Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid

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Science  19 Jul 2019:
Vol. 365, Issue 6450, pp. 268-272
DOI: 10.1126/science.aau4402
  • Fig. 1 Dynamics of a 2D fermionic superfluid in position and momentum space.

    (A and B) We prepare a 2D Fermi gas well below the superfluid critical temperature (0.05 < T/TF < 0.1) (14). The isotropic breathing mode is excited by resonantly modulating the harmonic trap at twice the trap frequency. Once the drive is stopped, the breathing oscillations continue for a variable time t, at which point we measure (C) the in situ density distribution ρ(r,t) and (D) the pair momentum distribution n(k,t) using a matter wave focusing technique. (E) Example of azimuthally averaged ρ(r,t) (orange) and n(k,t) (blue) taken at interaction strength ln(kFa2D) ≈ 1. The in situ density oscillates at twice the trap frequency, as expected. The momentum distribution exhibits sharp revivals at twice the rate of the in situ oscillation. The frequency doubling arises from the sinusoidal oscillation of the hydrodynamic velocity field, which vanishes at the inner and outer turning points of the breathing cycle, denoted by the vertical dashed lines.

  • Fig. 2 Scale-invariance breaking in momentum space.

    The in situ (left column) and pair momentum distributions (right column) at the inner and outer turning points for interaction strengths ln(kFa2D) ≈ −1.5, 1.0, 1.3, 1.5, and 2.0 (A to E, respectively). The diamonds and filled circles represent the distributions at adjacent inner and outer turning points. For a scale-invariant system, the in situ density profiles at to (red diamonds) and ti (blue circles) should be scalable with a single scaling factor λ, as well as the momentum distributions [n(k,to)→n(k,ti)] with the inverse factor λ−1. Such scaling behavior is observed both in the weakly interacting BEC and BCS regimes. However, in the strongly interacting crossover regime, we find a clear departure from scale invariance. Although the evolution of the ρ(r) is still self-similar, the momentum distribution shows a notable discrepancy from the expected result obtained with the inverse scaling factor from the in situ scaling (dashed black line). This scaling violation at strong interactions is attributed to the quantum anomaly.

  • Fig. 3 The quantum anomaly and spatial coherence.

    (A) The first-order correlation function g1(r,ti) at inner point (red) and rescaled correlation function g1r,to) at the outer points (blue), for ln(kFa2D) ~ −6 (upper panel, BEC) and ln(kFa2D) ~ 1.3 (lower panel, crossover), where λ is the real space scaling factor obtained in Fig. 2 . In the BEC regime, g1(r,ti) and g1r,to) coincide, whereas in the crossover regime, the two curves are conspicuously different. From the power-law decay of g1(r) ~ r−η, we extract the exponent η. (B) The ratio ηio across the BEC-BCS crossover. The scale-invariant expectation ηio = 1 is reproduced in the BEC regime. In the crossover regime, we observe a sharp dip in the ratio signaling the scaling violation in the long-range phase correlations. The minimum ratio is at ln(kFa2D) ~ 1.3, which coincides with the regime of many-body pairing observed in (29). (Inset) The ratio between the zero pair momentum occupation at the inner and outer turning points, divided by 1/λ2; as above, the largest anomaly is observed in the crossover region. The purple and green curves are guides to the eye.

Supplementary Materials

  • Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid

    Puneet A. Murthy, Nicolo Defenu, Luca Bayha, Marvin Holten, Philipp M. Preiss, Tilman Enss, Selim Jochim

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    • Materials and Methods 
    • Supplementary Text
    • Figs. S1 to S3
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