Localized vibrational modes in waveguide quantum optomechanics with spontaneously broken PT symmetry

We study theoretically two vibrating quantum emitters trapped near a one-dimensional waveguide and interacting with propagating photons. We demonstrate, that in the regime of strong optomechanical interaction the light-induced coupling of emitter vibrations can lead to formation of spatially localized vibration modes, exhibiting parity-time (PT ) symmetry breaking. These localized vibrations can be interpreted as topological defects in the quasiclassical energy spectrum.