Evidence of superfluidity in a supersolid under rotation Giulio Biagioni Dipartimento di Fisica e Astronomia and LENS, Università di Firenze, and CNR-INO, sezione di Pisa 106° SIF National Congress, 14-18 September 2020 Supersolid state of matter • Classical solid Crystalline order Macroscopic consequence: rigidity of the crystal • Superfluid Coherent wave function Macroscopic consequences: metastibility of supercurrents, reduced moment of inertia • Supersolid Both kinds of order Macroscopic consequences: ? Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 2 Our dipolar supersolid 휃 = 휋/2 162 푉푖푛푡(풓) = 푉푐표푛푡 풓 + 푉푑푖푝(풓) 퐷푖푝표푙푎푟 푎 Dy 휀 = = 푑푑 푑푑 퐶표푛푡푎푐푡 푎 휇 = 10휇 퐵 Isotropic and Repulsive repulsive 휃 = 0 Attractive Confinement Vertical trapping + anisotropy clustering effect ! Superfluid Normal solid (Bose-Einstein condensate) Supersolid (Droplet crystal) 휀푑푑 Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 3 Our dipolar supersolid 휀푑푑 lattice mode 8 10 Superfluid 1 5 0 0 9 3 k . y 5 k x Supersolid a ) 9 94 9 ( 7 a G 6 ( 2 0 . ) B 5 Droplet crystal 88 2 9 7 1 2 . 5 휀푑푑 5 8 28 48 100 t (ms) 1.25 superfluid mode Variance of ) 2 d 1.00 uniform random a r ( Evidence for double symmetry breaking e phase c 0.75 n a i r L. Tanzi et al., Phys. Rev. Lett., a L. Tanzi et al., Nature, 574, 774 (2020) V 0.50 e 122, 130405 (2019) s a h P 0.25 Cluster supersolid with ~3 − 4 droplets and ~104 atoms per droplet 0.00 15 30 45 60 75 Time (ms) Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 4 Related works G. Natale et al., Phys. Rev. Lett. 123, 050402 (2019) Innsbruck M. Guo et al., Nature 574, 386 (2019) Stuttgart Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 5 Superfluids under rotation 푖휑(푟) • Macroscopic wavefunction Ψ0 푟 = Ψ0(푟) 푒 ℏ 푣Ԧ = ∇휑 ⇒ ∇ ∧ 푣Ԧ=0 ⇒ ׯ 푣Ԧ ∙ 푑푙Ԧ = 0 ⇒ classical irrotational hydrodynamics • 푚 • Reduced moment of inertia ⇒ 퐼 = 1 − 푓푠 퐼푐 (in a cylindrical geometry) መ 푣Ԧ = 휔푅휃 • Normally, 푓푠 → 1 for 푇 → 0 ⇒ 퐼 = 0 z 휔 • No angular momentum is acquired < 퐿 >= 퐼휔 from the container when 휔 → 0 Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 6 Superfluids under rotation Helium-4 (1967) Hess-Fairbank Helium-3 (1982) related Meissner effect in superconductors BECs (2000) Giulio Biagioni Exploring the supersolid state of matter 7 Leggett’s argument: can a solid be superfluid? 푖휑(푟) Also supersolids are described by a macroscopic wavefunction Ψ0 푟 = Ψ0(푟) 푒 The density modulation appears in the form of the superfluid fraction: −1 (퐼 = 1 − 푓푠 퐼푐 with 푓푠 ≤ ׬푑푥/휌ҧ(푥 so that 0 < 퐼 < 퐼푐 at 푇 = 0 NCRI (Non Classical Rotational Inertia) 퐼 = 퐼푐 0 < 퐼 < 퐼푐 퐼 = 0 Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 8 The scissors mode How to probe the moment of inertia of our small and non-homogenous system? We employ a collective mode of the trapped condensate: the scissors mode In the small-angle limit: 휃 푡 = 휗0 sin(휔푠푐푡) Experiments with non-dipolar BECs: 푥 2 2 O.M. Maragò et al., Phys. Rev. Lett. 휔푠푐 = 휔푥 + 휔푦 84, 2056-2019 (2000) 푦 푧 Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 9 The scissors mode Useful link with the moment of inertia 2 2 휔푥 + 휔푦 퐼 = 퐼푐훼 훽 2 휔푠푐 2 2 2 2 2 2 2 2 ۄ Τ〈 푥 + 푦ۄ 훼 = 휔푦 − 휔푥 ൗ 휔푥 + 휔푦 훽 = 〈푥 − 푦 Trap deformation Cloud deformation D. Guéry-Odelin and S. Stringari, Phys. Rev. Lett. 83, 4452-4455 (1999) Analogy with torsional oscillators 퐾 퐼 = 2 휔표푠푐 Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 10 Scissors oscillation BEC 휃 휃′ 휃′ 휃′ Supersolid We excite the scissors mode .. then we extract the angle Single-frequency oscillation in both the changing temporary the at different times with a 2D BEC and the supersolid regime relative power between fit ODT2 and ODT3.. Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 11 Scissors frequencies and moment of inertia 2 2 휔푥 + 휔푦 퐼 = 퐼푐훼 훽 2 휔푠푐 퐼퐵퐸퐶 < 퐼푠푠 < 퐼푐 Reduced moment of inertia ⇒ proof of the superfluid behavior under rotation L. Tanzi et al., (2019) Preprint: arXiv:1912.01910. Accepted for publication in Science. Theory, including 훽, by the Trento group: S. M. Roccuzzo et al., Phys. Rev. Lett., 124:045702 (2020) Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 12 Superfluid fraction 2 2 2 Our definition of superfluid 1−훼훽 휔푥+휔푦 /휔푠푐 퐼 = 1 − 푓 퐼 + 푓 훽2퐼 ⇒ 푓 = fraction for an anisotropic system: 푠 푐 푠 푐 푠 1−훽2 numerical simulations 푓푠~1 (cluster supersolid) Comparison with the 1D Leggett’s −1 model: 푓푠 ≤ ׬푑 푥Τ휌ҧ (푥) (white droplets triangles, density profile from the superfluidity Trento group) 휇 휌 Our experiment: 0.88±0.14 Leggett formula Leggett: 0.25 Droplets superfluidity: 0.50 휀푑푑 = 1.50 휇 Helium experiments: ~0.01 −4 Leggett: 10 휀푑푑 = 1.42 15/09/2020 Evidence of superfluidity in a supersolid under rotation 13 Conclusions and outlook We have demonstrated the superfluid properties of the dipolar supersolid under rotation through a measurement of its moment of inertia. Next goals: • Realizing larger, 2D supersolids to detect a sub-unity superfluid fraction, study vortices and measure a finite shear modulus • Josephson effect without a barrier • Other types of supersolids with cold atoms (e.g. dipoles in 2D stabilized by 3-body forces, or lattice supersolids) Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 14 The team Current team: Luca Tanzi Giovanni Modugno Giulio Biagioni Nicolò Antolini Andrea Fioretti Carlo Gabbanini Former members: Eleonora Lucioni Francesca Famà Jacopo Catani Julian Maloberti Theory by: Russell Bisset, Luis Santos (Hannover); Alessio Recati, Sandro Stringari (Trento); Michele Modugno (Bilbao); Luca Pezzè, Augusto Smerzi (Firenze); Maria Luisa Chiofalo (Pisa), Adriano Angelone (Trieste) … Giulio Biagioni Evidence of superfluidity in a supersolid under rotation 15.