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High-temperature pairing in a strongly interacting two-dimensional Fermi gas

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Science  26 Jan 2018:
Vol. 359, Issue 6374, pp. 452-455
DOI: 10.1126/science.aan5950
  • Fig. 1 Exploring fermion pairing in a strongly interacting 2D Fermi gas.

    (A) Schematic phase diagram of the BEC-BCS crossover. In this work, we investigated the nature of pairing in the normal phase of the crossover regime between the weakly interacting Bose and Fermi liquids. (B) Illustration of RF spectroscopy of a 2D two-component Fermi gas. Pairing and many-body effects shift the atomic transition frequencies between the hyperfine states Embedded Image, which results in observable signatures in the RF response of the system. (C) Absorption images of the cloud [taken at ln(kFa2D) ≈ 1.5 and T/TF ~ 0.3] without RF (reference) and with RF at a particular frequency, and the difference between the two images. The ring feature in δn(r) reveals the density dependence of the RF response. (D) Spatially resolved spectral response function reconstructed from absorption images taken at different RF frequencies. At low temperatures in the spin-balanced sample, the occupation of the free-particle branch is too low to be observable, which makes it difficult to distinguish between mean-field shifts and pairing effects.

  • Fig. 2 Quasi-particle spectroscopy in the BEC and BCS limits.

    (A) We created a slightly imbalanced mixture of hyperfine states so as to artificially populate the free-particle branch. The density distributions of the majority and minority spins are shown, as well as the corresponding local imbalance (inset). (B and C) Schematic illustration of single-particle dispersion relations in the BEC and BCS limits at zero temperature. Paired atoms reside in the lowest branch (Bound) and are transferred to the continuum of unoccupied states. The excess majority atoms are unpaired and occupy the upper quasi-particle (Free) branch in the spectrum preferentially at k ~ 0 (BEC) and k ~ kF (BCS). The energy difference between the free-particle dispersion in a noninteracting system (blue dashed line) and the continuum (blue solid line) is the bare hyperfine transition energy and serves as the reference for (D) and (E). (D and E) The transition of paired atoms into the continuum yields an asymmetric response with a sharp threshold in the RF spectral function. The quasi-particle transition contributes another peak, which appears at ωRF = 0 on the BEC side and ωRF = –Δ on the BCS side, where Δ is the BCS gap parameter. Their relative difference yields the pairing energy ΔE, which reveals the distinction between two-body (ΔE ~ EB) and many-body pairing (ΔE > EB) in the two limits.

  • Fig. 3 From two-body dimers to many-body pairing.

    The spatially resolved response function I(r, ωRF) shows qualitatively different behavior for two different scattering lengths. (A and B) I(r, ωRF) for central ln(kFa2D) ~ –0.5 and 1.0, respectively. The gray lines correspond to local T/TF ~ 0.7 in (A) and T/TF ~ 1 in (B). The 3D visualization was obtained by using a linear interpolation between 3000 data points, each of which is an average of 30 realizations. The black solid line is the peak position of the free branch, the red line is the threshold position of the bound branch, and the black dashed line is displaced from the free peak by the two-body binding energy EB. The energy difference between free and bound branches is the pairing energy ΔE, which is seen to agree with EB in (A) (BEC regime) but exceeds EB in (B) (crossover regime). The differential density dependence of the energy of the two branches implies that the pair wave function is strongly modified by the many-body system. (C and D) Local spectra at a fixed radius indicated by gray lines in (A) and (B) corresponding to a homogeneous system with T/TF ~ 0.7 and 1, respectively. The solid blue curves are the fits to the data; the black and red curves are Gaussian and threshold fits to the two branches (21).

  • Fig. 4 Normal phase in the 2D BEC-BCS crossover regime.

    (A) Pairing energy ΔE in units of EB plotted as a function of T/TF for different interaction strengths [central ln(kFa2D)]. Each point in (A) is the result of fits to local spectra (Fig. 3, C and D), which are averaged over 30 shots. (B) Many-body–induced high-temperature pairing. We plot ΔE/EB as a function of ln(kFa2D) for fixed ratio T/TF ~ 0.5. Red and blue circles correspond to measurements taken with Embedded Image and Embedded Image mixtures, respectively. The dashed black line is a guide to the eye. The errors indicated as shaded bands in (A) and bars in (B) are obtained from the fitting procedure explained in (21). For ln(kFa2D) ≤ 0.5 (strong attraction), we have ΔE/EB ~ 1, with negligible density dependence, indicating two-body pairing. For larger ln(kFa2D) (less attraction), ΔE/EB exceeds 1 and reaches a maximum of 2.6 before showing a downward trend. At ln(kFa2D) ~ 1, we have a critical temperature of Tc ~ 0.17TF (8), which indicates the onset of many-body pairing at temperatures several times Tc.

Supplementary Materials

  • High-temperature pairing in a strongly interacting two-dimensional Fermi gas

    Puneet A. Murthy, Mathias Neidig, Ralf Klemt, Luca Bayha, Igor Boettcher, Tilman Enss, Marvin Holten, Gerhard Zürn, Philipp M. Preiss, Selim Jochim

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary text
    • Fig. S1 to S8
    • Table S1
    • References

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