Anomalous diffusion and localization in a disorder-free atomic mixture

Abstract

The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this paradigm may break down in complex systems, where quantum interference and memory effects render the particle propagation anomalous, often fostering localization. Here we report on the observation of such anomalous dynamics in a minimal setting: an ultracold mass-imbalanced mixture of two fermionic gases in three dimensions. We release light impurities into a gas of heavier atoms and follow their evolution across different collisional regimes. Under strong interspecies interactions, by lowering the temperature we unveil a crossover from normal diffusion to subdiffusion. Simultaneously, a localized fraction of the light gas emerges, displaying no discernible dynamics over hundreds of collisions. Our findings, incompatible with the conventional Fermi-liquid picture, are instead captured by a model of an atom propagating through a (quasi-)static disordered landscape of point-like scatterers. These results highlight the key role of quantum interference in our mixture, which emerges as a versatile platform for exploring disorder-free localization phenomena.

Figures (7)

• Figure 1: Experimental protocol and data analysis.a, Experimental sequence: Li$|1\rangle$ atoms (red) are initially confined at the center of a Cr$|2\rangle$ reservoir (green). A $0.9$ ms-long radio-frequency pulse maximizes the chromium transfer into the Cr$|1\rangle$ state (blue) near a Li$|1\rangle$-Cr$|1\rangle$ Feshbach resonance, and immediately after the vertical beam is switched off, allowing the Li cloud to axially expand in the presence of a weak harmonic confinement, characterized by a frequency of 17 Hz (13 Hz) for the Li (Cr) component. b, Examples of radially-integrated profiles of the expanding Li cloud. Inset: Time evolution of the corresponding mean-square displacement, which sets the color scale in the main panel. c, Examples of $\langle x^2(t) \rangle$ dynamics recorded for different $R^*/a$ values (dots), together with best fits (solid lines) to Eq. (\ref{['Eq1']}), limited to $t<t_{\text{max}}$ defined in the text, yielding different $\alpha$ values, see color legend. Error bars are the s.e.m. of 4–6 measurements. Data are arbitrarily shifted along the vertical direction for display purposes.
• Figure 1: Axial breathing dynamics of a non-interacting lithium cloud after release. Dots are experimental points, error bars are the s.e.m. of 4–6 measurements. The solid line is the best-fit based on the analytic predictions of Ref. Uhlenbeck1930 for the non-interacting case, see also Ref. ketterle2008.
• Figure 2: Lithium dynamics across the Li-Cr Feshbach resonance.a, Scaling exponent $\alpha$ and b, Generalized diffusion constant $D_{\alpha}$, obtained at different $R^*/a$ values for a Cr temperature $T_{\text{\tiny Cr}} = 550$ nK. Experimental data (dots) and semi-classical simulation predictions (solid lines) are determined from fits of $\langle x^2(t) \rangle$ to Eq. (\ref{['Eq1']}), and error bars represent the fit uncertainties. Horizontal dashed lines mark values measured for vanishing interactions. (c, d), Same as panels (a, b) for a lower $T_{\text{\tiny Cr}}=350$ nK.
• Figure 2: Experimental methods to extract $F_{\text{loc}}$.a, Examples of radially-integrated Li profiles (shaded areas) at short and long times for normally-diffusive data. The green curve is the best fit according to Eq. (\ref{['FLoc1']}), with the dashed black (solid blue) line representing the Gaussian (exponential) part. b, Same as a, but for subdiffusive data. The exponential part shows no dynamics over the experimental timescale. c, Examples of diffusive (red dots) and subdiffusive (violet, green, blue) time-correlation data $C(t)$, together with best fits (solid lines) according to Eq. (\ref{['FLoc2']}). d, Comparison between $F_{\text{loc,1}}$ and $F_{\text{loc,2}}$. The blue line is $y=x$.
• Figure 3: Crossover from normal to subdiffusive transport in the resonant regime. Generalized diffusion coefficient $D_{\alpha}$ (blue squares, left axis) and power-law exponent $\alpha$ (red circles, right axis) as a function of the dimensionless parameter $\langle k_{_T} / \bar{n}^{\text{\tiny 1/3}} \rangle$. Experimental data are compared with the results obtained from ISA simulations (solid lines with corresponding colors), based on fits to Eq. (\ref{['Eq1']}). As the system transitions from normal ($\alpha \geq 1$) to subdiffusive ($\alpha < 1$) behavior, the simulation qualitatively deviates from the experimental observation. Error bars and shaded areas represent the fit uncertainties for experimental and simulated data, respectively.