- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Thermal behavior of Bose-Einstein condensates of polar molecules

J. Sánchez-Baena1,*, G. Pascual1, R. Bombín2, F. Mazzanti1, and J. Boronat1

  • *Contact author: juan.sanchez.baena@upc.edu
PDF

Phys. Rev. Research 7, 033080 – Published 21 July, 2025

DOI: https://doi.org/10.1103/9sbg-6qqw

Abstract

We use the finite-temperature extended Gross-Pitaevskii equation (TeGPE) to study a condensate of dipolar NaCs molecules under the conditions of the recent breakthrough experiment [Bigagli et al., Nature 631, 289 (2024)]. We report the condensate fraction of the system and its density profile after a time-of-flight expansion for the coldest experimental case, finding excellent agreement with the experimental measurements. We also report the peak density of the ground state and establish a comparison with the experimental estimates. Our results, derived from the TeGPE formalism, successfully describe the Bose-Einstein condensation of polar molecules at finite temperature.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. A. V. Gorshkov, P. Rabl, G. Pupillo, A. Micheli, P. Zoller, M. D. Lukin, and H. P. Büchler, Suppression of inelastic collisions between polar molecules with a repulsive shield, Phys. Rev. Lett. 101, 073201 (2008).
  2. J. Lin, G. Chen, M. Jin, Z. Shi, F. Deng, W. Zhang, G. Quéméner, T. Shi, S. Yi, and D. Wang, Microwave shielding of bosonic NaRb molecules, Phys. Rev. X 13, 031032 (2023).
  3. C. Karam, R. Vexiau, N. Bouloufa-Maafa, O. Dulieu, M. Lepers, M. M. Z. A. Borgloh, S. Ospelkaus, and L. Karpa, Two-photon optical shielding of collisions between ultracold polar molecules, Phys. Rev. Res. 5, 033074 (2023).
  4. N. Bigagli, C. Warner, W. Yuan, S. Zhang, I. Stevenson, T. Karman, and S. Will, Collisionally stable gas of bosonic dipolar ground-state molecules, Nat. Phys. 19, 1579 (2023).
  5. B. Mukherjee and J. M. Hutson, Controlling collisional loss and scattering lengths of ultracold dipolar molecules with static electric fields, Phys. Rev. Res. 6, 013145 (2024).
  6. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose–Einstein condensation of dipolar molecules, Nature 631, 289 (2024).
  7. 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).
  8. 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 530, 194 (2016).
  9. M. Schmitt, M. Wenzel, F. Böttcher, I. Ferrier-Barbut, and T. Pfau, Self-bound droplets of a dilute magnetic quantum liquid, Nature 539, 259 (2016).
  10. 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).
  11. 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).
  12. F. Böttcher, M. Wenzel, J.-N. Schmidt, M. Guo, T. Langen, I. Ferrier-Barbut, T. Pfau, R. Bombín, J. Sánchez-Baena, J. Boronat, and F. Mazzanti, Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation, Phys. Rev. Res. 1, 033088 (2019).
  13. 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).
  14. 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).
  15. 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).
  16. 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 574, 382 (2019).
  17. M. Guo, F. Böttcher, J. Hertkorn, J.-N. Schmidt, M. Wenzel, H. P. Büchler, T. Langen, and T. Pfau, The low-energy goldstone mode in a trapped dipolar supersolid, Nature 574, 386 (2019).
  18. 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).
  19. 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 596, 357 (2021).
  20. G. Biagioni, Nicolò Antolini, A. Alaña, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Dimensional crossover in the superfluid-supersolid quantum phase transition, Phys. Rev. X 12, 021019 (2022).
  21. M. Sohmen, C. Politi, L. Klaus, L. Chomaz, M. J. Mark, M. A. Norcia, and F. Ferlaino, Birth, life, and death of a dipolar supersolid, Phys. Rev. Lett. 126, 233401 (2021).
  22. 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).
  23. J. Sánchez-Baena, T. Pohl, and F. Maucher, Superfluid-supersolid phase transition of elongated dipolar Bose-Einstein condensates at finite temperatures, Phys. Rev. Res. 6, 023183 (2024).
  24. 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).
  25. M. Lu, N. Q. Burdick, S. H. Youn, and B. L. Lev, Strongly dipolar Bose-Einstein condensate of dysprosium, Phys. Rev. Lett. 107, 190401 (2011).
  26. K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, Bose-Einstein condensation of erbium, Phys. Rev. Lett. 108, 210401 (2012).
  27. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Thermodynamics of a trapped Bose-condensed gas, J. Low Temp. Phys. 109, 309 (1997).
  28. A. Boudjemâa, Quantum dilute droplets of dipolar bosons at finite temperature, Ann. Phys. 381, 68 (2017).
  29. A. Boudjemâa, Fluctuations and quantum self-bound droplets in a dipolar Bose-Bose mixture, Phys. Rev. A 98, 033612 (2018).
  30. E. Aybar and M. Ö. Oktel, Temperature-dependent density profiles of dipolar droplets, Phys. Rev. A 99, 013620 (2019).
  31. S. F. Öztürk, E. Aybar, and M. Ö. Oktel, Temperature dependence of the density and excitations of dipolar droplets, Phys. Rev. A 102, 033329 (2020).
  32. A. R. P. Lima and A. Pelster, Quantum fluctuations in dipolar Bose gases, Phys. Rev. A 84, 041604 (2011).
  33. A. R. P. Lima and A. Pelster, Beyond mean-field low-lying excitations of dipolar Bose gases, Phys. Rev. A 86, 063609 (2012).
  34. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999).
  35. T. Karman, N. Bigagli, W. Yuan, S. Zhang, I. Stevenson, and S. Will, Double microwave shielding, PRX Quantum 6, 020358 (2025).
  36. F. Deng, X. Hu, W.-J. Jin, S. Yi, and T. Shi, Two- and many-body physics of ultracold molecules dressed by dual microwave fields, arXiv:2501.05210.
  37. A. Boudjemâa, Nonequilibrium quench dynamics of Bose-Einstein condensates of microwave-shielded polar molecules, Phys. Rev. A 111, 063315 (2025).
  38. S. Yi and L. You, Trapped condensates of atoms with dipole interactions, Phys. Rev. A 63, 053607 (2001).

Outline

Information

Phys. Rev. Research 7, 033080– Published 21 July, 2025
  • Received 17 February 2025
  • Accepted 7 July 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation