- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Dynamical signatures of superfluidity and shear rigidity in different phases of a dipolar Bose-Einstein condensate

Soumyadeep Halder1,*, Hari Sadhan Ghosh2, Axel Pelster3, and B. Prasanna Venkatesh1,†

  • *Contact author: soumya.hhs@gmail.com
  • †Contact author: prasanna.b@iitgn.ac.in
PDF

Phys. Rev. A 114, 013314 – Published 17 July, 2026

DOI: https://doi.org/10.1103/b8n6-kvb1

Abstract

We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors-mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation, i.e., we find an analog of the usual elastic-to-plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wave function with the ground state, as well as the droplet width and periodicity of the supersolid density of the condensate, which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (106)

  1. C. Ticknor, R. M. Wilson, and J. L. Bohn, Anisotropic superfluidity in a dipolar Bose gas, Phys. Rev. Lett. 106, 065301 (2011).
  2. M. Wenzel, F. Böttcher, J.-N. Schmidt, M. Eisenmann, T. Langen, T. Pfau, and I. Ferrier-Barbut, Anisotropic superfluid behavior of a dipolar Bose-Einstein condensate, Phys. Rev. Lett. 121, 030401 (2018).
  3. B. Seo, M. Huang, Z. Chen, M. K. Parit, Y. He, P. Chen, and G.-B. Jo, Mirror symmetry breaking of superradiance in a dipolar Bose-Einstein condensate, Phys. Rev. Res. 6, L042028 (2024).
  4. H. Kadau, M. Schmitt, M. Wenzel, C. Wink, T. Maier, I. Ferrier-Barbut, and T. Pfau, Observing the Rosensweig instability of a quantum ferrofluid, Nature (London) 530, 194 (2016).
  5. L. Santos, G. V. Shlyapnikov, and M. Lewenstein, Roton-maxon spectrum and stability of trapped dipolar Bose-Einstein condensates, Phys. Rev. Lett. 90, 250403 (2003).
  6. U. R. Fischer, Stability of quasi-two-dimensional Bose-Einstein condensates with dominant dipole-dipole interactions, Phys. Rev. A 73, 031602(R) (2006).
  7. L. Chomaz, R. M. W. van Bijnen, D. Petter, G. Faraoni, S. Baier, J. H. Becher, M. J. Mark, F. Wächtler, L. Santos, and F. Ferlaino, Observation of roton mode population in a dipolar quantum gas, Nat. Phys. 14, 442 (2018).
  8. D. Petter, G. Natale, R. M. W. Van Bijnen, A. Patscheider, M. J. Mark, L. Chomaz, and F. Ferlaino, Probing the roton excitation spectrum of a stable dipolar Bose gas, Phys. Rev. Lett. 122, 183401 (2019).
  9. J.-N. Schmidt, J. Hertkorn, M. Guo, F. Böttcher, M. Schmidt, K. S. H. Ng, S. D. Graham, T. Langen, M. Zwierlein, and T. Pfau, Roton excitations in an oblate dipolar quantum gas, Phys. Rev. Lett. 126, 193002 (2021).
  10. L. Klaus, T. Bland, E. Poli, C. Politi, G. Lamporesi, E. Casotti, R. N. Bisset, M. J. Mark, and F. Ferlaino, Observation of vortices and vortex stripes in a dipolar condensate, Nat. Phys. 18, 1453 (2022).
  11. F. Wächtler and L. Santos, Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates, Phys. Rev. A 94, 043618 (2016).
  12. R. N. Bisset, R. M. Wilson, D. Baillie, and P. B. Blakie, Ground-state phase diagram of a dipolar condensate with quantum fluctuations, Phys. Rev. A 94, 033619 (2016).
  13. F. Cinti and M. Boninsegni, Classical and quantum filaments in the ground state of trapped dipolar Bose gases, Phys. Rev. A 96, 013627 (2017).
  14. D. Baillie and P. B. Blakie, Droplet crystal ground states of a dipolar Bose gas, Phys. Rev. Lett. 121, 195301 (2018).
