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arXiv:1902.08548 · Physical Review Letters

Spectral Response and Contact of the Unitary Fermi Gas

Biswaroop Mukherjee, Parth Patel, Zhenjie Yan, Richard J. Fletcher, Julian Struck, Martin W. Zwierlein

Published May 23, 2019• 95 citations
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Abstract

We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.

DOI
10.1103/physrevlett.122.203402

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We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.
We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T^{2} dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝T^{-1/2}. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.
We present a calculation of the spectral functions and the associated rf response of ultracold fermionic atoms near a Feshbach resonance. The single-particle spectra are peaked at energies that can be modeled by a modified BCS dispersion. However, even at very low temperatures their width is comparable to their energy except for a small region around the dispersion minimum. The structure of the excitation spectrum of the unitary gas at infinite scattering length agrees with recent momentum-resolved rf spectra near the critical temperature. A detailed comparison is made with momentum integrated, locally resolved rf spectra of the unitary gas at arbitrary temperatures and shows very good agreement between theory and experiment. The pair size defined from the width of these spectra is found to coincide with that obtained from the leading gradient corrections to the effective-field theory of the superfluid.
We provide a comprehensive theoretical study of the radio-frequency (rf) spectra of a two-component Fermi gas with balanced populations in the normal region of the temperature-vs-coupling phase diagram. In particular, rf spectra are analyzed in terms of two characteristic peaks, which can be either distinct or overlapping. On the BEC side of the crossover, these two contributions are associated with a fermionic quasi-particle peak and a bosonic-like contribution due to pairing. On the BCS side of the crossover, the two peaks are instead associated with interactions between particles occurring, respectively, at high or low relative momenta. Through this two-peak analysis, we show how and to what extent the correlation between the widths of the rf spectra and the pair size, previously identified in the superfluid phase at low temperature, can be extended to the normal phase, as well as how the temperature-vs-coupling phase diagram of the BCS-BEC crossover can be partitioned in a number of distinct physical sectors. Several analytic results for the shape and widths of the rf spectra are also derived in appropriate temperature and coupling limits.
By selectively probing the center of a trapped gas, we measure the local, or homogeneous, contact of a unitary Fermi gas as a function of temperature. Tan's contact, C, is proportional to the derivative of the energy with respect to the interaction strength and is thus an essential thermodynamic quantity for a gas with short-range correlations. Theoretical predictions for the temperature dependence of C differ substantially, especially near the superfluid transition, T(c), where C is predicted to either sharply decrease, sharply increase, or change very little. For T/T(F)>0.4, our measurements of the homogeneous gas contact show a gradual decrease of C with increasing temperature, as predicted by theory. We observe a sharp decrease in C at T/T(F)=0.16, which may be due to the superfluid phase transition. While a sharp decrease in C below T(c) is predicted by some many-body theories, we find that none of the predictions fully account for the data.
A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe a dramatic decrease in the contact as the superfluid critical temperature is approached from below, followed by a gradual weak decrease as the temperature increases in the normal phase. Our theoretical results are in excellent agreement with the most recent precision ultracold atomic gas experiments. We also present results for the energy as a function of temperature in the continuum limit.
Understanding the dynamics of short-range correlations is a central challenge in strongly interacting Fermi gases. In ultracold gases, these correlations are quantified by the contact parameter, yet measurements to date have been limited to equilibrium systems or relatively slow, global dynamics. Here, we introduce a rapid spectroscopic technique based on projection of the interacting state onto an alternate scattering channel with a low-lying dimer state. We demonstrate contact measurements on the microsecond timescale-faster than the inverse Fermi energy. Using ^{40}K near a broad s-wave Feshbach resonance, we show that the strength of the dimer-projection feature scales proportionally with the contact parameter extracted from the high-frequency tail of radio-frequency spectroscopy, in agreement with coupled-channels calculations. Analysis of the spectra further reveals that the dimer feature provides the dominant contribution to the clock shift of the unitary Fermi gas, allowing the first experimental bound on this quantity. The observed deviations from universal predictions highlight the importance of multichannel effects. Our results open new avenues for studying contact correlators, hydrodynamic attractors, and quantum critical behavior.