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
  • Letter
  • Open Access

Probing the BCS-BEC crossover with persistent currents

Giovanni Pecci1, Piero Naldesi1, Luigi Amico2,3,4,5, and Anna Minguzzi1

  • 1Université Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France
  • 2Quantum Research Centre, Technology Innovation Institute, P.O. Box 9639, Abu Dhabi, United Arab Emirates
  • 3CNR-IMM and INFN-Sezione di Catania, Via S. Sofia 64, 95127 Catania, Italy
  • 4Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
  • 5LANEF Chaire d'Excellence, Université Grenoble-Alpes and CNRS, F-38000 Grenoble, France

Phys. Rev. Research 3, L032064 – Published 14 September, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032064

Abstract

We study the persistent currents of an attractive Fermi gas confined in a tightly confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the Bardeen-Cooper-Schrieffer (BCS) side, fermions display a parity effect in the persistent currents, i.e., their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the Bose-Einstein condensate (BEC) side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicating that persistent currents can be used to infer the formation of tightly bound bosonic pairs. Our predictions can be accessed in ultracold atom experiments through noise interferograms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (51)

  1. G. C. Strinati, P. Pieri, G. Röpke, P. Schuck, and M. Urban, The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems, Phys. Rep. 738, 1 (2018).
  2. M. Baldo, U. Lombardo, and P. Schuck, Deuteron formation in expanding nuclear matter from a strong coupling BCS approach, Phys. Rev. C 52, 975 (1995).
  3. R. F. Bishop, K. A. Gernoth, N. R. Walet, and Y. Xian, Recent Progress in Many-Body Theories (World Scientific, Singapore, 2000), Vol. 3.
  4. M. Randeria, J.-M. Duan, and L.-Y. Shieh, Bound States, Cooper Pairing, and Bose Condensation in Two Dimensions, Phys. Rev. Lett. 62, 981 (1989).
  5. R. Micnas, J. Ranninger, and S. Robaszkiewicz, Superconductivity in narrow-band systems with local nonretarded attractive interactions, Rev. Mod. Phys. 62, 113 (1990).
  6. M. Randeria, W. Zwerger, and M. Zwierlein, in The BCS-BEC Crossover and the Unitary Fermi Gas (Springer, New York, 2012), pp. 1–32.
  7. M. Inguscio, W. Ketterle, and C. Salomon, Ultra-Cold Fermi Gases (IOS Press, Clifton, VA, 2008), Vol. 164.
  8. G. Valtolina, A. Burchianti, A. Amico, E. Neri, K. Xhani, J. A. Seman, A. Trombettoni, A. Smerzi, M. Zaccanti, M. Inguscio et al., Josephson effect in fermionic superfluids across the BEC-BCS crossover, Science 350, 1505 (2015).
  9. W. Kwon, G. Del Pace, R. Panza, M. Inguscio, W. Zwerger, M. Zaccanti, F. Scazza, and G. Roati, Strongly correlated superfluid order parameters from dc Josephson supercurrents, Science 369, 84 (2020).
  10. H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer et al., Roadmap on structured light, J. Opt. 19, 013001 (2016).
  11. J.-P. Brantut, J. Meineke, D. Stadler, S. Krinner, and T. Esslinger, Conduction of ultracold fermions through a mesoscopic channel, Science 337, 1069 (2012).
  12. F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz, and S. Jochim, Deterministic preparation of a tunable few-fermion system, Science 332, 336 (2011).
  13. G. Zürn, A. N. Wenz, S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, Pairing in Few-Fermion Systems with Attractive Interactions, Phys. Rev. Lett. 111, 175302 (2013).
  14. L. Amico, M. Boshier, G. Birkl, A. Minguzzi, C. Miniatura, L. C. Kwek, D. Aghamalyan, V. Ahufinger, N. Andrei, A. S. Arnold et al., Roadmap on atomtronics, arXiv:2008.04439.
  15. L. Amico, G. Birkl, M. Boshier, and L.-C. Kwek, Focus on atomtronics-enabled quantum technologies, New J. Phys. 19, 020201 (2017).
  16. R. Dumke, Z. Lu, J. Close, N. Robins, A. Weis, M. Mukherjee, G. Birkl, C. Hufnagel, L. Amico, M. G. Boshier et al., Roadmap on quantum optical systems, J. Opt. 18, 093001 (2016).
  17. E. Burovski, N. Prokof'ev, B. Svistunov, and M. Troyer, Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity, Phys. Rev. Lett. 96, 160402 (2006).
  18. C.-C. Chien, Y. He, Q. Chen, and K. Levin, Superfluid-insulator transitions at noninteger filling in optical lattices of fermionic atoms, Phys. Rev. A 77, 011601(R) (2008).
  19. J. N. Fuchs, A. Recati, and W. Zwerger, Exactly Solvable Model of the BCS-BEC Crossover, Phys. Rev. Lett. 93, 090408 (2004).
  20. T. Iida and M. Wadati, Exact analysis of δ-function attractive fermions and repulsive bosons in one-dimension, J. Phys. Soc. Jpn. 74, 1724 (2005).
