The low-energy Goldstone mode in a trapped dipolar supersolid

Abstract

A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid 1, 2 . Since the first prediction in the 1950s 3 , experimental efforts to realize this state have focussed mainly on Helium, where supersolidity remains elusive 4 . Recently, supersolidity has also been studied intensively in ultracold quantum gases, and some of its defining properties have been induced in spin-orbit coupled Bose-Einstein condensates (BECs) 5 and BECs coupled to two crossed optical cavities 6, 7 . However, the periodicity of the crystals in both systems is fixed to the wavelength of the applied periodic optical potentials. Recently, hallmark properties of a supersolid -the periodic density modulation and simultaneous global phase coherence -have been observed in arrays of dipolar quantum droplets 8-10 , where the crystallization happens in a self-organized manner due to intrinsic interactions. In this letter, we prove the genuine supersolid nature of these droplet arrays by directly observing the low-energy Goldstone mode. The dynamics of this mode is reminiscent of the effect of second sound in other superfluid systems 11,12 and features an out-ofphase oscillation of the crystal array and the superfluid density. This mode exists only due to the phase rigidity of the experimentally realized state, and therefore confirms the genuine superfluidity of the supersolid. arXiv:1906.04633v1 [cond-mat.quant-gas]

Self-bound supersolid stripe phase in binary Bose-Einstein condensates

“…The transition here results from the interplay between long-range anisotropic and shortrange isotropic interactions with quantum fluctuations, as discussed above, with its mechanism now being well understood. Subsequent works [40][41][42] have demonstrated the measurement of the Goldstone modes depicting the spontaneous symmetry breaking related to the SS phase. In a spin-orbit-coupled BEC [32][33][34][35][36][37][38][39], the formation of density modulations in the SS phase appear as a result of momentum transfer achieved through the Raman coupling between pseudospin states formed by two atomic hyperfine ground states.…”

Three-body interaction near a narrow two-body zero crossing

“…Two-body interactions of different kinds (contact and dipole-dipole in the dipolar case and interspecies and intraspecies in the mixture case) are tuned to compete with each other such that the resulting weak overall attraction gets compensated by a higher-order Lee-Huang-Yang (LHY) term [8][9][10]. An impressive experimental progress has been made in the dipolar case on pursuing supersolidity through the formation of coherent arrays of quantum droplets [11][12][13][14][15].…”

Saga of Superfluid Solids

“…In experiments, dipolar quantum droplets arranged in periodic arrays have been observed in trapped dipolar Bose-Einstein condensates of 162 Dy, 164 Dy and 166 Er [202][203][204][205]. The existence of periodic droplet structures of quantum gases with superfluid properties is confirmed by the observation of the low-energy Goldstone mode [204,205].…”