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Tanzi L, Maloberti JG, Biagioni G, Fioretti A, Gabbanini C, Modugno G. Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia. Science 2021; 371:1162-1165. [PMID: 33602866 DOI: 10.1126/science.aba4309] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 02/02/2021] [Indexed: 11/02/2022]
Abstract
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.
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Affiliation(s)
- L Tanzi
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy.,LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - J G Maloberti
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy.,LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - G Biagioni
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy.,LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - A Fioretti
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy
| | - C Gabbanini
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy
| | - G Modugno
- CNR-INO, Sede Secondaria di Pisa, 56124 Pisa, Italy. .,LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
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Tanzi L, Roccuzzo SM, Lucioni E, Famà F, Fioretti A, Gabbanini C, Modugno G, Recati A, Stringari S. Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Nature 2019; 574:382-385. [DOI: 10.1038/s41586-019-1568-6] [Citation(s) in RCA: 91] [Impact Index Per Article: 18.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2019] [Accepted: 08/29/2019] [Indexed: 11/09/2022]
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Tanzi L, Lucioni E, Famà F, Catani J, Fioretti A, Gabbanini C, Bisset RN, Santos L, Modugno G. Observation of a Dipolar Quantum Gas with Metastable Supersolid Properties. Phys Rev Lett 2019; 122:130405. [PMID: 31012602 DOI: 10.1103/physrevlett.122.130405] [Citation(s) in RCA: 61] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Indexed: 06/09/2023]
Abstract
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.
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Affiliation(s)
- L Tanzi
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - E Lucioni
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
| | - F Famà
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
| | - J Catani
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
- CNR-INO, Sede Secondaria Sesto Fiorentino, 50019 Sesto Fiorentino, Italy
| | - A Fioretti
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
| | - C Gabbanini
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
| | - R N Bisset
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - G Modugno
- CNR-INO, Sede Secondaria "Adriano Gozzini," via Moruzzi 1, 56124 Pisa, Italy
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Italy
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Cheiney P, Cabrera CR, Sanz J, Naylor B, Tanzi L, Tarruell L. Bright Soliton to Quantum Droplet Transition in a Mixture of Bose-Einstein Condensates. Phys Rev Lett 2018; 120:135301. [PMID: 29694210 DOI: 10.1103/physrevlett.120.135301] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- P Cheiney
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - C R Cabrera
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - J Sanz
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - B Naylor
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - L Tanzi
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - L Tarruell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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Cabrera CR, Tanzi L, Sanz J, Naylor B, Thomas P, Cheiney P, Tarruell L. Quantum liquid droplets in a mixture of Bose-Einstein condensates. Science 2017; 359:301-304. [DOI: 10.1126/science.aao5686] [Citation(s) in RCA: 328] [Impact Index Per Article: 46.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Accepted: 11/28/2017] [Indexed: 11/02/2022]
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Lucioni E, Tanzi L, D'Errico C, Moratti M, Inguscio M, Modugno G. Modeling the transport of interacting matter waves in a disordered system by a nonlinear diffusion equation. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:042922. [PMID: 23679504 DOI: 10.1103/physreve.87.042922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2013] [Indexed: 06/02/2023]
Abstract
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.
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Affiliation(s)
- E Lucioni
- LENS and Dipartimento di Fisica e Astronomia, Universitá di Firenze, and INO-CNR, 50019 Sesto Fiorentino, Italy
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Lucioni E, Deissler B, Tanzi L, Roati G, Zaccanti M, Modugno M, Larcher M, Dalfovo F, Inguscio M, Modugno G. Observation of subdiffusion in a disordered interacting system. Phys Rev Lett 2011; 106:230403. [PMID: 21770486 DOI: 10.1103/physrevlett.106.230403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2010] [Revised: 04/21/2011] [Indexed: 05/31/2023]
Abstract
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.
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Affiliation(s)
- E Lucioni
- LENS and Dipartimento di Fisica e Astronomia, Università di Firenze, and INO-CNR, Sesto Fiorentino, Italy.
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