Suppression of Interband Heating for Random Driving

Heating to high-lying states strongly limits the experimental observation of driving induced nonequilibrium phenomena, particularly when the drive has a broad spectrum. Here we show that, for entire families of structured random drives known as random multipolar drives, particle excitation to higher bands can be well controlled even away from a high-frequency driving regime. This opens a window for observing drive-induced phenomena in a long-lived prethermal regime in the lowest band.

Figure 1

Dynamics of the energy (a) and imbalance (b) for the $s$-band BHM. A prethermal plateau appears in both panels with a lifetime ${\tau }_{\mathrm{pre}}$ increasing with driving frequency $1/T$. (c) Algebraic scaling ${\tau }_{\mathrm{pre}}\sim T^{-(2n+1)}$ can be observed for $n\ge 1$, whereas for $n=0$, heating rapidly happens ($t\sim 1$). The follow parameters are used for numerical simulation $J_s=1$, $\delta J_s=0.9$, $U_s=5$, $\mu =10$.

Figure 2

(a) Dynamics of the relative population in $s$ band for the 2 RMD. Solid or dashed lines correspond to zero or finite single particle excitations to the $d$ band, respectively. Particle loss has a strong dependence on the driving frequency for $\eta =1$. (b) Dependence of the particle loss timescale ${\tau }_{\mathrm{loss}}$ on the driving frequency $1/T$ for $\eta =1$. Although in general larger $1/T$ induces more particle loss (the $t\sim T$ is depicted as a black dashed line to guide the eye), there exist several frequency windows where excitation to the $d$ band is significantly suppressed. The parameters $\delta J_s=1.2$, $J_d=7$, $U_s=5$, $U_d=3$, $U_{sd}=2$, $\mu =10$, $\mathrm{\Delta }=220$ are used for numerical simulation.

Figure 3

(a) Dynamics of the imbalance in the $s$ band for 2 RMD. For $1/T=44$, the imbalance rapidly decays to zero, whereas for $1/T=36$, the prethermalization remains almost unchanged as notable particle loss only occurs at a later timescale. (b) When particle loss occurs slowly (red dots), the prethermal lifetime ${\tau }_{\mathrm{pre}}$ fits well to an algebraic scaling with exponent $\alpha \approx 2n+1$. Otherwise, the $s$ band thermalizes faster (blue dots).