  Strong coupling between light and matter occurs when the two interact
strongly enough to form new hybrid modes called polaritons. Here we report on
the strong coupling of both the electric and magnetic degrees of freedom to an
ultrafast terahertz (THz) frequency electromagnetic wave. In our system,
optical phonons in a slab of ferroelectric lithium niobate (LiNbO$_3$) are
strongly coupled to a THz electric field to form phonon-polaritons, which are
simultaneously strongly coupled to magnons in an adjacent slab of canted
antiferromagnetic erbium orthoferrite (ErFeO$_3$) via the THz magnetic field.
The strong coupling leads to the formation of new magnon-phonon-polariton
modes, which we experimentally observe in the wavevector-frequency dispersion
curve as an avoided crossing and in the time-domain as a normal-mode beating.
Our simple yet versatile on-chip waveguide platform provides a promising avenue
by which to explore both ultrafast THz spintronics applications and the quantum
nature of the interaction.
