  We demonstrate the existence of a novel quasiparticle: an exciton in a
semiconductor doubly dressed with two photons of different wavelengths: near
infrared cavity photon and terahertz (THz) photon, with the THz coupling
strength approaching the ultra-strong coupling regime. This quasiparticle is
composed of three different bosons, being a mixture of a matter-light
quasiparticle. Our observations are confirmed by a detailed theoretical
analysis, treating quantum mechanically all three bosonic fields. The doubly
dressed quasiparticles retain the bosonic nature of their constituents, but
their internal quantum structure strongly depends on the intensity of the
applied terahertz field.
