Fig. 4: Quantum sensing of the Higgs collective mode and terahertz (THz) dynamical inversion symmetry breaking in the multi-dimensional THz coherent nonlinear spectra.
a, b Correlated differential transmission signal \({{{{{{{{\mathcal{E}}}}}}}}}_{{{{{{{{\rm{NL}}}}}}}}}(t,\tau )\) for calculations with and without electromagnetic propagation effects leading to persistent inversion-symmetry breaking. The signal with propagation effects persists even when the pump and probe pulses do not overlap in time. c, d The corresponding two-dimensional spectra. Green circles indicate the dominant inversion-symmetry breaking signals (ISWM). Lightwave propagation generates a series of inversion-symmetry breaking wave-mixing signals along the ωτ-axis (coherence time) for fixed ωt = ωH (vertical dashed magenta line) at the Higgs mode frequency in addition to the correlated wave-mixing peaks at ωt = ωH + ω0 (vertical dashed black line). e, f Slices of \({{{{{{{{\mathcal{E}}}}}}}}}_{{{{{{{{\rm{NL}}}}}}}}}\) for ωt = ωH (vertical magenta dashed line in c and d) and ωt = ωH + ω0 (vertical black dashed line in c and d). The full calculation with lightwave propagation (shaded area) is compared with the calculation without propagation (blue line), and the calculation with propagation but without pump-probe coherent modulation of the order parameter, δ∣Δpp∣ = 0 (red line). Vertical dashed lines indicate dominant inversion-symmetry breaking wave-mixing (e) and correlated wave mixing (CWM) (f) signals. The correlated high-order wave mixing peak at ωt = ωH + ω0 is not affected by propagation-induced inversion symmetry-breaking effects, while the inversion-symmetry breaking wave-mixing signals at the Higgs mode frequency ωt = ωH vanish when propagation effects and/or δ∣Δpp∣ are switched off.