  15. C. Mishra, L. Santos, and R. Nath, Self-bound doubly dipolar Bose-Einstein condensates, Phys. Rev. Lett. 124, 073402 (2020).
  16. Y.-C. Zhang, T. Pohl, and F. Maucher, Phases of supersolids in confined dipolar Bose-Einstein condensates, Phys. Rev. A 104, 013310 (2021).
  17. Y.-C. Zhang, T. Pohl, and F. Maucher, Metastable patterns in one- and two-component dipolar Bose-Einstein condensates, Phys. Rev. Res. 6, 023023 (2024).
  18. L.-J. He, J. Sánchez-Baena, F. Maucher, and Y.-C. Zhang, Accessing elusive two-dimensional phases of dipolar Bose-Einstein condensates by finite temperature, Phys. Rev. Res. 7, 023019 (2025).
  19. J. Sánchez-Baena, Tilted dipolar bosons in the quasi-two-dimensional regime: From liquid stripes to droplets, Phys. Rev. A 112, 023310 (2025).
  20. I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, and T. Pfau, Observation of quantum droplets in a strongly dipolar Bose gas, Phys. Rev. Lett. 116, 215301 (2016).
  21. L. Chomaz, S. Baier, D. Petter, M. J. Mark, F. Wächtler, L. Santos, and F. Ferlaino, Quantum-fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macrodroplet in a dipolar quantum fluid, Phys. Rev. X 6, 041039 (2016).
  22. F. Böttcher, J.-N. Schmidt, M. Wenzel, J. Hertkorn, M. Guo, T. Langen, and T. Pfau, Transient supersolid properties in an array of dipolar quantum droplets, Phys. Rev. X 9, 011051 (2019).
  23. L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Ferlaino, Long-lived and transient supersolid behaviors in dipolar quantum gases, Phys. Rev. X 9, 021012 (2019).
  24. L. Tanzi, E. Lucioni, F. Famà, J. Catani, A. Fioretti, C. Gabbanini, R. N. Bisset, L. Santos, and G. Modugno, Observation of a dipolar quantum gas with metastable supersolid properties, Phys. Rev. Lett. 122, 130405 (2019).
  25. D. S. Petrov, Quantum mechanical stabilization of a collapsing Bose-Bose mixture, Phys. Rev. Lett. 115, 155302 (2015).
  26. A. J. Leggett, Can a solid be “superfluid”? Phys. Rev. Lett. 25, 1543 (1970).
  27. H. Watanabe and T. Brauner, Spontaneous breaking of continuous translational invariance, Phys. Rev. D 85, 085010 (2012).
  28. U. R. Fischer and B. Xiong, Identifying strongly correlated supersolid states on the optical lattice by quench-induced π-states, Europhys. Lett. 99, 66003 (2012).
  29. J. Léonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Supersolid formation in a quantum gas breaking a continuous translational symmetry, Nature (London) 543, 87 (2017).
  30. L. Tanzi, S. M. Roccuzzo, E. Lucioni, F. Famà, A. Fioretti, C. Gabbanini, G. Modugno, A. Recati, and S. Stringari, Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas, Nature (London) 574, 382 (2019).
  31. M. A. Norcia, C. Politi, L. Klaus, E. Poli, M. Sohmen, M. J. Mark, R. N. Bisset, L. Santos, and F. Ferlaino, Two-dimensional supersolidity in a dipolar quantum gas, Nature (London) 596, 357 (2021).
  32. L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Dipolar physics: A review of experiments with magnetic quantum gases, Rep. Prog. Phys. 86, 026401 (2023).
  33. T. Bland, E. Poli, C. Politi, L. Klaus, M. A. Norcia, F. Ferlaino, L. Santos, and R. N. Bisset, Two-dimensional supersolid formation in dipolar condensates, Phys. Rev. Lett. 128, 195302 (2022).
  34. B. T. E. Ripley, D. Baillie, and P. B. Blakie, Two-dimensional supersolidity in a planar dipolar Bose gas, Phys. Rev. A 108, 053321 (2023).
