Fig. 2.

Metastability measurement. Shown is the observation of two distinct steady-state imbalances $\overline{\mathrm{\Theta }}$, shown in orange and green, and exemplary time traces. We prepare an MI and then quench the detuning from ${\mathrm{\Delta }}_{\text{𝖼}}/2\pi =-50$ MHz to ${\mathrm{\Delta }}_{\text{𝖼}}^{\text{𝖿}}$ closer to resonance within $20$ ms, increasing $U_{\text{𝗅}}$. (A) Mean values of the imbalance $\overline{\mathrm{\Theta }}$. Errors are SD. The imbalance $\overline{\mathrm{\Theta }}$ is separated by a gap of $5.2(1.4)\times {10}^3$ atoms into two levels. (B) Histogram as a function of $\overline{\mathrm{\Theta }}$ and ${\mathrm{\Delta }}_{\text{𝖼}}^{\text{𝖿}}$ with bin sizes of $700$ atoms in $\overline{\mathrm{\Theta }}$ and $0.5$ MHz in ${\mathrm{\Delta }}_{\text{𝖼}}^{\text{𝖿}}$. (C) Histogram of the normalized sum of all counts with respect to $\overline{\mathrm{\Theta }}$. For the normalization see Evaluation of the Metastability Measurement. (D) Exemplary time traces for quenches ending at ${\mathrm{\Delta }}_{\text{𝖼}}^{\text{𝖿}}/2\pi =-28$ MHz (Left) and ${\mathrm{\Delta }}_{\text{𝖼}}^{\text{𝖿}}/2\pi =-18$ MHz (Right). The shaded regions indicate where the averaged imbalance $\overline{\mathrm{\Theta }}$ is extracted. This experiment was performed with $25(2)\times {10}^3$ atoms at maximum lattice depths of $(V_{\text{𝗑}},V_{\text{𝗒}},V_{\text{𝗓}})=(17.3E_{\text{𝖱}}^{\text{𝟩𝟪𝟧}},30.7E_{\text{𝖱}}^{\text{𝟨𝟩𝟣}},11.1E_{\text{𝖱}}^{\text{𝟩𝟪𝟧}})$.