Abstract
Ultrastrong coupling of light and matter creates new opportunities to modify chemical reactions or develop novel nanoscale devices. One-dimensional Luttinger-liquid plasmons in metallic carbon nanotubes are long-lived excitations with extreme electromagnetic field confinement. They are promising candidates to realize strong or even ultrastrong coupling at infrared frequencies. We applied near-field polariton interferometry to examine the interaction between propagating Luttinger-liquid plasmons in individual carbon nanotubes and surface phonon polaritons of silica and hexagonal boron nitride. We extracted the dispersion relation of the hybrid Luttinger-liquid plasmon-phonon polaritons (LPPhPs) and explained the observed phenomena by the coupled harmonic oscillator model. The dispersion shows pronounced mode splitting, and the obtained value for the normalized coupling strength shows we reached the ultrastrong coupling regime with both native silica and hBN phonons. Our findings predict future applications to exploit the extraordinary properties of carbon nanotube plasmons, ranging from nanoscale plasmonic circuits to ultrasensitive molecular sensing.