Abstract
The microscopic origin of high-temperature superconductivity in cuprates remains unknown. It is widely believed that substantial progress could be achieved by better understanding of the pseudogap phase, a normal non-superconducting state of cuprates1,2. In particular, a central issue is whether the pseudogap could originate from strong pairing fluctuations3. Unitary Fermi gases4,5, in which the pseudogap—if it exists—necessarily arises from many-body pairing, offer ideal quantum simulators to address this question. Here we report the observation of a pair-fluctuation-driven pseudogap in homogeneous unitary Fermi gases of lithium-6 atoms, by precisely measuring the fermion spectral function through momentum-resolved microwave spectroscopy and without spurious effects from final-state interactions. The temperature dependence of the pairing gap, inverse pair lifetime and single-particle scattering rate are quantitatively determined by analysing the spectra. We find a large pseudogap above the superfluid transition temperature. The inverse pair lifetime exhibits a thermally activated exponential behaviour, uncovering the microscopic virtual pair breaking and recombination mechanism. The obtained large, temperature-independent single-particle scattering rate is comparable with that set by the Planckian limit6. Our findings quantitatively characterize the pseudogap in strongly interacting Fermi gases and they lend support for the role of preformed pairing as a precursor to superfluidity.
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Data availability
The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.10115338.
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Acknowledgements
We acknowledge R. Qi for sharing the scattering data of lithium-6 atoms. This work was supported by the National Key R&D Program of China (grant no. 2018YFA0306501), NSFC of China (grant no. 11874340), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0301900), the Chinese Academy of Sciences (CAS), the Anhui Initiative in Quantum Information Technologies and the Shanghai Municipal Science and Technology Major Project (grant no. 2019SHZDZX01). Y.-A.C. was supported by the XPLORER PRIZE from Tencent Foundation.
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Y.-A.C., X.-C.Y. and J.-W.P. conceived the research. X. Luo, Y.-Y.Z. and X.-C.Y. stabilized the magnetic field. X. Li, S.W., X. Luo, Y.-Y.Z., K.X., H.-C.S., Y.-Z.N. and X.-C.Y. performed the experiment and collected the data. X. Li, S.W., Q.C., H.H., Y.-A.C., X.-C.Y. and J.-W.P. contributed to the data analysis and writing of the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Pair momentum distributions in the vicinity of the superfluid phase transition.
After ballistic expansion for one quarter of the radial trap period, the one-dimensional momentum distribution n1D(k) maps out the original pair momentum distribution of a unitary Fermi gas before the interaction quench30. Each data point corresponds to the average of approximately 15 individual measurements. In the subplot, we show log(n1D(k)) as a function of k2 at low momentum. The solid lines are the Boltzmann distribution fitting to the thermal wings. Pair condensation is clearly observed for T ≤ Tc.
Extended Data Fig. 2 Schematic diagram for the magnetic field stabilization.
a, The experimental platform is enclosed with several layers of mu-metal plates. b, The ultrastable magnet power supply for generating the required magnetic field of 689.68 G, which is further stabilized with an analog proportional integral derivative controller. c, The active magnetic field compensation system that includes (1) a current measurement setup, consisting of a high precision current sensor and an 8.5-digit multimeter; (2) a proportional integral controlled compensation current source, consisting of a digital proportional integral, a waveform generator, and a voltage-controlled bipolar current source; and (3) a pair of compensation coils. d, A series of low-pass filters, which are composed of several capacitors and inductors. e, The microwave pulse is synchronized to the mains electricity.
Extended Data Fig. 3 The residual 50 Hz noise and Rabi oscillations between the |3⟩ and |4⟩ hyperfine levels.
a, The data points (red circles) are obtained by measuring the resonant frequency of the |3⟩ to |4⟩ microwave transition as a function of delay time td, i.e., the time duration between the synchronization trigger and the microwave pulse. The red solid line is the sine fitting curve with 50 Hz frequency. The red arrow indicates the moment of the synchronization trigger. b, Data points: the normalized atom number in level |4⟩ as a function of microwave duration. Every data point corresponds to an average value of approximately 10 independent measurements. The error bar represents one standard error. The solid line is the fitting curve described by equation (3).
Extended Data Fig. 4 Density distribution after ballistic expansion and n(k, Δω) of the unitary Fermi gas at 0.77Tc.
a, The azimuthally averaged 2D density distribution after 5 ms ballistic expansion at Δω = 2π × 35 kHz. The inset displays the average result of n2D(x, y) of approximately 100 raw images. b, The 3D reconstructed distribution n3D(r), obtained by performing an inverse Abel transform to the n2D(r) in a. c, Momentum-resolved microwave spectrum n(k, Δω). d, Plot of n(k, Δω) in a logarithmic scale. The blue dashed line denotes the cutoff contour line.
Extended Data Fig. 5 The contour plots of A(k, ω).
The black dashed circles in the panels at 1.23Tc and 1.51Tc highlight the saddle region.
Extended Data Fig. 6 Analysis of the energy dispersion.
a, The contour plot of A(k, ω) at Tc. The green line is a guideline indicating an EDC slice at ∼ kF that is presented in c. b, The contour plot of A(k, Δω) at Tc, where Δω = ϵk/ħ-ω. The gray dashed lines are the cut lines of the MEDCs and the red circles are the peak positions of these lines. The orange line shows the MEDC used in d near kF, with a red star highlighted for the peak position. c, d, The spectral slices along the green (EDC) and the orange (MEDC) lines illustrated in a and b. The solid line in d is the fitting result of the MEDC by equation (20).
Extended Data Fig. 7 The evolution of EDC as a function of k for various T.
The red circles denote the peak energies of the left peak in EDCs (that is, the lower branch) for T ≤ 1.11Tc and of the combined single branch for T ≥ 1.23Tc. The red dashed line represents the chemical potential μ.
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Li, X., Wang, S., Luo, X. et al. Observation and quantification of the pseudogap in unitary Fermi gases. Nature 626, 288–293 (2024). https://doi.org/10.1038/s41586-023-06964-y
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DOI: https://doi.org/10.1038/s41586-023-06964-y
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