  35. Y. He, H. Zhen, M. K. Parit, M. Huang, N. Defenu, J. Boronat, J. Sánchez-Baena, and G.-B. Jo, Observation of a supersolid stripe state in two-dimensional dipolar gases, arXiv:2512.13280.
  36. A. Trautmann, P. Ilzhöfer, G. Durastante, C. Politi, M. Sohmen, M. J. Mark, and F. Ferlaino, Dipolar quantum mixtures of erbium and dysprosium atoms, Phys. Rev. Lett. 121, 213601 (2018).
  37. R. N. Bisset, L. A. Peña Ardila, and L. Santos, Quantum droplets of dipolar mixtures, Phys. Rev. Lett. 126, 025301 (2021).
  38. J. C. Smith, P. B. Blakie, and D. Baillie, Approximate theories for binary magnetic quantum droplets, Phys. Rev. A 104, 053316 (2021).
  39. J. C. Smith, D. Baillie, and P. B. Blakie, Quantum droplet states of a binary magnetic gas, Phys. Rev. Lett. 126, 025302 (2021).
  40. C. Politi, A. Trautmann, P. Ilzhöfer, G. Durastante, M. J. Mark, M. Modugno, and F. Ferlaino, Interspecies interactions in an ultracold dipolar mixture, Phys. Rev. A 105, 023304 (2022).
  41. S. Halder, S. Das, and S. Majumder, Two-dimensional miscible-immiscible supersolid and droplet crystal state in a homonuclear dipolar bosonic mixture, Phys. Rev. A 107, 063303 (2023).
  42. D. Scheiermann, L. A. Peña Ardila, T. Bland, R. N. Bisset, and L. Santos, Catalyzation of supersolidity in binary dipolar condensates, Phys. Rev. A 107, L021302 (2023).
  43. S. Halder, S. Das, and S. Majumder, Induced supersolidity in a Dy-Er mixture, Phys. Rev. A 109, 063321 (2024).
  44. W. Kirkby, A.-C. Lee, D. Baillie, T. Bland, F. Ferlaino, P. B. Blakie, and R. N. Bisset, Excitations of a binary dipolar supersolid, Phys. Rev. Lett. 133, 103401 (2024).
  45. L.-J. He, B. Liu, and Y.-C. Zhang, Quantum droplets in dipolar condensate mixtures with arbitrary dipole orientations, Phys. Rev. A 110, 013308 (2024).
  46. D. Scheiermann, A. Gallemí, and L. Santos, Excitation spectrum of a double supersolid in a trapped dipolar Bose mixture, Phys. Rev. A 111, 033310 (2025).
  47. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose–Einstein condensation of dipolar molecules, Nature (London) 631, 289 (2024).
  48. M. Ciardi, K. R. Pedersen, T. Langen, and T. Pohl, Self-bound superfluid membranes and monolayer crystals of ultracold polar molecules, Phys. Rev. Lett. 135, 153401 (2025).
  49. T. Langen, J. Boronat, J. Sánchez-Baena, R. Bombín, T. Karman, and F. Mazzanti, Dipolar droplets of strongly interacting molecules, Phys. Rev. Lett. 134, 053001 (2025).
  50. T. Langen, G. Valtolina, D. Wang, and J. Ye, Quantum state manipulation and cooling of ultracold molecules, Nat. Phys. 20, 702 (2024).
  51. I. Stevenson, S. Singh, A. Elkamshishy, N. Bigagli, W. Yuan, S. Zhang, C. H. Greene, and S. Will, Three-body recombination of ultracold microwave-shielded polar molecules, Phys. Rev. Lett. 133, 263402 (2024).
  52. S. Zhang, W. Yuan, N. Bigagli, H. Kwak, T. Karman, I. Stevenson, and S. Will, Observation of self-bound droplets of ultracold dipolar molecules, Nature (London) 651, 601 (2026).
  53. W.-J. Jin, F. Deng, S. Yi, and T. Shi, Bose-Einstein condensates of microwave-shielded polar molecules, Phys. Rev. Lett. 134, 233003 (2025).
