Fig. 3: Long-time dynamics.
From: Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
a Imbalance time traces at Δ↓ = 3.30(3)J and J/h = 0.54(1)kHz for U = 0J (spin-polarized, light blue) and U = 5J (spin-resolved measurement, dark blue). The shaded trace is an ED calculation for L = 16 (“Methods”). Each data point is averaged over 12 individual experimental realizations. Inset: ED calculation for L = 16 in a clean system with Δ↓ = Δ↑ = 3J, ωh = 0 and U = 5J using a Néel-ordered initial CDW. The dashed lines show the analytic prediction for the non-interacting steady-state imbalance [Eq. (3)]. b Steady-state imbalance versus Δ↓ measured at U = 0J (spin-polarized, light blue) and U = 5J (spin-resolved measurement, dark blue). Each data point is averaged over ten equally spaced times in a time window between 70τ and 100τ (U = 0J) and 340τ and 370τ (U = 5J). The solid line shows the analytic prediction for \({{{{\mathcal{I}}}}}^{\downarrow }\) [Eq. (3)] and the dashed line indicates the first root of the Bessel function at Δ↓ ≈ 1.5J. c Spin-resolved steady-state imbalance versus interaction strength at Δ↓ = 1.10(1)J. Each point is averaged over ten time steps equally spaced between 170τ and 200τ. d Spin-resolved steady-state imbalance versus interaction strength as in (c) for Δ↓ = 3.30(3)J. The shaded trace is an ED simulation, which is averaged over the same time steps as in (c) and where the width indicates the 1σ standard deviation. e Resonances extracted from interaction scans for U > 0 as in (d) for different tilt values (Supplementary Note 12). The color plot shows ED calculations for the same parameters as in the experiment, but with ωh = 0, for L = 13 sites. The dashed line indicates the analytic prediction for the resonance \({U}_{{{{\rm{res}}}}}\simeq 2{{{\Delta }}}_{\downarrow }-8{J}^{2}/(3{{{\Delta }}}_{\downarrow })\). The gray shaded area in (b),(c) indicates our calibrated detection resolution. In all panels error bars denote the SEM.
