Two-dimensional supersolidity in a dipolar quantum gas – Nature.com

  • 1.

    Gross, E. P. Unified theory of interacting bosons. Phys. Rev. 106, 161–162 (1957).

    ADS  CAS  MATH  Google Scholar 

  • 2.

    Gross, E. P. Classical theory of boson wave fields. Ann. Phys. 4, 57–74 (1958).

    ADS  MathSciNet  MATH  Google Scholar 

  • 3.

    Andreev, A. F. & Lifshitz, I. M. Quantum theory of defects in crystals. Sov. Phys. JETP 29, 1107–1114 (1969).

    ADS  Google Scholar 

  • 4.

    Chester, G. V. Speculations on Bose–Einstein condensation and quantum crystals. Phys. Rev. A 2, 256–258 (1970).

    ADS  Google Scholar 

  • 5.

    Leggett, A. J. Can a solid be “superfluid”? Phys. Rev. Lett. 25, 1543–1546 (1970).

    ADS  CAS  Google Scholar 

  • 6.

    Chan, M. H.-W., Hallock, R. & Reatto, L. Overview on solid 4He and the issue of supersolidity. J. Low Temp. Phys. 172, 317–363 (2013).

    ADS  CAS  Google Scholar 

  • 7.

    Lu, Z.-K., Li, Y., Petrov, D. S. & Shlyapnikov, G. V. Stable dilute supersolid of two-dimensional dipolar bosons. Phys. Rev. Lett. 115, 075303 (2015).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 8.

    Baillie, D. & Blakie, P. B. Droplet crystal ground states of a dipolar Bose gas. Phys. Rev. Lett. 121, 195301 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 9.

    Roccuzzo, S. M. & Ancilotto, F. Supersolid behavior of a dipolar Bose–Einstein condensate confined in a tube. Phys. Rev. A 99, 041601 (2019).

    ADS  CAS  Google Scholar 

  • 10.

    Boninsegni, M. & Prokof’ev, N. V. Colloquium: Super-solids: what and where are they? Rev. Mod. Phys. 84, 759–776 (2012).

    ADS  CAS  Google Scholar 

  • 11.

    Tanzi, L. et al. Observation of a dipolar quantum gas with metastable supersolid properties. Phys. Rev. Lett. 122, 130405 (2019).

    ADS  CAS  PubMed  Google Scholar 

  • 12.

    Böttcher, F. et al. Transient supersolid properties in an array of dipolar quantum droplets. Phys. Rev. X 9, 011051 (2019).

    Google Scholar 

  • 13.

    Chomaz, L. et al. Long-lived and transient supersolid behaviors in dipolar quantum gases. Phys. Rev. X 9, 021012 (2019).

    CAS  Google Scholar 

  • 14.

    Guo, M. et al. The low-energy Goldstone mode in a trapped dipolar super-solid. Nature 574, 386–389 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 15.

    Natale, G. et al. Excitation spectrum of a trapped dipolar supersolid and its experimental evidence. Phys. Rev. Lett. 123, 050402 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 16.

    Tanzi, L. et al. Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Nature 574, 382–385 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 17.

    Birkl, G., Kassner, S. & Walther, H. Multiple-shell structures of laser-cooled 24Mg+ ions in a quadrupole storage ring. Nature 357, 310–313 (1992).

    ADS  CAS  Google Scholar 

  • 18.

    Raizen, M. G., Gilligan, J. M., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Ionic crystals in a linear Paul trap. Phys. Rev. A 45, 6493–6501 (1992).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 19.

    Fishman, S., De Chiara, G., Calarco, T. & Morigi, G. Structural phase transitions in low-dimensional ion crystals. Phys. Rev. B 77, 064111 (2008).

    ADS  Google Scholar 

  • 20.

    Shimshoni, E., Morigi, G. & Fishman, S. Quantum zigzag transition in ion chains. Phys. Rev. Lett. 106, 010401 (2011).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 21.

    Hew, W. K. et al. Incipient formation of an electron lattice in a weakly confined quantum wire. Phys. Rev. Lett. 102, 056804 (2009).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 22.

    Mehta, A. C., Umrigar, C. J., Meyer, J. S. & Baranger, H. U. Zigzag phase transition in quantum wires. Phys. Rev. Lett. 110, 246802 (2013).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 23.

    Astrakharchik, G. E., Morigi, G., De Chiara, G. & Boronat, J. Ground state of low-dimensional dipolar gases: linear and zigzag chains. Phys. Rev. A 78, 063622 (2008).

    ADS  Google Scholar 

  • 24.

    Ruhman, J., Dalla Torre, E. G., Huber, S. D. & Altman, E. Nonlocal order in elongated dipolar gases. Phys. Rev. B 85, 125121 (2012).

    ADS  Google Scholar 

  • 25.

