Real-space observation of flat-band ultrastrong coupling between optical phonons and surface plasmon polaritons

Strong and ultrastrong coupling are pivotal phenomena in science and technology, where light-matter hybridization opens new avenues for manipulating quantum states, material properties or chemical reactions. Here we use pump-probe nanospectroscopy for real-space mapping of vibrational ultrastrong coupling between optical phonons in a thin SiC layer and surface plasmon polaritons in a semiconductor (InAs) substrate. By adjusting the InAs carrier density through photoexcitation, we align the flat dispersion limit of the surface plasmon polaritons to the SiC transverse optical phonon, yielding hybridized modes in an intriguingly wide wavevector range. This flat-band ultrastrong coupling contrasts conventional ultrastrong coupling, where hybridization typically occurs in a narrow wavevector range. We further predict flat-band coupling for weak oscillators, illustrated by strong coupling of molecular vibrations with low-loss surface phonon polaritons at their dispersion limit. Achieving strong and ultrastrong coupling over a large wavevector range, and thus many hybrid modes, may benefit polariton chemistry and phase transitions induced by strong and ultrastrong coupling.