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.
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Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold Fermi gases. Preprint at 〈http://arxiv.org/abs/0706.3360〉 (2007)
Chandrasekhar, B. S. A note on the maximum critical field of high-field superconductors. Appl. Phys. Lett. 1, 7–8 (1962)
Clogston, A. M. Upper limit for the critical field in hard superconductors. Phys. Rev. Lett. 9, 266–267 (1962)
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)
Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A563 (1964)
Larkin, A. I. & Ovchinnikov, Y. N. Inhomogeneous state of superconductors. Sov. Phys. JETP 20, 762–769 (1965)
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)
Burovski, E., Prokofev, N., Svistunov, B. & Troyer, M. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett. 96, 160402 (2006)
Haussmann, R., Rantner, W., Cerrito, S. & Zwerger, W. Thermodynamics of the BCS-BEC crossover. Phys. Rev. A. 75, 023610 (2007)
Lobo, C., Recati, A., Giorgini, S. & Stringari, S. Normal state of a polarized Fermi gas at unitarity. Phys. Rev. Lett. 97, 200403 (2006)
Carlson, J. & Reddy, S. Asymmetric two-component fermion systems in strong coupling. Phys. Rev. Lett. 95, 060401 (2005)
Sheehy, D. E. & Radzihovsky, L. BEC-BCS Crossover in “magnetized” Feshbach-resonantly paired superfluids. Phys. Rev. Lett. 96, 060401 (2006)
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)
Gubbels, K. B., Romans, M. W. & Stoof, H. T. Sarma phase in trapped unbalanced Fermi gases. Phys. Rev. Lett. 97, 210402 (2006)
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)
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)
Zwierlein, M. W., Schirotzek, A., Schunck, C. H. & Ketterle, W. Fermionic superfluidity with imbalanced spin populations. Science 311, 492–496 (2006)
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)
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)
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)
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)
Griffiths, R. B. Thermodynamics near the two-fluid critical mixing point in He3-He4 . Phys. Rev. Lett. 24, 715–717 (1970)
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)
Bedaque, P. F., Caldas, H. & Rupak, G. Phase separation in asymmetrical fermion superfluids. Phys. Rev. Lett. 91, 247002 (2003)
Bulgac, A. & Forbes, M. M. Zero-temperature thermodynamics of asymmetric Fermi gases at unitarity. Phys. Rev. A 75, 031605(R) (2007)
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)
Chevy, F. Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations. Phys. Rev. A 74, 063628 (2006)
De Silva, T. N. & Mueller, E. J. Surface tension in unitary Fermi gases with population imbalance. Phys. Rev. Lett. 97, 070402 (2006)
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)
Machida, K., Mizushima, T. & Ichioka, M. Generic phase diagram of fermion superfluids with population imbalance. Phys. Rev. Lett. 97, 120407 (2006)
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.
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)
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Shin, Yi., Schunck, C., Schirotzek, A. et al. Phase diagram of a two-component Fermi gas with resonant interactions. Nature 451, 689–693 (2008). https://doi.org/10.1038/nature06473
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