Cavity enhanced second-order nonlinear photonic logic circuits

TL;DR

This paper proposes a theoretical design for all-optical logic circuits using second-order nonlinear bimodal cavities, demonstrating potential energy efficiency advantages over third-order nonlinear designs at realistic cavity quality factors.

Contribution

The paper introduces a novel theoretical framework for second-order nonlinear photonic logic circuits and compares their performance and energy efficiency with third-order designs.

Findings

$ ext{Chi}^{(2)}$ design is more energy-efficient at realistic Q factors.

$ ext{Chi}^{(3)}$ design requires ultra high Q to match energy consumption.

Second-order nonlinear cavities outperform third-order in practical conditions.

Abstract

A large obstacle for realizing quantum photonic logic is the weak optical nonlinearity of available materials, which results in large power consumption. In this paper, we present the theoretical design of all-optical logic with second order ($\chi^{(2)}$) nonlinear bimodal cavities and their networks. Using semiclassical models derived from the Wigner quasi-probability distribution function, we analyze the power consumption and signal-to-noise ratio (SNR) of networks implementing an optical AND gate and an optical latch. Comparison between the second and third order $(\chi^{(3)})$ optical logic reveals that while the $\chi^{(3)}$ design outperforms the $\chi^{(2)}$ design in terms of the SNR for the same input power, employing the $\chi^{(3)}$ nonlinearity necessitates the use of cavities with ultra high quality factors ($Q\sim 10^6$) to achieve gate power consumption comparable to that of the $\chi^{(2)}$ design at significantly smaller quality factors ($Q \sim 10^4$). Using realistic estimates of the $\chi^{(2)}$ and $\chi^{(3)}$ nonlinear susceptibilities of available materials, we show that at achievable quality factors ($Q \sim 10^4$), the $\chi^{(2)}$ design is an order of magnitude more energy efficient than the corresponding $\chi^{(3)}$ design.