- 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

Trapping-potential dependence of the unitary Fermi gas at the BCS-BEC crossover

Silas R. Beane1, Adèle Le Borgne2, Domenico Orlando2,3, and Susanne Reffert2

PDF

Phys. Rev. A 114, 023304 – Published 4 August, 2026

DOI: https://doi.org/10.1103/vmkb-l2qv

Abstract

Cold-atom experiments that measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical scale in the superfluid effective-field theory (EFT) description of the unitary Fermi gas which, among other things, describes the acoustic branch of excitations in the far infrared well below the scale of the superfluid gap. In this EFT there is a clear hierarchy of scales, and corrections to the homogeneous system due to the trapping potential may be organized into three regions with distinct power counting that relies on both the EFT derivative expansion and the Wentzel–Kramers–Brillouin approximation, which is an expansion in gradients of the trapping potential. The energy spectrum of the superfluid system is obtained in each of the regions by explicit computation of the phonon-field fluctuations and by the modifications to the dynamic structure factor due to the corresponding density fluctuations. This work presents a systematic and quantitative method for treating the presence of a trapping potential, which is essential for interpreting experimental realizations of the unitary Fermi gas. It provides clear predictions for how the trapping potential modifies the dispersion relation’s curvature, a key factor in characterizing the relaxation mechanisms of the superfluid. The most significant deviations from linear dispersion due to the trapping potential are found in the far-infrared region of the superfluid EFT.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. The BCS-BEC Crossover and the Unitary Fermi Gas, Lecture Notes in Physics, edited by W. Zwerger (Springer, Berlin, Heidelberg, 2012), Vol. 836.
  2. J. Carlson, S. Gandolfi, K. E. Schmidt, and S. Zhang, Auxiliary-field quantum Monte Carlo method for strongly paired fermions, Phys. Rev. A 84, 061602 (2011).
  3. M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).
  4. G. Zürn, T. Lompe, A. N. Wenz, S. Jochim, P. S. Julienne, and J. M. Hutson, Precise characterization of Feshbach resonances using trap-sideband-resolved rf spectroscopy of weakly bound molecules, Phys. Rev. Lett. 110, 135301 (2013).
  5. M. Greiter, F. Wilczek, and E. Witten, Hydrodynamic relations in superconductivity, Mod. Phys. Lett. B 3, 903 (1989).
  6. D. T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Ann. Phys. (NY) 321, 197 (2006).
  7. J. L. Mañes and M. A. Valle, Effective theory for the Goldstone field in the BCS–BEC crossover at T=0, Ann. Phys. (NY) 324, 1136 (2009).
  8. Y. Nishida and D. T. Son, Nonrelativistic conformal field theories, Phys. Rev. D 76, 086004 (2007).
  9. S. Hellerman, D. Orlando, S. Reffert, and M. Watanabe, On the CFT operator spectrum at large global charge, J. High Energy Phys. 12 (2015) 071.
  10. L. A. Gaumé, D. Orlando, and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rep. 933, 1 (2021).
  11. S. Favrod, D. Orlando, and S. Reffert, The large-charge expansion for Schrödinger systems, J. High Energy Phys. 12 (2018) 052.
  12. S. M. Kravec and S. Pal, Nonrelativistic conformal field theories in the large charge sector, J. High Energy Phys. 02 (2019) 008.
  13. D. Orlando, V. Pellizzani, and S. Reffert, Near-Schrödinger dynamics at large charge, Phys. Rev. D 103, 105018 (2021).
  14. V. Pellizzani, Operator spectrum of nonrelativistic CFTs at large charge, Phys. Rev. D 105, 125018 (2022).
