Here we present a fully quantum mechanical transfer function model for travelling wave whispering gallery mode resonators. Micro-resonators, such as ring and disk resonators, have been key to the development of high performance chip-scale photonic systems due to their compact footprint, sensitivity and low power operation. In this work we present the first understanding of these resonators to any arbitrary multi-photon state. This was achieved by developing a model that utilizes an efficient scheme for determining the quantum electrodynamic transfer functions relating the Bosonic input/output mode operators in the resonator. This approach has been applied to the understanding of both single photon and two-photon states. In this work we will present a key result on a resonant Hong-Ou-Mandel effect that is inherently realized for any resonator-waveguide coupling constants and can operate over a wide range of resonance conditions. Furthermore, the transfer function approach allows for the straightforward understanding of any resonator-waveguide network with arbitrary modes. This will directly enable the application of quantum resonators to the realization of robust, scalable and efficient Linear Optical Quantum Computing (LOQC) gates. Consequently, it is expected that resonators can be used for both Nonlinear Sign Shift and CNOT gates. And these gates can robustly controlled and efficiently tuned using standard electro-optic effects available in a variety of material systems, such as, Silicon.

Date Published: 28 May 2013
PDF: 10 pages
Proc. SPIE 8749, Quantum Information and Computation XI, 87490R (28 May 2013); doi: 10.1117/12.2015882

Published in SPIE Proceedings Vol. 8749:
Quantum Information and Computation XI
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)