supersolid to a uniform superfluid and an incoherent crystal state, respectively. I illustrate and specify the general formulae using relevant ansatzes for the supersolid states of dipolar gases in these regimes. This work brings an intuitive understanding of a concomitant study based on experiments and mean-field numerical simulations. It generally highlights new possibilities for probing supersolid states while providing a simple framework to describe such intriguing states.