Abstract
We discuss the feasibility of a quantum nondemolition measurement (QND) of photon number based on cross phase modulation due to the Kerr effect in photonic crystal waveguides (PCW's). In particular, we derive the equations for two modes propagating in PCW's and their coupling by a third order nonlinearity. The reduced group velocity and small cross-sectional area of the PCW lead to an enhancement of the interaction relative to bulk materials. We show that in principle, such experiments may be feasible with current photonic technologies, although they are limited by material properties. Our analysis of the propagation equations is sufficiently general to be applicable to the study of soliton formation, all-optical switching and can be extended to processes involving other orders of the nonlinearity.
Highlights
In this paper we focus on the feasibility of realizing the quantum nondemolition measurement (QND) photon number measurement proposed in [1] in photonic crystal waveguides (PCW’s)
We show that the reduction of group velocity and small interaction volumes in PCWs lead to an effective enhancement of the third order nonlinearity and, theoretically, make QND experiments with high quality structures and attainable laser power levels feasible
We have derived the equations of motion for a probe and signal wave interacting via the third order nonlinearity in a photonic crystal waveguide
Summary
In this paper we focus on the feasibility of realizing the QND photon number measurement proposed in [1] in photonic crystal waveguides (PCW’s). The radiative lifetime of such QD’s coupled to PhC cavities is ≈ 0.2 − 1ns In this experiment, a weak signal pulse is combined with a strong coherent probe in one arm of a Michaelson interferometer. This means that Np > 1023 probe photons are needed for the bulk experiment in order to overcome the shot noise when the probe is in a coherent state and the signal is in a number state This requires a source that can produce a 48kJ pulse with a nanosecond width. The area of the PhC waveguide is of order λ n
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