Supersolidity and intertwined order parameters in a quantum gas

Supersolidity is a paradoxical state of matter featuring the crystalline order of a solid and the dissipationless flow of a superfluid. The realization of this state of matter requires the breaking of two continuous symmetries, the phase invariance of a superfluid and the translational invariance to form the crystal. Proposed for He almost 50 years ago, its experimental verification remained elusive.

I will report on the realization of a supersolid state achieved by coupling a superfluid Bose-Einstein condensate (BEC) to the modes of two crossed optical cavity modes. Self-organization to individual cavities only breaks a discrete spatial symmetry and realizes a ‘lattice supersolid’. By equally coupling the BEC to both cavity modes we enforce symmetry enhancement of the free energy to a U(1) symmetry that corresponds to a continuous spatial symmetry. This symmetry is broken when a crystalline density modulation is imprinted on the superfluid wavefunction upon scattering in both cavities. We reveal the high ground state degeneracy of this state by measuring the crystal position over many realizations through the light fields leaking from the cavities [1]. A measurement of the excitation spectrum reveals the simultaneous existence of a Higgs and a Goldstone mode [2]. The existence of this state results from the exact balancing of two competing ordering tendencies.

In the last part of the talk I will report on the realization of a phase where these ordering tendencies ‘intertwine’ and give rise to a broad mixed phase where the orders can compete, coexist or even couple to each other. Intriguingly, in the latter case, the presence of one order parameter lowers the critical point of the other. This phase is reminiscent of condensed matter systems such as multiferroics or high-temperature superconductors, were different order parameters can be coupled and result in enhanced functionalities [3].

References:
[1] Nature, 543, 87-90(2017)
[2] arXiv:1704.05803(to appear in Science)
[3] arXiv:1711.07988