This PDF file includes:

• Section S1. Experimental methods
• Section S1.1. Sample preparation
• Section S1.2. 2D IR spectrometer
• Section S1.3. 3D Fourier transformation
• Section S1.4. Nonlinear signal pump and probe power dependence
• Section S2. Supporting results
• Section S2.1. Transmission and transient pump-probe spectra of uncoupled systems
• Section S2.2. 2D IR and transient pump-probe spectra and 2D-IR spectral cuts
• Section S2.3. 2D IR spectra for various molecular concentrations
• Section S2.4. Early-time dynamics of 2D IR spectral cuts
• Section S2.5. Two-component spectral fitting of absorptive pump-probe spectra
• Section S3. Theory
• Section S3.1. Scaling of polariton nonlinearities
• Section S3.2. Feynman diagrams for the AC signal
• Section S3.3. Phenomenological simulation of polariton bleach
• Section S3.4. Cavity coherence volume
• Fig. S1. Scheme of 2D IR experimental setup.
• Fig. S2. 3D FFT frequency domain (ω₁-ω₂-ω₃) spectra.
• Fig. S3. IR power dependence.
• Fig. S4. Linear transmission and pump-probe spectra of uncoupled W(CO)₆/hexane systems with 12- and 25-μm cavity longitudinal lengths.
• Fig. S5. Pump-probe and 2D IR spectra and their spectral cuts at LP/UP pump frequencies.
• Fig. S6. 2D IR spectra of the 25-μm system at t₂ = 0 ps with various concentrations.
• Fig. S7. Early-time dynamics of 2D IR spectral cuts at ω₁ = ω_LP/ω_Dark and AC/DC components of LP/UP cuts between 0 and 6 ps.
• Fig. S8. Spectral fitting of 25-μm systems with t₂ = 0 ps at ω₁ = ω_LP and ω₁ = ω_UP.
• Fig. S9. Feynman diagrams representing the oscillating nonlinear responses (AC components) in each region.
• Table S1. Parameters of two-component fitting.
• References (42–46)

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