Extended Data Figure 3: Adiabaticity of the modulation ramp in the many-body system.

a, Starting from the static lattice, the modulation amplitude is ramped up and subsequently kept at a fixed value to allow for a 5 ms equilibration time. The ramp up time depends on the chosen configuration and is 3.333 ms (2 ms) for a modulation frequency of ω/(2π) = 3 kHz (6 kHz). We start the detection of nearest-neighbour spin–spin correlations C in the effective Hamiltonian H_eff by quenching the tunnelling to zero as we ramp up the lattice depth in all directions during the modulation within 100 μs. To estimate the adiabaticity of the final state, we perform a second type of measurement in which we revert the driving ramp and subsequently wait an additional 5 ms before the detection in the reverted static Hamiltonian . If the ramp scheme of the modulation is fully adiabiatic, we expect a reversal of the correlations to their static value. b, The nearest-neighbour spin–spin correlator C is plotted against the modulation amplitude in the off-resonant driving regime (U/h = 0.93(2) kHz, ω/(2π) = 6 kHz). The filled green circles are measured in the modulated system (same data as in Fig. 2b) and the open green circles after ramping off the modulation. The correlations no longer reach the level of the static case at K₀ = 0 after reverting the ramp. We attribute this to some extent to a reduced lifetime of correlations, which is found to be 14(5) ms at K₀ = 1.26(4), compared to 92(16) ms in the static case. c, Spin–spin correlator for different driving strengths K₀ in the near-resonant regime for U < ħω (blue; U = 4.4(1) kHz, ω/(2π) = 6 kHz) and in the regime of enhanced antiferromagnetic correlations (red; U/h = 3.8(1) kHz, ω/(2π) = 3 kHz). Filled data points represent the effective states in the modulated system and open data points are measured after ramping off the modulation. Again, correlations do not reach the static value after reverting the driving ramp, owing to the finite lifetime (see also Extended Data Fig. 1). Data points and error bars denote the mean and standard error of 10 individual measurements at different times within one driving period (see Methods).

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