We develop a systematic method for deriving a quantum optical multi-mode Hamiltonian for the interaction of photons and phonons in nanophotonic dielectric materials by applying perturbation theory to the electromagnetic Hamiltonian. The Hamiltonian covers radiation pressure and electrostrictive interactions on equal footing. As a paradigmatic example, we apply our method to a cylindrical nanoscale waveguide. We use the resulting multi-mode Hamiltonian to derive an effective phonon-mediated interaction between photons propagating in the material. We predict strong non-linear phase shifts even among two photons, comparable to what can be achieved in nonlinear atomic media (comprising cold Rydberg atoms).
Hashem Zoubi and Klemens Hammerer, "Photon-phonon coupling in nanophotonics
(Conference Presentation)," Proc. SPIE 9884, Nanophotonics VI, 98840H (Presented at SPIE Photonics Europe: April 04, 2016; Published: 26 July 2016); https://doi.org/10.1117/12.2230177.5042210260001.
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