Quantum liquid-crystal order in resonant atomic gases

I review recent studies that predict a realization of quantum liquid-crystalline orders in resonant atomic gases. As examples of such putative systems I will discuss an s-wave resonant imbalanced Fermi gas and a p-wave resonant Bose gas. In the former, the liquid-crystalline smectic, nematic and rich variety of other descendant states emerge from strongly quantum- and thermally-fluctuating Fulde–Ferrell and Larkin–Ovchinnikov states, driven by a competition between resonant pairing and Fermi-surface mismatch. In the latter, at intermediate detuning the p-wave resonant interaction generically drives Bose-condensation at a finite momentum, set by a competition between atomic kinetic energy and atom–molecule hybridization. Because of the underlying rotationally-invariant environment of the atomic gas trapped isotropically, the putative striped superfluid is a realization of a quantum superfluid smectic, that can melt into a variety of interesting phases, such as a quantum nematic. I will discuss the corresponding rich phase diagrams and transitions, as well the low-energy properties of the phases and fractional topological defects generic to striped superfluids and their fluctuation-driven descendants.

► I review quantum liquid crystals realized in resonant atomic gases.
► Fulde–Ferrell–Larkin–Ovchinnikov state is a quantum superfluid smectic.
► A p-wave Feshbach resonant Bose gas exhibits a spinor-1 superfluid smectic state.
► I analyze low-energy fluctuations, topological defects and phase transitions in these systems.
► I map out rich phase diagrams for these systems.