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Spin-imbalance in a one-dimensional Fermi gas



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.

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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.


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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.

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Authors and Affiliations



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.

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Correspondence to Randall G. Hulet.

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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)

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Liao, Ya., Rittner, A., Paprotta, T. et al. Spin-imbalance in a one-dimensional Fermi gas. Nature 467, 567–569 (2010).

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