The Formation of Photon-Molecules in Nanoscale Waveguides

We investigate the formation of photon bound states in a system of interacting photons inside nanoscale wires. The photons interact through the exchange of vibrational modes induced along the waveguide mainly due to radiation pressure. The problem of many-body photons is treated in using the formalism of contour Green's functions under the T-matrix approximation. The complex pole of the T-matrix is a signature for the appearance of photon-molecules. The analysis of such singularity provides the critical temperature at which the T-matrix approximation breaks down and photon-molecules appear. For strongly interacting slow photons the amplitude of the photon-molecule wavefunction acquires a significant quantum nonlinear phase inside the nanowire. Photon bound-states can be implemented for quantum information processing as quantum logic gates, e.g. for $\pi$ phase shift the photon-molecule is shown to serve as a Z-controlled gate.