Measurement of the superfluid fraction of a supersolid by Josephson effect.

A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising1-12. It might be related to the supersolid phase of matter, in which the spontaneous breaking of gauge and translational symmetries leads to a spatially modulated macroscopic wavefunction13-16. This relation was recognized only in some cases1,2,5-9 and there is the need for a universal property quantifying the differences between supersolids and ordinary matter, such as the superfluid fraction, which measures the reduction in superfluid stiffness resulting from the spatial modulation16-18. The superfluid fraction was introduced long ago16, but it has not yet been assessed experimentally. Here we demonstrate an innovative method to measure the superfluid fraction based on the Josephson effect, a ubiquitous phenomenon associated with the presence of a physical barrier between two superfluids or superconductors19, which might also be expected for supersolids20, owing to the spatial modulation. We demonstrate that individual cells of a supersolid can sustain Josephson oscillations and we show that, from the current-phase dynamics, we can derive directly the superfluid fraction. Our study of a cold-atom dipolar supersolid7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents16-18. Our results open a new direction of research that may unify the description of all supersolid-like systems.

Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia.

A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Nonclassical rotational effects have also been considered in the context of the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here, we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. Using a dipolar gas of dysprosium atoms, we studied a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, previously investigated in ordinary superfluids. From the measured moment of inertia, we deduced a superfluid fraction that is different from zero and of order of unity, providing direct evidence of the superfluid nature of the dipolar supersolid.

Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas.

Supersolids are exotic materials combining the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. The supersolid phase of matter was predicted 50 years ago1-3 for solid helium4-8. Ultracold quantum gases have recently been made to exhibit periodic order typical of a crystal, owing to various types of controllable interaction9-13. A crucial feature of a D-dimensional supersolid is the occurrence of D + 1 gapless excitations, reflecting the Goldstone modes associated with the spontaneous breaking of two continuous symmetries: the breaking of phase invariance, corresponding to the locking of the phase of the atomic wave functions at the origin of superfluid phenomena, and the breaking of translational invariance due to the lattice structure of the system. Such modes have been the object of intense theoretical investigations1,14-18, but they have not yet been observed experimentally. Here we demonstrate supersolid symmetry breaking through the appearance of two distinct compressional oscillation modes in a harmonically trapped dipolar Bose-Einstein condensate, reflecting the gapless Goldstone excitations of the homogeneous system. We observe that the higher-frequency mode is associated with an oscillation of the periodicity of the emergent lattice and the lower-frequency mode characterizes the superfluid oscillations. This work also suggests the presence of two separate quantum phase transitions between the superfluid, supersolid and solid-like configurations.

Observation of a Dipolar Quantum Gas with Metastable Supersolid Properties.

The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids.

Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates.

Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states: bright solitons and quantum droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We show theoretically that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bistable region. We measure their spin composition, extract their density for a broad range of parameters, and map out the boundary of the region separating solitons from droplets.

Quantum liquid droplets in a mixture of Bose-Einstein condensates.

Quantum droplets are small clusters of atoms self-bound by the balance of attractive and repulsive forces. Here, we report on the observation of droplets solely stabilized by contact interactions in a mixture of two Bose-Einstein condensates. We demonstrate that they are several orders of magnitude more dilute than liquid helium by directly measuring their size and density via in situ imaging. We show that the droplets are stablized against collapse by quantum fluctuations and that they require a minimum atom number to be stable. Below that number, quantum pressure drives a liquid-to-gas transition that we map out as a function of interaction strength. These ultradilute isotropic liquids remain weakly interacting and constitute an ideal platform to benchmark quantum many-body theories.

Modeling the transport of interacting matter waves in a disordered system by a nonlinear diffusion equation.

We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation that well reproduce the experimental observations for both short and asymptotic expansion times. Our study establishes a connection between the peculiar shape of the expanding density profiles and the microscopic nonlinear diffusion coefficients.

Observation of subdiffusion in a disordered interacting system.

We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow expansion with a subdiffusive behavior when a controlled repulsive interaction is added. The measured features of the subdiffusion are compared to numerical simulations and a heuristic model. The observations confirm the nature of subdiffusion as interaction-assisted hopping between localized states and highlight a role of the spatial correlation of the disorder.