    Santos, L., Shlyapnikov, G. V. & Lewenstein, M. Roton-maxon spectrum and stability of trapped dipolar Bose–Einstein condensates. Phys. Rev. Lett. 90, 250403 (2003).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 26.

    Ronen, S., Bortolotti, D. C. E. & Bohn, J. L. Radial and angular rotons in trapped dipolar gases. Phys. Rev. Lett. 98, 030406 (2007).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 27.

    Wilson, R. M., Ronen, S., Bohn, J. L. & Pu, H. Manifestations of the roton mode in dipolar Bose–Einstein condensates. Phys. Rev. Lett. 100, 245302 (2008).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 28.

    Bisset, R. N., Baillie, D. & Blakie, P. B. Roton excitations in a trapped dipolar Bose–Einstein condensate. Phys. Rev. A 88, 043606 (2013).

    ADS  Google Scholar 

  • 29.

    Gallemí, A., Roccuzzo, S. M., Stringari, S. & Recati, A. Quantized vortices in dipolar supersolid Bose–Einstein-condensed gases. Phys. Rev. A 102, 023322 (2020).

    ADS  Google Scholar 

  • 30.

    Roccuzzo, S. M., Gallemí, A., Recati, A. & Stringari, S. Rotating a supersolid dipolar gas. Phys. Rev. Lett. 124, 045702 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 31.

    Ancilotto, F., Barranco, M., Pi, M. & Reatto, L. Vortex properties in the extended supersolid phase of dipolar Bose–Einstein condensates. Phys. Rev. A 103, 033314 (2021).

    ADS  CAS  Google Scholar 

  • 32.

    Zhang, Y.-C., Maucher, F. & Pohl, T. Supersolidity around a critical point in dipolar Bose–Einstein condensates. Phys. Rev. Lett. 123, 015301 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 33.

    Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

    ADS  CAS  PubMed  Google Scholar 

  • 34.

    Léonard, J., Morales, A., Zupancic, P., Esslinger, T. & Donner, T. Supersolid formation in a quantum gas breaking a continuous translational symmetry. Nature 543, 87–90 (2017).

    ADS  PubMed  Google Scholar 

  • 35.

    Kadau, H. et al. Observing the Rosensweig instability of a quantum ferrofluid. Nature 530, 194–197 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 36.

    Ferrier-Barbut, I., Kadau, H., Schmitt, M., Wenzel, M. & Pfau, T. Observation of quantum droplets in a strongly dipolar Bose gas. Phys. Rev. Lett. 116, 215301 (2016).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 37.

    Chomaz, L. et al. Quantum-fluctuation-driven crossover from a dilute Bose–Einstein condensate to a macrodroplet in a dipolar quantum fluid. Phys. Rev. X 6, 041039 (2016).

    Google Scholar 

  • 38.

    Wächtler, F. & Santos, L. Quantum filaments in dipolar Bose–Einstein condensates. Phys. Rev. A 93, 061603 (2016).

    ADS  Google Scholar 

  • 39.

    Bisset, R. N., Wilson, R. M., Baillie, D. & Blakie, P. B. Ground-state phase diagram of a dipolar condensate with quantum fluctuations. Phys. Rev. A 94, 033619 (2016).

    ADS  Google Scholar 

  • 40.

    Lavoine, L. & Bourdel, T. Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures. Phys. Rev. A 103, 033312 (2021).

    ADS  CAS  Google Scholar 

  • 41.

    Sohmen, M. et al. Birth, life, and death of a dipolar supersolid. Phys. Rev. Lett. 126, 233401 (2021).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 42.

    Hadzibabic, Z., Stock, S., Battelier, B., Bretin, V. & Dalibard, J. Interference of an array of independent Bose–Einstein condensates. Phys. Rev. Lett. 93, 180403 (2004).

    ADS  PubMed  PubMed Central  Google Scholar 

  • 43.

    Schmidt, J.-N. et al. Roton excitations in an oblate dipolar quantum gas. Phys. Rev. Lett. 126, 193002 (2021).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 44.

    Pyka, K. et al. Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals. Nat. Commun. 4, 2291 (2013).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 45.

    Ulm, S. et al. Observation of the Kibble–Zurek scaling law for defect formation in ion crystals. Nat. Commun. 4, 2290 (2013).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 46.

    Trautmann, A. et al. Dipolar quantum mixtures of erbium and dysprosium atoms. Phys. Rev. Lett. 121, 213601 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  • 47.

    Chomaz, L. et al. Observation of roton mode population in a dipolar quantum gas. Nat. Phys. 14, 442–446 (2018).

    PubMed  PubMed Central  Google Scholar 

  • 48.

    Lima, A. R. P. & Pelster, A. Quantum fluctuations in dipolar Bose gases. Phys. Rev. A 84, 041604 (2011).

    ADS  Google Scholar 

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