Fig. 3: Time-resolved nonlinear dynamics of the polaritonic saturable absorber.

a Experimental principle of two-dimensional THz spectroscopy. The two THz pulses (red and blue waveforms, delayed by a delay time τ) prepare and probe the nonlinear dynamics of the saturable absorber. The emitted THz waveform \({\mathcal{E}}\)_AB is sampled electro-optically as a function of the delay time t. b Colour plot of the emitted nonlinear electric field, \({\mathcal{E}}\)_NL = \({\mathcal{E}}\)_AB − \({\mathcal{E}}\)_A − \({\mathcal{E}}\)_B as a function of the electro-optic delay time t and τ at a peak THz intensity of I = 7 W cm⁻². c Two-dimensional Fourier transform of the electric field in b. d Simulated 2D spectra, calculated from a semiclassical theory. e Experimental (red curve) and simulated pump–probe signal (black curve) as a function of the delay time τ for a fixed electro-optic delay time of t = 1.66 ps. The maxima are offset from time zero by Δτ = 0.5 ps. Dashed blue curve: exponential decay with a characteristic time of 3.3 ps, as a guide to the eye. f Calculated dynamics of the cavity field amplitude (|E_cav|, red curve), and the population of the second subband (ρ₂₂, blue curve). Black dashed curve, fit of ρ₂₂ by a time-integral of a Gaussian envelope function, demonstrating a rise time of ∼900 ps.