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Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

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Abstract

We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03TF .

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Notes

  1. As emphasized by Radzihovsky [11], FFLO is a pair-density wave rather than a genuine supersolid because there is only a single order parameter, not two independent ones.

  2. Note that in many publications, the form factor χ(x) in (2) is replaced by a delta function, which leads to the incorrect result re = –2\({{r}^{ \star }}\) for all Feshbach resonances.

  3. This must be distinguished carefully from the notion of open or closed channel dominated resonances discussed above, which is defined at the level of two-body interactions, independent of the Fermion density.

  4. Dimensional analysis is sufficient to formulate a scaling function for the pressure because it does not develop an anomalous dimension, in contrast to observables like the collisional relaxation rate [35] or the closed channel fraction (8), which involve the additional microscopic lengths \(\bar {a}\) or \({{r}^{ \star }}\).

  5. This happens in mean field calculations, where FFLO disappears in the ground state at a finite negative 1/(kFa)* = –2.86 [40] or 1/(kFa)* = – 0.46 [41].

  6. Strictly speaking, Γ–1(Q, Ωn = 0) ~ |Q|2 – η involves an anomalous dimension η which is, however, very small for the transition to superfluidity in three dimensions and is anyway not properly contained in our approach.

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Authors and Affiliations

  1. Physik-Department, Technische Universität München, D-85748, Garching, Germany

    B. Frank, J. Lang & W. Zwerger

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  1. B. Frank
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  2. J. Lang
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  3. W. Zwerger
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Correspondence to W. Zwerger.

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Contribution for the JETP special issue in honor of L. P. Pitaevskii’s 85th birthday

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Frank, B., Lang, J. & Zwerger, W. Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases. J. Exp. Theor. Phys. 127, 812–825 (2018). https://doi.org/10.1134/S1063776118110031

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