  54. J. C. A. Matos, P. Giannakeas, M. Ciardi, T. Pohl, and J. M. Rost, Transitional supersolidity in ion doped helium droplets, Phys. Rev. Lett. 134, 186001 (2025).
  55. L. Tanzi, J. G. Maloberti, G. Biagioni, A. Fioretti, C. Gabbanini, and G. Modugno, Evidence of superfluidity in a dipolar supersolid from nonclassical rotational inertia, Science 371, 1162 (2021).
  56. A. Gallemí and L. Santos, Superfluid properties of a honeycomb dipolar supersolid, Phys. Rev. A 106, 063301 (2022).
  57. G. Chauveau, C. Maury, F. Rabec, C. Heintze, G. Brochier, S. Nascimbene, J. Dalibard, J. Beugnon, S. M. Roccuzzo, and S. Stringari, Superfluid fraction in an interacting spatially modulated Bose-Einstein condensate, Phys. Rev. Lett. 130, 226003 (2023).
  58. K. Mukherjee, M. N. Tengstrand, T. A. Cardinale, and S. M. Reimann, Supersolid stacks in antidipolar Bose-Einstein condensates, Phys. Rev. A 108, 023302 (2023).
  59. P. Ilzhöfer, M. Sohmen, G. Durastante, C. Politi, A. Trautmann, G. Natale, G. Morpurgo, T. Giamarchi, L. Chomaz, M. J. Mark, and F. Ferlaino, Phase coherence in out-of-equilibrium supersolid states of ultracold dipolar atoms, Nat. Phys. 17, 356 (2021).
  60. G. Biagioni, N. Antolini, B. Donelli, L. Pezzè, A. Smerzi, M. Fattori, A. Fioretti, C. Gabbanini, M. Inguscio, L. Tanzi, and G. Modugno, Measurement of the superfluid fraction of a supersolid by Josephson effect, Nature (London) 629, 773 (2024).
  61. I. Ferrier-Barbut, M. Wenzel, F. Böttcher, T. Langen, M. Isoard, S. Stringari, and T. Pfau, Scissors mode of dipolar quantum droplets of dysprosium atoms, Phys. Rev. Lett. 120, 160402 (2018).
  62. S. M. Roccuzzo, A. Recati, and S. Stringari, Moment of inertia and dynamical rotational response of a supersolid dipolar gas, Phys. Rev. A 105, 023316 (2022).
  63. H. Zhen, Y. He, S. Saha, M. K. Parit, M. Huang, N. Defenu, and G.-B. Jo, Breaking of scale invariance in a strongly dipolar 2D Bose gas, arXiv:2510.13730.
  64. R. Bombín, F. Mazzanti, and J. Boronat, Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipolar stripes, Phys. Rev. A 100, 063614 (2019).
  65. Y. He, Z. Chen, H. Zhen, M. Huang, M. K. Parit, and G.-B. Jo, Exploring the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional dipolar Bose gas, Sci. Adv. 11, eadr2715 (2025).
  66. A. Gallemí, S. M. Roccuzzo, S. Stringari, and A. Recati, Quantized vortices in dipolar supersolid Bose-Einstein-condensed gases, Phys. Rev. A 102, 023322 (2020).
  67. M. Šindik, A. Recati, S. M. Roccuzzo, L. Santos, and S. Stringari, Creation and robustness of quantized vortices in a dipolar supersolid when crossing the superfluid-to-supersolid transition, Phys. Rev. A 106, L061303 (2022).
  68. E. Casotti, E. Poli, L. Klaus, A. Litvinov, C. Ulm, C. Politi, M. J. Mark, T. Bland, and F. Ferlaino, Observation of vortices in a dipolar supersolid, Nature (London) 635, 327 (2024).
  69. S. Halder, H. S. Ghosh, A. Saboo, A. M. Martin, and S. Majumder, Roadmap to vortex nucleation below the critical rotation frequency in a dipolar Bose-Einstein condensate, Phys. Rev. A 111, 023301 (2025).
  70. S. Das and V. W. Scarola, Unveiling supersolid order via vortex trajectory correlations, Phys. Rev. Lett. 134, 163401 (2025).
