Measurement of the superfluid fraction of a supersolid by Josephson effect
Giulio Biagioni, Nicolò Antolini, Beatrice Donelli, Luca Pezzè, Augusto Smerzi, M. Fattori, A. Fioretti, C. Gabbanini, M. Inguscio, Luca Tanzi, Giovanni Carlo Modugno
Abstract A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising 1–12 . 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 wavefunction 13–16 . This relation was recognized only in some cases 1,2,5–9 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 modulation 16–18 . The superfluid fraction was introduced long ago 16 , 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 superconductors 19 , which might also be expected for supersolids 20 , 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 supersolid 7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents 16–18 . Our results open a new direction of research that may unify the description of all supersolid-like systems.
Abstract A new class of superfluids and superconductors with spatially periodic modulation of the superfluid density is arising 1–12 . 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 wavefunction 13–16 . This relation was recognized only in some cases 1,2,5–9 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 modulation 16–18 . The superfluid fraction was introduced long ago 16 , 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 superconductors 19 , which might also be expected for supersolids 20 , 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 supersolid 7 reveals a relatively large sub-unity superfluid fraction that makes realistic the study of previously unknown phenomena such as partially quantized vortices and supercurrents 16–18 . Our results open a new direction of research that may unify the description of all supersolid-like systems.
Abstract The Josephson effect is a macroscopic quantum tunneling phenomenon in a system with superfluid property, when it is split into two parts by a barrier. Here, we examine the Josephson effect in a driven-dissipative supersolid realized by coupling Bose–Einstein condensates to an optical ring cavity. We show that the spontaneous breaking of spatial translation symmetry in supersolid makes the location of the splitting barrier have a significant influence on the Josephson effect. Remarkably, for the same splitting barrier, depending on its location, two different types of DC Josephson currents are found in the supersolid phase (compared to only one type found in the superfluid phase). Thus, we term it a bi-Josephson effect. We examine the Josephson relationships and critical Josephson currents in detail, revealing that the emergence of supersolid order affects these two types of DC Josephson currents differently—one is enhanced, while the other is suppressed. The findings of this work unveil unique Josephson physics in the supersolid phase, and show new opportunities to build novel Josephson devices with supersolids.
Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance due to the appearance of a crystal structure and phase invariance due to phase locking of single-particle wave functions, responsible for superfluid phenomena. While originally predicted to be present in solid helium, ultracold quantum gases provided a first platform to observe supersolids, with particular success coming from dipolar atoms. Phase locking in dipolar supersolids has been probed through e.g. measurements of the phase coherence and gapless Goldstone modes, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases and supersolids with two-dimensional crystalline order, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase. Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with multiple spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars.
The famous two-fluid model of finite-temperature superfluids has been recently extended to describe the mixed classical-superfluid dynamics of the newly discovered supersolid phase of matter. We show that for rigidly rotating supersolids one can derive a more appropriate single-fluid model, in which the seemingly classical and superfluid contributions to the motion emerge from a spatially varying phase of the global wave function. That allows one to design experimental protocols to excite and detect the peculiar rotation dynamics of annular supersolids, including partially quantized supercurrents, in which each atom brings less than ℏ units of angular momentum. Our results are valid for a more general class of density-modulated superfluids.
Supersolids are a fundamental quantum phase of matter where the global phase and translational symmetries are spontaneously broken.The recently discovered supersolidity in quantum gases of strongly magnetic atoms gives the opportunity to explore in depth how superfluidity and crystalline order are mixed in this fascinating phase.The dipolar supersolid is usually created from a Bose-Einstein condensate, i.e., a standard superfluid, crossing a quantum phase transition that is related to the crystallization transitions of ordinary matter.In this work, we assess experimentally and theoretically the character of the superfluidsupersolid quantum phase transition.We find that one-row supersolids can have already two types of phase transitions, discontinuous and continuous, that are reminiscent of the first-and second-order transitions predicted in the thermodynamic limit in 2D and 1D, respectively.The dimensional crossover is peculiar to supersolids, is controlled via the transverse confinement and the atom number, and can be justified on the general ground of the Landau theory of phase transitions.The quasiadiabatic crossing of a continuous phase transition opens new directions of investigation for supersolids.
Abstract Supersolid states simultaneously feature properties typically associated with a solid and with a superfluid. Like a solid, they possess crystalline order, manifesting as a periodic modulation of the particle density; but unlike a typical solid, they also have superfluid properties, resulting from coherent particle delocalization across the system. Such states were initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a solid could have superfluid properties1–5. Although supersolidity has not been observed in solid helium (despite much effort)6, ultracold atomic gases provide an alternative approach, recently enabling the observation and study of supersolids with dipolar atoms7–16. However, unlike the proposed phenomena in helium, these gaseous systems have so far only shown supersolidity along a single direction. Here we demonstrate the extension of supersolid properties into two dimensions by preparing a supersolid quantum gas of dysprosium atoms on both sides of a structural phase transition similar to those occurring in ionic chains17–20, quantum wires21, 22 and theoretically in chains of individual dipolar particles23, 24. This opens the possibility of studying rich excitation properties25–28, including vortex formation29–31, and ground-state phases with varied geometrical structure7, 32 in a highly flexible and controllable system.
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.