  15. S. Hellerman, D. Krichevskiy, D. Orlando, V. Pellizzani, S. Reffert, and I. Swanson, The unitary Fermi gas at large charge and large N, J. High Energy Phys. 05 (2024) 323.
  16. S. Hellerman and I. Swanson, Droplet-edge operators in nonrelativistic conformal field theories, arXiv:2010.07967.
  17. S. R. Beane, D. Orlando, and S. Reffert, Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory, Phys. Rev. D 110, 025011 (2024).
  18. S. R. Beane, D. Orlando, and S. Reffert, Unnuclear matter at large-charge, Phys. Rev. D 112, 014028 (2025).
  19. Y. Nishida and D. T. Son, An epsilon expansion for Fermi gas at infinite scattering length, Phys. Rev. Lett. 97, 050403 (2006).
  20. Y. Castin, Open questions for strongly interacting Fermi gases with zero-range interactions, C. R. Phys. 26, 393 (2025).
  21. H. Kurkjian, Y. Castin, and A. Sinatra, Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas, Ann. Phys. (Berlin, Ger.) 529, 1600352 (2017).
  22. H. Biss, L. Sobirey, N. Luick, M. Bohlen, J. J. Kinnunen, G. M. Bruun, et al., Excitation spectrum and superfluid gap of an ultracold Fermi gas, Phys. Rev. Lett. 128, 100401 (2022).
  23. Y. Castin, Comment on “excitation spectrum and superfluid gap of an ultracold Fermi gas”, Phys. Rev. Lett. 133, 109301 (2024).
  24. T.-L. Ho and Q. Zhou, Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases, Nat. Phys. 6, 131 (2010).
  25. S. M. Kravec and S. Pal, The spinful large charge sector of non-relativistic CFTs: From phonons to vortex crystals, J. High Energy Phys. 05 (2019) 194.
  26. S. Hellerman, D. Orlando, V. Pellizzani, S. Reffert, and I. Swanson, Nonrelativistic CFTs at large charge: Casimir energy and logarithmic enhancements, J. High Energy Phys. 05 (2022) 135.
  27. S. Y. Chang and G. F. Bertsch, Unitary Fermi gas in a harmonic trap, Phys. Rev. A 76, 021603 (2007).
  28. M. G. Endres, D. B. Kaplan, J.-W. Lee, and A. N. Nicholson, Lattice Monte Carlo calculations for unitary fermions in a harmonic trap, Phys. Rev. A 84, 043644 (2011).
  29. J. Carlson and S. Gandolfi, Predicting energies of small clusters from the inhomogeneous unitary Fermi gas, Phys. Rev. A 90, 011601 (2014).
  30. X. Y. Yin and D. Blume, Trapped unitary two-component Fermi gases with up to ten particles, Phys. Rev. A 92, 013608 (2015).
  31. H. Kurkjian, Y. Castin, and A. Sinatra, Concavity of the collective excitation branch of a Fermi gas in the BEC-BCS crossover, Phys. Rev. A 93, 013623 (2016).
  32. G. Rupak and T. Schäfer, Density functional theory for non-relativistic fermions in the unitarity limit, Nucl. Phys. A 816, 52 (2009).
  33. D. Banerjee, S. Chandrasekharan, and D. Orlando, Conformal dimensions via large charge expansion, Phys. Rev. Lett. 120, 061603 (2018).
  34. L. Alvarez-Gaume, D. Orlando, and S. Reffert, Large charge at large N, J. High Energy Phys. 12 (2019) 142.
  35. N. A. Dondi and G. Sberveglieri, NLO in the large charge sector of the critical O(N) model at large N, J. High Energy Phys. 02 (2025) 005.
  36. K. Sturm, Dynamic structure factor: An introduction, Z. Naturforsch., A: Phys. Sci. 48, 233 (1993).
  37. Y. Kanada-En'yo, N. Hinohara, T. Suhara, and P. Schuck, Dineutron correlations in quasi-two-dimensional systems in a simplified model, and possible relation to neutron-rich nuclei, Phys. Rev. C 79, 054305 (2009).

Outline

Information

Phys. Rev. A 114, 023304– Published 4 August, 2026
  • Received 12 December 2025
  • Accepted 19 May 2026
Article part of CHORUS
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation