Supersolid formation in a quantum gas breaking a continuous translational symmetry

A supersolid with continuous translational symmetry breaking along one direction is realized by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. Symmetry smashing supersolids (Esslinger 21067, Physics Letter, Leonie Mueck) Supersolidity is a state of matter that combines the spatial order of a crystal with superfluid properties. Superfluids are phase invariant, and crystals break continuous translational symmetry, so a supersolid must break both of these symmetries. Previous studies have predicted that helium is a supersolid at very low temperatures, but unambiguous proof of supersolidity in helium, or in any system, has been missing. Here, Tilman Esslinger and colleagues get a step closer to verifying supersolidity in an ultracold quantum gas system. They observe the breaking of continuous translational symmetry along one direction by coupling a Bose–Einstein condensate of atoms to two optical cavities. Using this experimental platform, other exotic states of matter could be created, such as supersolids in the presence of disorder. Elsewhere in this issue, Jun-Ru Li and colleagues create a special stripe phase in a one-dimensional spin–orbit-coupled Bose–Einstein condensate and observe supersolid properties. The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal 1 , 2 . Despite having been proposed for helium almost 50 years ago 3 , 4 , experimental verification of supersolidity remains elusive 5 , 6 . A variant with only discrete translational symmetry breaking on a preimposed lattice structure—the ‘lattice supersolid’ 7 —has been realized, based on self-organization of a Bose–Einstein condensate 8 , 9 . However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous translational symmetry breaking along one direction in a quantum gas. The continuous symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the