Strong coupling of collective intermolecular vibrations in organic materials at terahertz frequencies

Several years ago, strong coupling between electronic molecular transitions and photonic structures was shown to modify the electronic landscape of the molecules and affect their chemical behavior. Since then, this concept has evolved into a new field known as polaritonic chemistry. An important ingredient in the progress of this field was the demonstration of strong coupling with intra-molecular vibrations, which enabled the modification of processes occurring at the electronic ground-state. Here we demonstrate strong coupling with collective, inter-molecular vibrations occurring in organic materials in the low-terahertz region (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lesssim$$\end{document}≲1012 Hz). Using a cavity filled with α-lactose molecules, we measure the temporal evolution and observe coherent Rabi oscillations, corresponding to a splitting of 68 GHz. These results take strong coupling into a new class of materials and processes, including skeletal polymer motions, protein dynamics, metal organic frameworks and other materials, in which collective, spatially extended degrees of freedom participate in the dynamics.


Supplementary Note 1: Signal processing and deconvolution scheme
Time-resolved electro-optic sampling measurements suffer from various satellite signals that accompany the signals of interest, particularly in such long-time measurements as used in our experiments (~100ps long). Those artifact signals originate from various reflections of both the THzfield and the optical read-out pulse in the electro-optic detection crystal (typically GaP/ZnTe).
Moreover, in our case, additional internal reflections within the 1 mm-thick quartz substrates used for the mirrors CM1 and CM2 (between the Au layers and the quartz-air interface) are also observed in the raw data that is measured.
While the multiple reflections of the THz field in the GaP sampling crystal result in repetitive signals which extend toward the positive-time direction of our measurement (namely following the "real" THz field, with periodicity of ~12 ps for our 0.5 mm GaP crystal), the reflections of the optical readout pulse are manifested as signals at negative time. As shown in Supplementary Figure 1 To overcome this difficulty we implement a deconvolution scheme by which the signal of interest can be extracted from the raw signal 1,2 . First, we obtain the transfer function of the TD-THz spectrometer, ℎሺ‫ݐ‬ሻ, by performing a reference measurement of a thin empty cavity (~65 µm), such with ܲሺߥሻ = ℱሼ‫‬ሺ‫ݐ‬ሻሽ and ܴ݂݁ሺߥሻ = ℱሼ‫݂݁ݎ‬ሺ‫ݐ‬ሻሽ being the Fourier transforms of the real transmitted pulse and the measured reference, respectively.
In a similar manner, for each one of the measured signals of the cavity (with and without the αlactose), the raw (measured) signal ‫ݏ‬ ሺ‫ݐ‬ሻ is given by the convolution of the real signal ‫ݏ‬ሺtሻ with the transfer function ℎሺ‫ݐ‬ሻ. Therefore, the real signal transmitted through the cavity can be obtained using The result of such deconvolution procedure for an empty cavity is shown in Supplementary Figure 3.

Supplementary Note 2: Intensity independence of the Rabi splitting
In order to verify that the Rabi splitting is not induced by the THz probe pulse, we repeated the measurements on a cavity with an α-lactose pellet under similar conditions as in Figure 4b with several different intensities of the THz pulse, which was achieved by varying the intensity of the pump beam which generated the THz field. Supplementary Figure 4 shows the power spectra of the transmitted THz fields (with peak field strengths of 50, 30 and 17 kV/cm for the input pulses). For all three cases the frequencies of the polaritonic resonances, and hence also the Rabi splitting values, do 4 not vary with the pulse intensity, confirming that the THz pulse only acts as a probe for the linear modes of the coupled system. Notice that the sample used in these measurements is slightly different than the one used for Figures 3-5, however, all three measurements shown in Supplementary Figure 4 were conducted with the same sample.  Figure 4d. Δ = ߥ c − ߥ vib is the detuning between the cavity resonance and the α-lactose absorption peak.