Supersolidity and intertwined order parameters in a quantum gas

Matthew A. Norcia, Claudia Politi, Lauritz Klaus +6 more

Claudia Politi

Mukund Vengalattore

Karthik Chandrashekara, Christian Gölzhäuser, Lily Platt +6 more

Supersolids are exotic quantum states in which long-range phase coherence coexists, and may interplay, with emergent spatial orders. A particularly rich phase diagram featuring several competing spatial orders is predicted for dipolar supersolids with two-dimensional crystals, yet the experimental observation of this structural variety has remained limited. Here we experimentally form competing triangular and stripe density-modulated states in a quantum gas of highly magnetic atoms confined in a surfboard-shaped trap by tuning contact interaction strength and dipole orientation. We define a structural order parameter and study its statistical behavior. Thereby, we identify both the triangular and stripe phases and the transition between them, the associated critical behavior being marked by enhanced non-Gaussian fluctuations. Furthermore, we observe each spatial structure in both the phase-coherent supersolid regime and the phase-incoherent insulating one, near and far from the unmodulated-to-modulated transition, respectively. Our results establish a versatile platform in which multiple phases of the two-dimensional-supersolid phase diagram, and more generally, intertwined symmetry-breaking phenomena, can be investigated.

Nikolas Liebster, Marius Sparn, Elinor Kath +3 more

Milan Rakic

Supersolids are a fascinating quantum phase of matter that have both superfluid and solid properties, and are in some ways an extension of a superfluid, in that it possesses an additional rich and dynamic set of phenomenological features. Supersolids are an example of strongly correlated intertwined order, which is the notion that systems can form phases of matter that are more than the sum of its parts. Put simply, a supersolid is not a superfluid + solid. This intertwined order generates new and exciting physics which looks a little like its constituent components, but also not at all. In this thesis we develop a homogenisation technique, which begins with a microscopic theory of a supersolid and ends with a phenomenological Lagrangian. By doing this we marry two opposite ends of supersolid theory, providing the phenomenological toolset to study supersolids, but rooted in the foundation of microscopic theory. We derive the mathematical framework necessary to employ homogenisation, apply it to the Gross-Pitaevskii Lagrangian, elucidate crucial contributions from the thermodynamic ensemble of a supersolid, and obtain an effective theory of the Goldstone modes. We conduct numerics on a soft-core bosonic system, applying homogenisation to our simulated supersolids, and verify our results with Bogoliubov theory. We find an unexpected result that the supersolid has two distinct values for bulk compressibility, which takes it outside of the class of materials for which this thermodynamic relation holds. To the best of our knowledge, this is the first such example of this particular physical feature in any material. We then extend homogenisation to include beyond-meanfield effects, in order to apply it to a dipolar BEC. The dipolar BEC has a considerably richer phase diagram, in which we find several exciting results.