Abstract
The Kibble–Zurek mechanism is a theoretical framework that describes the formation and scaling of topological defects in symmetry-breaking phase transitions. It was originally conceptualized for superfluid helium. The theory predicts that the number of quantum vortices should scale as a power law with the rate at which the system passes through the lambda transition, but demonstrating this effect has been elusive in experiments using superfluid systems. Here, we report the observation of Kibble–Zurek scaling in a homogeneous, strongly interacting Fermi gas undergoing a superfluid phase transition. We investigate the superfluid transition using temperature and interaction strength as two distinct control parameters. The microscopic physics of condensate formation is markedly different for the two quench parameters, as shown by the two orders of magnitude difference in the condensate formation timescale. However, regardless of the thermodynamic direction in which the system passes through a phase transition, the Kibble–Zurek exponent is identically observed to be about 0.68, in good agreement with theoretical predictions. This work experimentally demonstrates the theoretical proposal laid out for liquid helium, which is in the same universality class as strongly interacting Fermi gases.
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Acknowledgements
We thank E.-G. Moon for helpful discussions and J. W. Park for helpful discussions and a critical reading of the manuscript. This work was supported by the National Research Foundation of Korea (Grants Nos. NRF-2023R1A2C3006565 and NRF-2023M3K5A1094811) and the Institute for Basic Science in Korea (Grant No. IBS-R009-D1). K.L. acknowledges support from the National Research Foundation of Korea (Grant No. NRF-2019H1A2A1074494).
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All authors contributed substantially to the work presented in this manuscript. K.L. and Y.S. conceived the idea. K.L., S.K. and T.K. maintained and developed the experimental apparatus. K.L. and T.K. collected the data. K.L. analysed the data. K.L. and Y.S. wrote the original draft. Y.S. supervised the experiment.
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Extended data
Extended Data Fig. 1 Condensate fraction growth.
Condensate fraction (η) as a function of the hold time (th) after quench. The solid (open) circles show the growth of condensate fraction for a temperature quench with tq = 63 ms (tq = 50 ms) at Uf = 0.3Uc (Uf = 0.5Uc). The solid and open circles share an identical quench rate for passing through the critical point. The diamonds indicate the condensate fraction growth for an interaction quench with tq = 2 ms. The inset displays the initial growth rates (γg) calculated in the shaded region of the main figure. Each data point is an average of at least 5 experimental realizations and its error bar denotes the standard deviation of the measurements.
Extended Data Fig. 2 Inverse s-wave scattering length versus Feshbach magnetic field.
The solid line depicts the experimental data of the inverse s-wave scattering length (a−1) as a function of the magnetic field (B) with respect to Bf = 830 G44. Here, a0 denotes the Bohr radius. The shaded region represents the quench range of the magnetic field in our experiment. The dashed line indicates the point of continuous phase transition.
Extended Data Fig. 3 Determination of the KZ scaling region.
The exponent αKZ was determined from a power-law fit to the data points for tq≥tL. Measurement results of αKZ and the \({\chi }_{\nu }^{2}\) statistics as functions of the lower bound tL of the fitting region (a) for the temperature quench with Uf = 0.3Uc and (b) for the interaction quench. The error bars for αKZ denote the standard deviation of the scaling exponent obtained from the power-law fit. The dashed line is a guide for the eye with αKZ = 0.67. The shaded region indicates the KZ scaling region.
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Source Data Extended Data Fig. 1
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Lee, K., Kim, S., Kim, T. et al. Universal Kibble–Zurek scaling in an atomic Fermi superfluid. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02592-z
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DOI: https://doi.org/10.1038/s41567-024-02592-z
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