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Science

A supersolid rotation

Jelena Stajic

Published Mar 11, 2021• 0 citations
Publisher

Abstract

Quantum Gases When a bucket of water is rotated, the water rotates with the vessel, contributing to the total moment of inertia. If such an experiment were done with a superfluid, it would decouple from the vessel and would not contribute to rotation. Tanzi et al. studied an intermediate case, a supersolid, which is predicted to only partially decouple, resulting in a moment of inertia smaller than the classical value. Whereas previous such experiments were done with helium, the authors used a gas of highly magnetic dysprosium atoms in an optical trapping potential that was suddenly changed, causing the gas to oscillate. Measuring the frequency of these oscillations provides evidence for a reduced moment of inertia. Science , this issue p. [1162][1] [1]: /lookup/doi/10.1126/science.aba4309

DOI
10.1126/science.371.6534.1117-c

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Quantum Gases
When a bucket of water is rotated, the water rotates with the vessel, contributing to the total moment of inertia. If such an experiment were done with a superfluid, it would decouple from the vessel and would not contribute to rotation. Tanzi et al. studied an intermediate case, a supersolid, which is predicted to only partially decouple, resulting in a moment of inertia smaller than the classical value. Whereas previous such experiments were done with helium, the authors used a gas of highly magnetic dysprosium atoms in an optical trapping potential that was suddenly changed, causing the gas to oscillate. Measuring the frequency of these oscillations provides evidence for a reduced moment of inertia.
Science , this issue p. 1162
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.
We show that knowledge of the time-dependent response of a trapped gas, subject to a sudden rotation of a confining harmonic potential, allows for the determination of the moment of inertia of dipolar supersolid configurations. While in the presence of one-dimensional arrays of droplets the frequency of the resulting scissors oscillation provides accurate access to the value of the moment of inertia, two-dimensional-like configurations are characterized by low-frequency resonances in the rotating signal, reflecting the presence of significant rigid-body components in the rotational motion. Using the formalism of response-function theory and simulations based on the so-called extended time-dependent Gross-Pitaevskii equation, we point out the crucial role played by the low-frequency components in the determination of the moment of inertia and of its deviations from the irrotational value. We also propose a protocol based on the stationary rotation of the trap, followed by its sudden stop, which might provide a promising alternative to the experimental evaluation of the moment of inertia.
Distinctive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment of inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation, we show that the moment of inertia determines the value of the frequency of the scissors mode, which is significantly affected by the reduction of superfluidity in the supersolid phase. The case of an in-plane isotropic trapping is instead well suited to study the formation of quantized vortices, which are shown to be characterized, in the supersolid phase, by a sizeable deformed core, caused by the presence of the surrounding density peaks.
When a vessel containing a superfluid is set in rotational motion, the superfluid does not rotate uniformly with it; instead, quantized vortices develop. Vortices have been observed in a range of superfluids, including helium, atomic Bose-Einstein condensates, and type II superconductors in a magnetic field. Freilich et al. (p. [1182][1]) visualized real-time vortex dynamics in the most tunable of superfluid systems, an atomic Bose-Einstein condensate. A small section of condensate was displaced from the trap and imaged as it fell in the gravitational field. The technique is applicable to exploring other complex dynamic systems, such as vortex reconnections and the role of vortices in quantum turbulence. [1]: /lookup/doi/10.1126/science.1191224
The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions (6Li){(}^{6}\mathrm{Li})(6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to Tc{T}_{c}Tc​ is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.
Quantum Gases A superfluid can flow without viscosity but only if the speed of the flow is lower than the so-called critical velocity. Sobirey et al. measured the critical velocity of a system of ultracold fermionic atoms confined to two dimensions. The researchers trapped a gas of lithium-6 atoms in a box-shaped potential and then moved another, periodic potential through the trap. The response of the gas to this perturbation showed a sudden increase when the speed of the periodic potential reached the critical velocity. Science , abc8793, this issue p. [844][1] [1]: /lookup/doi/10.1126/science.abc8793