Dipole-Mode Spectrum and Hydrodynamic Crossover in a Resonantly Interacting Two-Species Fermion Mixture

TL;DR

We address how energy- and momentum-transport arise in a mass-imbalanced two-species Fermi gas as interspecies interactions are tuned through a resonant s-wave channel. The authors combine a simple center-of-mass friction-and-mean-field model with precision two-species dipole-mode spectroscopy in a Dy-K mixture to characterize the collisionless-to-hydrodynamic crossover across a Feshbach resonance. They observe a persistent crossover mode and a second mode that splits into two purely damped modes in the hydrodynamic regime; among these, a fast-damping mode provides a precise measure of interspecies drag, and a microscopic friction coefficient is extracted, showing universal behavior on resonance. Overall, the work provides a quantitative framework for hydrodynamic transport in resonantly interacting two-component Fermi gases and establishes a versatile spectroscopic tool for exploring strongly correlated states in mass-imbalanced mixtures.

Abstract

Ultracold quantum-gas mixtures of fermionic atoms with resonant control of interactions offer a unique test-bed to explore few- and many-body quantum states with unconventional properties. The emergence of such strongly correlated systems, as for instance symmetry-broken superfluids, is usually accompanied by hydrodynamic collective behavior. Thus, experimental progress in this field naturally requires a deep understanding of hydrodynamic regimes. Here, we report on experiments employing a tunable Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K near quantum degeneracy. We investigate the full spectrum of dipole modes across a Feshbach resonance and characterize the crossover from collisionless to deep hydrodynamic behavior in measurements of frequencies and damping rates. We compare our results with a theoretical model that considers the motion of the mass centers of the two species and we identify the contributions of friction and mean-field interaction. We show that one oscillating mode exists over the whole range of interactions, exhibiting striking changes of frequency and damping in the deep hydrodynamic regime. We observe the second oscillating mode to split into two purely exponential damping modes. One of these exponential modes shows very fast damping, faster than any other relevant timescale, and is largely insensitive against experimental imperfections. It provides an accurate measure for the interspecies drag effect, which generalizes the concept of spin drag explored in other experiments. We characterize the interspecies drag locally in terms of a microscopic friction coefficient and we discuss its unitarity-limited universal behavior on top of the resonance.

Figures (11)

• Figure 1: Predictions of the theoretical model for the dependence of dipole-mode frequencies (a) and damping rates (b) on the friction parameter $\beta$. Here we assume $\kappa=0$ (no reactive coupling) and typical experimental conditions ($\omega_{\rm Dy}/2\pi = \qty{59}{Hz}$, $\omega_{\rm K}/2\pi = \qty{177}{Hz}$, $N_{\rm Dy}/N_{\rm K} = 2.5$).
• Figure 2: Center-of-mass oscillations of the Dy (blue) and K (orange) clouds for increasing interaction strength. The vertical position is obtained from time-of-flight images and plotted versus the hold time in the trap. The atom number ratio is fixed, $N_{\rm Dy}/N_{\rm K}=2.42$. (a) Near the zero crossing of the scattering length, where $x\rightarrow \pm\infty$, the two clouds oscillate independently. (b) and (c) When approaching the resonance, $x = 1.6$ and $0.7$, increasing interaction effects are observed. (d) On resonance, $x=0$, the interspecies interaction results in a locked hydrodynamic motion of both components. The positions of the clouds are detected after a time of flight of 10ms for Dy and 5ms for K. For better comparison, the K signal is rescaled by a factor of 2. The uncertainties are smaller than the size of the symbols and the solid curves represent fits based on our theoretical model (see text).
• Figure 3: Mode spectrum across the resonance. The pseudo-color plot shows the amplitude spectrum derived by Fourier transforming the oscillation signals recorded for (a) the K atoms and for (b) the Dy atoms. The solid white line and the black-white dashed line are the theoretical curves for the K mode and the Dy crossover mode (for details see Sec. \ref{['sec:Dycrossovermode']}). Note that the horizontal stripes visible in (b) are an artefact related to the Fourier transform of the rectangular time window.
• Figure 4: Resonance behavior of (a) frequency and (b) damping rate of the Dy crossover mode. The blue data points represent the measured values with 1$\sigma$ error bars (in most cases smaller than the symbol size). The red solid curves show the results of a joint fit to frequency and damping based on the model presented in Sec. \ref{['sec:modespectrum']}. The red shaded area represents the 95% confidence band of the fit.
• Figure 5: (a) Phase shift $\Delta\phi=\phi_{\rm K}-\phi_{\rm Dy}$ and (b) amplitude ratio $A_{\rm K}/A_{\rm Dy}$ of the two species oscillating in the Dy crossover mode. The blue data points represent the measured values with 1$\sigma$ error bars. The red solid curves show the result of our model with the same parameter values as used in Fig. \ref{['fig:DymodeFreqAndDamping']} (no independent fit carried our here).