  21. A. J. Leggett, in Granular Nanoelectronics, edited by D. K.Ferry, J. R. Barker, and C. Jacoboni (Springer, US, Boston, 1991), pp. 297–311.
  22. C. Schilling and R. Schilling, Number-parity effect for confined fermions in one dimension, Phys. Rev. A 93, 021601(R) (2016).
  23. M. Manninen, S. Viefers, and S. Reimann, Quantum rings for beginners II: Bosons versus fermions, Physica E 46, 119 (2012).
  24. L. Corman, L. Chomaz, T. Bienaimé, R. Desbuquois, C. Weitenberg, S. Nascimbene, J. Dalibard, and J. Beugnon, Quench-Induced Supercurrents in an Annular Bose Gas, Phys. Rev. Lett. 113, 135302 (2014).
  25. K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link, Phys. Rev. Lett. 110, 025302 (2013).
  26. S. Eckel, F. Jendrzejewski, A. Kumar, C. J. Lobb, and G. K. Campbell, Interferometric Measurement of the Current-Phase Rrelationship of a Superfluid Weak Link, Phys. Rev. X 4, 031052 (2014).
  27. R. Mathew, A. Kumar, S. Eckel, F. Jendrzejewski, G. K. Campbell, M. Edwards, and E. Tiesinga, Self-heterodyne detection of the in situ phase of an atomic superconducting quantum interference device, Phys. Rev. A 92, 033602 (2015).
  28. The slight discrepancy between DMRG and Bethe ansatz results for U/J=−5 is due to the string hypothesis made in the latter.
  29. J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Colloquium: Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83, 1523 (2011).
  30. M. Olshanii, Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons, Phys. Rev. Lett. 81, 938 (1998).
  31. M. Valiente and K. Mølmer, Quasi-one-dimensional scattering in a discrete model, Phys. Rev. A 84, 053628 (2011).
  32. E. Lieb and F. Wu, Absence of Mott Transition in the 1D Hubbard Model, Phys. Rev. Lett 20, 1445 (1968).
  33. B. S. Shastry and B. Sutherland, Twisted Boundary Conditions and Effective Mass in Heisenberg-Ising and Hubbard Rings, Phys. Rev. Lett. 65, 243 (1990).
  34. N. Andrei, Integrable models in condensed matter physics, Low-Dimensional Quantum Field Theories for Condensed Matter Physicists (World Scientific Publishing Co., Singapore, 1995), 457 pages.
  35. F. Marsiglio, Evaluation of the BCS approximation for the attractive Hubbard model in one dimension, Phys. Rev. B 55, 575 (1997).
  36. X.-W. Guan, M. T. Batchelor, and C. Lee, Fermi gases in one dimension: From Bethe ansatz to experiments, Rev. Mod. Phys. 85, 1633 (2013).
  37. M. T. Batchelor, M. Bortz, X. W. Guan, and N. Oelkers, Exact results for the 1D interacting Fermi gas with arbitrary polarization, J. Phys.: Conf. Ser. 42, 5 (2006).
  38. V. Ya. Krivnov and A. A. Ovchinnikov, New method in the theory of a weakly ideal one-dimensional Fermi gas. correlation functions, JETP 49, 328 (1979).
  39. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032064 for further details about the calculations.
  40. T. Choy and F. Haldane, Failure of Bethe-Ansatz solutions of generalisations of the Hubbard chain to arbitrary permutation symmetry, Phys. Lett. A 90, 83 (1982).
  41. T. Choy, Some exact results for a degenerate Hubbard model in one dimension, Phys. Lett. A 80, 49 (1980).
  42. N. Byers and C. N. Yang, Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders, Phys. Rev. Lett. 7, 46 (1961).
  43. X. Waintal, G. Fleury, K. Kazymyrenko, M. Houzet, P. Schmitteckert, and D. Weinmann, Persistent Currents in One Dimension: The Counterpart of Leggett's Theorem, Phys. Rev. Lett. 101, 106804 (2008).
  44. C. Kohstall, S. Riedl, E. R. S. Guajardo, L. A. Sidorenkov, J. H. Denschlag, and R. Grimm, Observation of interference between two molecular Bose–Einstein condensates, New J. Phys. 13, 065027 (2011).
  45. M. Greiner, C. A. Regal, and D. S. Jin, Emergence of a molecular Bose-Einstein condensate from a Fermi gas, Nature (London) 426, 537 (2003).
  46. M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, Vortices and superfluidity in a strongly interacting Fermi gas, Nature (London) 435, 1047 (2005).
  47. T. Haug, J. Tan, M. Theng, R. Dumke, L.-C. Kwek, and L. Amico, Readout of the atomtronic quantum interference device, Phys. Rev. A 97, 013633 (2018).
  48. G. Pecci, P. Naldesi, A. Minguzzi, and L. Amico, Phase coherence in an interacting Fermi gas, arXiv:2105.10408.
  49. T. Ren and I. Aleiner, Bethe-ansatz analysis of near-resonant two-component systems in one dimension, Phys. Rev. A 99, 023611 (2019).
  50. Q. Chen, K. Levin, and J. Stajic, Applying BCS-BEC crossover theory to high-temperature superconductors and ultracold atomic Fermi gases, Low Temp. Phys. 32, 406 (2006).
  51. Y. Uemura, Bose-Einstein to BCS crossover picture for high-Tc cuprates, Physica C 282, 194 (1997).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation