Skip to main content

Thank you for visiting 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.

Phase diagram of a two-component Fermi gas with resonant interactions


The pairing of fermions lies at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state, and the quest for superconductors with high critical temperature equates to a search for systems with strong pairing mechanisms. Ultracold atomic Fermi gases present a highly controllable model system for studying strongly interacting fermions1. Tunable interactions (through Feshbach collisional resonances) and the control of population or mass imbalance among the spin components provide unique opportunities to investigate the stability of pairing2,3,4—and possibly to search for exotic forms of superfluidity5,6. A major controversy has surrounded the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly (that is, at unitarity). Here we present the phase diagram of a spin-polarized Fermi gas of 6Li atoms at unitarity, experimentally mapping out the superfluid phases versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization; this is the signature of a first-order superfluid-to-normal phase transition, and disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully paired superfluid to a partially polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Schematic of spatial structure of a strongly interacting Fermi gas in a harmonic trap.
Figure 2: Double in situ phase-contrast imaging of a trapped Fermi mixture.
Figure 3: Density profiles of trapped Fermi mixtures with imbalanced populations.
Figure 4: Temperature determination using in situ density profiles.
Figure 5: The σ T phase diagram for a homogeneous spin-polarized Fermi gas with resonant interactions.


  1. 1

    Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold Fermi gases. Preprint at 〈〉 (2007)

  2. 2

    Chandrasekhar, B. S. A note on the maximum critical field of high-field superconductors. Appl. Phys. Lett. 1, 7–8 (1962)

    CAS  Article  ADS  Google Scholar 

  3. 3

    Clogston, A. M. Upper limit for the critical field in hard superconductors. Phys. Rev. Lett. 9, 266–267 (1962)

    Article  ADS  Google Scholar 

  4. 4

    Sarma, G. On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor. J. Phys. Chem. Solids 20, 1029–1032 (1963)

    Article  ADS  Google Scholar 

  5. 5

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

    Article  ADS  Google Scholar 

  6. 6

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

    MathSciNet  Google Scholar 

  7. 7

    Bulgac, A., Drut, J. E. & Magierski, P. Spin 1/2 fermions in the unitary regime: a superfluid of a new type. Phys. Rev. Lett. 96, 090404 (2006)

    Article  ADS  Google Scholar 

  8. 8

    Burovski, E., Prokofev, N., Svistunov, B. & Troyer, M. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett. 96, 160402 (2006)

    Article  ADS  Google Scholar 

  9. 9

    Haussmann, R., Rantner, W., Cerrito, S. & Zwerger, W. Thermodynamics of the BCS-BEC crossover. Phys. Rev. A. 75, 023610 (2007)

    Article  ADS  Google Scholar 

  10. 10

    Lobo, C., Recati, A., Giorgini, S. & Stringari, S. Normal state of a polarized Fermi gas at unitarity. Phys. Rev. Lett. 97, 200403 (2006)

    CAS  Article  ADS  Google Scholar 

  11. 11

    Carlson, J. & Reddy, S. Asymmetric two-component fermion systems in strong coupling. Phys. Rev. Lett. 95, 060401 (2005)

    CAS  Article  ADS  Google Scholar 

  12. 12

    Sheehy, D. E. & Radzihovsky, L. BEC-BCS Crossover in “magnetized” Feshbach-resonantly paired superfluids. Phys. Rev. Lett. 96, 060401 (2006)

    Article  ADS  Google Scholar 

  13. 13

    Yi, W. & Duan, L.-M. Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap. Phys. Rev. A 74, 013610 (2006)

    Article  ADS  Google Scholar 

  14. 14

    Gubbels, K. B., Romans, M. W. & Stoof, H. T. Sarma phase in trapped unbalanced Fermi gases. Phys. Rev. Lett. 97, 210402 (2006)

    CAS  Article  ADS  Google Scholar 

  15. 15

    Chien, C.-C., Chen, Q., He, Y. & Levin, K. Superfluid phase diagrams of trapped Fermi gases with population imbalance. Phys. Rev. Lett. 98, 110404 (2007)

    Article  ADS  Google Scholar 

  16. 16

    Parish, M. M., Marchetti, F. M., Lamacraft, A. & Simons, B. D. Finite-temperature phase diagram of a polarized Fermi condensate. Nature Phys. 3, 124–128 (2007)

    CAS  Article  ADS  Google Scholar 

  17. 17

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

    CAS  Article  ADS  Google Scholar 

  18. 18

    Zwierlein, M. W., Schunck, C. H., Schirotzek, A. & Ketterle, W. Direct Observation of the superfluid phase transition in ultracold Fermi gases. Nature 442, 54–58 (2006)

    CAS  Article  ADS  Google Scholar 

  19. 19

    Shin, Y., Zwierlein, M. W., Schunck, C. H., Schirotzek, A. & Ketterle, W. Observation of phase separation in a strongly interacting imbalanced Fermi gas. Phys. Rev. Lett. 97, 030401 (2006)

    CAS  Article  ADS  Google Scholar 

  20. 20

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

    CAS  Article  ADS  Google Scholar 

  21. 21

    Partridge, G. B., Li, W., Karmar, R. I., Liao, Y. & Hulet, R. G. Deformation of a trapped Fermi gas with unequal spin populations. Phys. Rev. Lett. 97, 190407 (2006)

    CAS  Article  ADS  Google Scholar 

  22. 22

    Griffiths, R. B. Thermodynamics near the two-fluid critical mixing point in He3-He4 . Phys. Rev. Lett. 24, 715–717 (1970)

    CAS  Article  ADS  Google Scholar 

  23. 23

    Luo, L., Clancy, B., Joseph, J., Kinast, J. & Thomas, J. E. Measurement of the entropy and critical temperature of a strongly interacting Fermi gas. Phys. Rev. Lett. 98, 080402 (2007)

    CAS  Article  ADS  Google Scholar 

  24. 24

    Bedaque, P. F., Caldas, H. & Rupak, G. Phase separation in asymmetrical fermion superfluids. Phys. Rev. Lett. 91, 247002 (2003)

    Article  ADS  Google Scholar 

  25. 25

    Bulgac, A. & Forbes, M. M. Zero-temperature thermodynamics of asymmetric Fermi gases at unitarity. Phys. Rev. A 75, 031605(R) (2007)

    Article  ADS  Google Scholar 

  26. 26

    Schunck, C. H., Shin, Y., Schirotzek, A., Zwierlein, M. W. & Ketterle, W. Pairing without superfluidity: the ground state of an imbalanced Fermi mixture. Science 316, 867–870 (2007)

    CAS  Article  ADS  Google Scholar 

  27. 27

    Chevy, F. Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations. Phys. Rev. A 74, 063628 (2006)

    Article  ADS  Google Scholar 

  28. 28

    De Silva, T. N. & Mueller, E. J. Surface tension in unitary Fermi gases with population imbalance. Phys. Rev. Lett. 97, 070402 (2006)

    Article  ADS  Google Scholar 

  29. 29

    Haque, M. & Stoof, H. T. C. Trapped fermionic clouds distorted from the trap shape due to many-body effects. Phys. Rev. Lett. 98, 260406 (2006)

    Article  Google Scholar 

  30. 30

    Machida, K., Mizushima, T. & Ichioka, M. Generic phase diagram of fermion superfluids with population imbalance. Phys. Rev. Lett. 97, 120407 (2006)

    CAS  Article  ADS  Google Scholar 

Download references


We thank M. W. Zwierlein and A. Keshet for a critical reading of the manuscript. This work was supported by NSF, ONR, MURI and DARPA.

Author information



Corresponding author

Correspondence to Yong-il Shin.

Supplementary information

Supplementary Information

The file contains Supplementary Figures 1-3 and Legends, Supplementary Discussion and additional references. This document contains three figures showing the cooling trajectory of a Fermi mixture with small population imbalance, the expansion of a sample, and the anharmonicity effect on the temperature determination, respectively, as well as supplementary discussion on thermometry of ultracold Fermi gases and polarized superfluid at finite temperature. (PDF 290 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shin, Yi., Schunck, C., Schirotzek, A. et al. Phase diagram of a two-component Fermi gas with resonant interactions. Nature 451, 689–693 (2008).

Download citation

Further reading


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.


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