Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spin-imbalance in a one-dimensional Fermi gas

Subjects

Abstract

Superconductivity and magnetism generally do not coexist. Changing the relative number of up and down spin electrons disrupts the basic mechanism of superconductivity, where atoms of opposite momentum and spin form Cooper pairs. Nearly forty years ago Fulde and Ferrell1 and Larkin and Ovchinnikov2 (FFLO) proposed an exotic pairing mechanism in which magnetism is accommodated by the formation of pairs with finite momentum. Despite intense theoretical and experimental efforts, however, polarized superconductivity remains largely elusive3. Unlike the three-dimensional (3D) case, theories predict that in one dimension (1D) a state with FFLO correlations occupies a major part of the phase diagram4,5,6,7,8,9,10,11,12. Here we report experimental measurements of density profiles of a two-spin mixture of ultracold 6Li atoms trapped in an array of 1D tubes (a system analogous to electrons in 1D wires). At finite spin imbalance, the system phase separates with an inverted phase profile, as compared to the 3D case. In 1D, we find a partially polarized core surrounded by wings which, depending on the degree of polarization, are composed of either a completely paired or a fully polarized Fermi gas. Our work paves the way to direct observation and characterization of FFLO pairing.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Theoretical T = 0 phase diagram (adapted from ref. 6).
Figure 2: Axial density profiles of a spin-imbalanced 1D ensemble of tubes.
Figure 3: Experimental phase diagram as a function of polarization in the central tube.

References

  1. Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A563 (1964)

    Google Scholar 

  2. Larkin, A. I. & Ovchinnikov, Y. N. Inhomogeneous state of superconductors. Sov. Phys. JETP 20, 762–769 (1965)

    Google Scholar 

  3. Casalbuoni, R. & Nardulli, G. Inhomogeneous superconductivity in condensed matter and QCD. Rev. Mod. Phys. 76, 263–320 (2004)

    CAS  Google Scholar 

  4. Yang, K. Inhomogeneous superconducting state in quasi-one-dimensional systems. Phys. Rev. B 63, 140511(R) (2001)

    Google Scholar 

  5. Mizushima, T., Machida, K. & Ichioka, M. Direct imaging of spatially modulated superfluid phases in atomic fermion systems. Phys. Rev. Lett. 94, 060404 (2005)

    CAS  Google Scholar 

  6. Orso, G. Attractive Fermi gases with unequal spin populations in highly elongated traps. Phys. Rev. Lett. 98, 070402 (2007)

    CAS  Google Scholar 

  7. Hu, H., Liu, X.-J. & Drummond, P. D. Phase diagram of a strongly interacting polarized Fermi gas in one dimension. Phys. Rev. Lett. 98, 070403 (2007)

    Google Scholar 

  8. Guan, X. W., Batchelor, M. T., Lee, C. & Bortz, M. Phase transitions and pairing signature in strongly attractive Fermi atomic gases. Phys. Rev. B 76, 085120 (2007)

    Google Scholar 

  9. Feiguin, A. E. & Heidrich-Meisner, F. Pairing states of a polarized fermi gas trapped in a one-dimensional optical lattice. Phys. Rev. B 76, 220508 (2007)

    Google Scholar 

  10. Parish, M. M., Baur, S. K., Mueller, E. J. & Huse, D. A. Quasi-one-dimensional polarized Fermi superfluids. Phys. Rev. Lett. 99, 250403 (2007)

    Google Scholar 

  11. Casula, M., Ceperley, D. M. & Mueller, E. J. Quantum Monte Carlo study of one-dimensional trapped fermions with attractive contact interactions. Phys. Rev. A 78, 033607 (2008)

    Google Scholar 

  12. Kakashvili, P. & Bolech, C. J. Paired states in spin-imbalanced atomic Fermi gases in one dimension. Phys. Rev. A 79, 041603 (2009)

    Google Scholar 

  13. Sheehy, D. E. & Radzihovsky, L. BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids. Ann. Phys. 322, 1790–1924 (2007)

    CAS  Google Scholar 

  14. Bulgac, A. & Forbes, M. M. Unitary Fermi supersolid: the Larkin-Ovchinnikov phase. Phys. Rev. Lett. 101, 215301 (2008)

    Google Scholar 

  15. Zwierlein, M. W., Schirotzek, A., Schunck, C. H. & Ketterle, W. Fermionic superfluidity with imbalanced spin populations. Science 311, 492–496 (2006)

    CAS  Google Scholar 

  16. Partridge, G. B., Li, W., Kamar, R. I., Liao, Y.-a. & Hulet, R. G. Pairing and phase separation in a polarized Fermi gas. Science 311, 503–505 (2006)

    CAS  Google Scholar 

  17. Partridge, G. B. et al. Deformation of a trapped Fermi gas with unequal spin populations. Phys. Rev. Lett. 97, 190407 (2006)

    CAS  Google Scholar 

  18. Shin, Y.-I., Schunck, C. H., Schirotzek, A. & Ketterle, W. Phase diagram of a two-component Fermi gas with resonant interactions. Nature 451, 689–693 (2008)

    CAS  Google Scholar 

  19. Nascimbène, S. et al. Collective oscillations of an imbalanced Fermi gas: axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402 (2009)

    Google Scholar 

  20. Zhao, E. & Liu, W. V. Theory of quasi-one-dimensional imbalanced Fermi gases. Phys. Rev. A 78, 063605 (2008)

    Google Scholar 

  21. Uji, S. et al. Vortex dynamics and the Fulde-Ferrell-Larkin-Ovchinnikov state in a magnetic-field-induced organic superconductor. Phys. Rev. Lett. 97, 157001 (2006)

    CAS  Google Scholar 

  22. Radovan, H. et al. Magnetic enhancement of superconductivity from electron spin domains. Nature 425, 51–55 (2003)

    CAS  Google Scholar 

  23. Kenzelmann, M. et al. Coupled superconducting and magnetic order in CeCoIn5 . Science 321, 1652–1654 (2008)

    CAS  Google Scholar 

  24. Moritz, H., Stöferle, T., Günter, K., Köhl, M. & Esslinger, T. Confinement induced molecules in a 1D Fermi gas. Phys. Rev. Lett. 94, 210401 (2005)

    Google Scholar 

  25. Houbiers, M., Stoof, H. T. C., McAlexander, W. I. & Hulet, R. G. Elastic and inelastic collisions of 6Li atoms in magnetic and optical traps. Phys. Rev. A 57, R1497–R1500 (1998)

    CAS  Google Scholar 

  26. Bartenstein, M. et al. Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules. Phys. Rev. Lett. 94, 103201 (2005)

    CAS  Google Scholar 

  27. Tokatly, I. V. Dilute Fermi gas in quasi-one-dimensional traps: from weakly interacting fermions via hard core bosons to a weakly interacting Bose gas. Phys. Rev. Lett. 93, 090405 (2004)

    CAS  Google Scholar 

  28. Fuchs, J. N., Recati, A. & Zwerger, W. Exactly solvable model of the BCS-BEC crossover. Phys. Rev. Lett. 93, 090408 (2004)

    CAS  Google Scholar 

  29. Liu, X.-J., Hu, H. & Drummond, P. D. Finite-temperature phase diagram of a spin-polarized ultracold Fermi gas in a highly elongated harmonic trap. Phys. Rev. A 78, 023601 (2008)

    Google Scholar 

  30. Bradley, C. C., Sackett, C. A. & Hulet, R. G. Bose-Einstein condensation of lithium: observation of limited condensate number. Phys. Rev. Lett. 78, 985–989 (1997)

    CAS  Google Scholar 

  31. Bergeman, T., Moore, M. G. & Olshanii, M. Atom-atom scattering under cylindrical harmonic confinement: numerical and analytic studies of the confinement induced resonance. Phys. Rev. Lett. 91, 163201 (2003)

    CAS  Google Scholar 

  32. Kinast, J. et al. Heat capacity of a strongly interacting Fermi gas. Science 307, 1296–1299 (2005)

    CAS  Google Scholar 

  33. Gaudin, M. Un systeme a une dimension de fermions en interaction. Phys. Lett. A 24, 55–56 (1967)

    CAS  Google Scholar 

  34. Yang, C. N. Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Phys. Rev. Lett. 19, 1312–1315 (1967)

    Google Scholar 

  35. Takahashi, M. One-dimensional electron gas with delta-function interaction at finite temperature. Prog. Theor. Phys. 46, 1388–1406 (1971)

    Google Scholar 

  36. Zhao, E., Guan, X.-W., Liu, W. V., Batchelor, M. T. & Oshikawa, M. Analytic thermodynamics and thermometry of Gaudin-Yang Fermi gases. Phys. Rev. Lett. 103,140–404(2009).

    Google Scholar 

  37. Heidrich-Meisner, F., Feiguin, A. E., Schollwoeck, U. & Zwerger, W. The BCS-BEC crossover and the disappearance of FFLO-correlations in a spin-imbalanced, one-dimensional Fermi gas. Phys. Rev. A 81,023629 (2010).

  38. Mora, C., Egger, R., Gogolin, A. O. & Komnik, A. Atom-dimer scattering for confined ultracold fermion gases. Phys. Rev. Lett. 93,170403(2004).

  39. Baur, S. K., Shumway, J. & Mueller, E. J. FFLO vs Bose-Fermi mixture in polarized 1D Fermi gas on a Feshbach resonance: a 3-body study. Phys. Rev. A 81,033628 (2010).

  40. Blume, D. & Rakshit, D. Excitation spectrum and effective interactions of a highly elongated Fermi gas. Phys. Rev. A 80,013601 (2009).

Download references

Acknowledgements

We thank S. E. Pollack for providing software to remove fringes from the images and M. Revelle for help on the experiment. E.J.M. would like to thank C. Bolech and P. Kakashvili for discussion of techniques for analysing the data. This work was supported under ARO Award W911NF-07-1-0464 with funds from the DARPA OLE programme, and by the NSF, the ONR, the Welch Foundation (grant C-1133) and the Keck Foundation.

Author information

Authors and Affiliations

Authors

Contributions

Y.-a.L., T.P., A.S.C.R., G.B.P., W.L. and R.G.H. constructed the apparatus. Y.-a.L., A.S.C.R. and T.P. acquired and processed the data. S.K.B. and E.J.M. did the theory and extracted the phase boundaries from the data. R.G.H and E.J.M. supervised the investigation. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to Randall G. Hulet.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Information comprising Imaging, Temperature, Central tube radius, Truncation to 1D model and the 1D FFLO-Bose/Fermi mixture crossover. Also included are additional references and Supplementary Figures 1- 3 with legends. (PDF 485 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Liao, Ya., Rittner, A., Paprotta, T. et al. Spin-imbalance in a one-dimensional Fermi gas. Nature 467, 567–569 (2010). https://doi.org/10.1038/nature09393

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature09393

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing