The low-energy Goldstone mode in a trapped dipolar supersolid (1906.04633v1)

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. Since the first prediction in the 1950s, experimental efforts to realize this state have focussed mainly on Helium, where supersolidity remains elusive. 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) and BECs coupled to two crossed optical cavities. 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, 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 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.

• The paper presents direct experimental evidence of a low-energy Goldstone mode that confirms the supersolid state in dipolar quantum droplets.
• It employs ultracold 162Dy atoms to reveal counterflow oscillations between the superfluid component and the crystal-like structure.
• Results show a clear correlation between droplet imbalance and spatial displacement, highlighting the phase rigidity fundamental to supersolidity.

The Low-Energy Goldstone Mode in a Trapped Dipolar Supersolid

The concept of a supersolid represents a unique and non-trivial state of matter where the matter exhibits both superfluidity and a crystal-like structure. This paper presents direct observations of the low-energy Goldstone mode within trapped arrays of dipolar quantum droplets, thus providing a strong evidence for the supersolid state in these arrays. The researchers' work indicates that the phase rigidity and superfluidity inherent to supersolids were effectively captured through these observations.

The paper revolves around the exploration of a specific low-energy excitatory mode, namely the Goldstone mode. When continuous symmetries are spontaneously broken, Goldstone and Higgs modes emerge, corresponding to phase and amplitude fluctuations, respectively, of an order parameter. In the context of dipolar quantum droplets, the researchers identify the Goldstone mode by a unique oscillatory behavior of both superfluid density and crystal structure in these systems.

The methodology involves using dipolar quantum gases, which have inherent length scales for density modulation due to roton-like dispersion. By employing ultracold systems of $^{162}$Dy, the researchers paper the dynamics of trapped droplet arrays and identify characteristics of the Goldstone mode. Through their experimental work, they excite the system and observe an out-of-phase oscillation, distinct from the center of mass oscillations, highlighting the counterflow between the superfluid background and the crystalline structure. This counterintuitive motion provides a vivid demonstration of the supersolid nature of the droplet arrays.

One strong outcome from this paper is the clear correlation between droplet imbalance and their spatial displacement, signifying the out-of-phase mode's unique properties. This correlation forms the crux of their evidence for supersolidity — confirming the existence of the phase rigidity intrinsic to this state of matter. When the droplets are displaced, an opposite flow in the superfluid compensates precisely, maintaining the overall center of mass.

The implications of these findings are manifold. On a theoretical level, this work provides crucial verification of the predicted properties of supersolids, particularly in dipolar systems which are prone to unique interactions due to their anisotropic nature. Practically, understanding such quantum phases could have informative crossover into materials science and technologies striving for lossless energy conduction.

Future work could illuminate other collective excitations, including the elusive Higgs modes. Moreover, exploration of larger droplet systems or two-dimensional arrays might unveil even richer excitation spectra, furthering our grasp of supersolid phenomena. Continued work in this domain might refine our understanding of quantum phase transitions and provide further insight into the multi-faceted landscape of quantum many-body systems.

In conclusion, by directly measuring phase rigidity through the low-energy Goldstone mode, the researchers validate one of the quintessential features of supersolids. Their experimental and theoretical synthesis paves the way for deeper exploration into similar exotic quantum states, broadening the scope of quantum physics and potentially innovating future technological applications.