  71. M. N. Tengstrand, D. Boholm, R. Sachdeva, J. Bengtsson, and S. M. Reimann, Persistent currents in toroidal dipolar supersolids, Phys. Rev. A 103, 013313 (2021).
  72. H. S. Ghosh, S. Halder, S. Das, and S. Majumder, Induced supersolidity and hypersonic flow of a dipolar Bose-Einstein condensate in a rotating bubble trap, Phys. Rev. A 110, 033322 (2024).
  73. K. Mukherjee, T. A. Cardinale, and S. M. Reimann, Selective rotation and attractive persistent currents in antidipolar ring supersolids, Phys. Rev. A 111, 033304 (2025).
  74. G. Natale, R. M. W. van Bijnen, A. Patscheider, D. Petter, M. J. Mark, L. Chomaz, and F. Ferlaino, Excitation spectrum of a trapped dipolar supersolid and its experimental evidence, Phys. Rev. Lett. 123, 050402 (2019).
  75. D. Petter, A. Patscheider, G. Natale, M. J. Mark, M. A. Baranov, R. van Bijnen, S. M. Roccuzzo, A. Recati, B. Blakie, D. Baillie, L. Chomaz, and F. Ferlaino, Bragg scattering of an ultracold dipolar gas across the phase transition from Bose-Einstein condensate to supersolid in the free-particle regime, Phys. Rev. A 104, L011302 (2021).
  76. C. Josserand, Y. Pomeau, and S. Rica, Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid, Phys. Rev. Lett. 98, 195301 (2007).
  77. A. B. Kuklov, N. V. Prokof'ev, and B. V. Svistunov, How solid is supersolid?, Physics 4, 109 (2011).
  78. P. B. Blakie, L. Chomaz, D. Baillie, and F. Ferlaino, Compressibility and speeds of sound across the superfluid-to-supersolid phase transition of an elongated dipolar gas, Phys. Rev. Res. 5, 033161 (2023).
  79. L. M. Platt, D. Baillie, and P. B. Blakie, Sound waves and fluctuations in one-dimensional supersolids, Phys. Rev. A 110, 023320 (2024).
  80. E. Poli, D. Baillie, F. Ferlaino, and P. B. Blakie, Excitations of a two-dimensional supersolid, Phys. Rev. A 110, 053301 (2024).
  81. M. Šindik, T. Zawiślak, A. Recati, and S. Stringari, Sound, superfluidity, and layer compressibility in a ring dipolar supersolid, Phys. Rev. Lett. 132, 146001 (2024).
  82. Q. Zhao, X. Zhao, and J. Qin, From elastic to inelastic deformation of a dipolar supersolid, Phys. Rev. A 112, 043311 (2025).
  83. G. A. Bougas, T. Bland, H. R. Sadeghpour, and S. I. Mistakidis, Signatures of rigidity and second sound in dipolar supersolids, Phys. Rev. A 113, L041305 (2026).
  84. P. Senarath Yapa and T. Bland, Anomalous dispersion of shear waves in dipolar supersolids, Phys. Rev. A 112, L021303 (2025).
  85. D. Bohle, A. Richter, W. Steffen, A. E. L. Dieperink, N. Lo Iudice, F. Palumbo, and O. Scholten, New magnetic dipole excitation mode studied in the heavy deformed nucleus Gd156 by inelastic electron scattering, Phys. Lett. B 137, 27 (1984).
  86. O. M. Maragò, S. A. Hopkins, J. Arlt, E. Hodby, G. Hechenblaikner, and C. J. Foot, Observation of the scissors mode and evidence for superfluidity of a trapped Bose-Einstein condensed gas, Phys. Rev. Lett. 84, 2056 (2000).
  87. M. J. Wright, S. Riedl, A. Altmeyer, C. Kohstall, E. R. S. Guajardo, J. H. Denschlag, and R. Grimm, Finite-temperature collective dynamics of a Fermi gas in the BEC-BCS crossover, Phys. Rev. Lett. 99, 150403 (2007).
  88. G. Bismut, B. Pasquiou, E. Maréchal, P. Pedri, L. Vernac, O. Gorceix, and B. Laburthe-Tolra, Collective excitations of a dipolar Bose-Einstein condensate, Phys. Rev. Lett. 105, 040404 (2010).
  89. R. M. W. Van Bijnen, N. G. Parker, S. J. J. M. F. Kokkelmans, A. M. Martin, and D. H. J. O'Dell, Collective excitation frequencies and stationary states of trapped dipolar Bose-Einstein condensates in the Thomas-Fermi regime, Phys. Rev. A 82, 033612 (2010).
  90. C. Qu, C.-H. Li, Y. P. Chen, and S. Stringari, Scissors modes of a Bose-Einstein condensate in a synthetic magnetic field, Phys. Rev. A 108, 053316 (2023).
  91. D. Guéry-Odelin and S. Stringari, Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas, Phys. Rev. Lett. 83, 4452 (1999).
  92. S. M. Roccuzzo, A. Gallemí, A. Recati, and S. Stringari, Rotating a supersolid dipolar gas, Phys. Rev. Lett. 124, 045702 (2020).
  93. L. E. Young-S. and S. K. Adhikari, Dipole-mode and scissors-mode oscillations of a dipolar supersolid, Phys. Rev. A 107, 053318 (2023).
  94. M. A. Norcia, E. Poli, C. Politi, L. Klaus, T. Bland, M. J. Mark, L. Santos, R. N. Bisset, and F. Ferlaino, Can angular oscillations probe superfluidity in dipolar supersolids?, Phys. Rev. Lett. 129, 040403 (2022).
  95. F. Wächtler and L. Santos, Quantum filaments in dipolar Bose-Einstein condensates, Phys. Rev. A 93, 061603(R) (2016).
  96. S. Halder, K. Mukherjee, S. I. Mistakidis, S. Das, P. G. Kevrekidis, P. K. Panigrahi, S. Majumder, and H. R. Sadeghpour, Control of Dy164 Bose-Einstein condensate phases and dynamics with dipolar anisotropy, Phys. Rev. Res. 4, 043124 (2022).
  97. A. R. P. Lima and A. Pelster, Quantum fluctuations in dipolar Bose gases, Phys. Rev. A 84, 041604(R) (2011).
  98. A. R. P. Lima and A. Pelster, Beyond mean-field low-lying excitations of dipolar Bose gases, Phys. Rev. A 86, 063609 (2012).
  99. R. Schützhold, M. Uhlmann, Y. Xu, and U. R. Fischer, Mean-field expansion in Bose–Einstein condensates with finite-range interactions, Int. J. Mod. Phys. B 20, 3555 (2006).
  100. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation and Superfluidity (Oxford University Press, Oxford, 2016).
  101. A. J. Leggett, On the superfluid fraction of an arbitrary many-body system at T = 0, J. Stat. Phys. 93, 927 (1998).
  102. E. Poli, A. Litvinov, E. Casotti, C. Ulm, L. Klaus, M. J. Mark, G. Lamporesi, T. Bland, and F. Ferlaino, Synchronization in rotating supersolids, Nat. Phys. 21, 1820 (2025).
  103. J. Sánchez-Baena, C. Politi, F. Maucher, F. Ferlaino, and T. Pohl, Heating a dipolar quantum fluid into a solid, Nat. Commun. 14, 1868 (2023).
  104. R. Bombín, J. Boronat, F. Mazzanti, and J. Sánchez-Baena, Creating and melting a supersolid by heating a quantum dipolar system, Phys. Rev. Lett. 135, 173401 (2025).
  105. J. M. Brown and T. G. Walker, Perspective: Practical atom-based quantum sensors, Phys. Rev. A 112, 040102 (2025).
  106. B. Bao, Y. Hua, R. Wang, and D. Li, Quantum-based magnetic field sensors for biosensing, Adv. Quantum Technol. 6, 2200146 (2023).

Outline

Information

Phys. Rev. A 114, 013314– Published 17 July, 2026
  • Received 13 January 2026
  • Revised 31 May 2026
  • Accepted 1 July 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation