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Cavity enhanced second-order nonlinear quantum photonic logic circuits

Rahul Trivedi, Uday K. Khankhoje, Arka Majumdar

Published Nov 26, 2015• 1 citation
OpenAlex

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.

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Abstract Kerr nonlinear cavities displaying optical thresholding have been proposed for the realization of ultra-low power photonic logic gates. In the ultra-low photon number regime, corresponding to energy levels in the attojoule scale, quantum input–output models become important to study the effect of unavoidable quantum fluctuations on the performance of such logic gates. However, being a quantum anharmonic oscillator, a Kerr-cavity has an infinite dimensional Hilbert space spanned by the Fock states of the oscillator. This poses a challenge to simulate and analyze photonic logic gates and circuits composed of multiple Kerr nonlinearities. For simulation, the Hilbert of the oscillator is typically truncated to the span of only a finite number of Fock states. This paper develops a quasi-principal components approach to identify important subspaces of a Kerr-cavity Hilbert space and exploits it to construct an approximate reduced model of the Kerr-cavity on a smaller Hilbert space. Using this approach, we find a reduced dimension model with a Hilbert space dimension of 15 that can closely match the magnitudes of the mean transmitted and reflected output fields of a conventional truncated Fock state model of dimension 75, when driven by an input coherent field that switches between two levels. For the same input, the reduced model also closely matches the magnitudes of the mean output fields of Kerr-cavity-based AND and NOT gates and a NAND latch obtained from simulation of the full 75 dimension model.
A central goal in photonic quantum information processing is the ability to perform high-fidelity logic gates between multiple optical qubits. Here, we present our recent theoretical work on using optical nonlinearities to implement controlled-phase gates between two optical qubits. Our approach is based on using dynamically coupled cavities to convert photons travelling in a waveguide into highly confined cavity modes. This conversion enables very strong interactions between photons in quasi-monochromatic modes, which enables high fidelity gates. We will discuss gate protocols based on second- and third order nonlinear materials as well as interactions with two-level emitters.
Weak material nonlinearity at optical frequencies poses a serious hurdle to realizing optical bistability at low optical powers, which is a critical component for digital optical computing. In this paper, we explore the cavity enhancement of the second-order optical nonlinearity in order to determine the feasibility of few photon optical bistability. Starting from a quantum optical formalism of a doubly resonant cavity (required to meet the condition of phase matching), we derive a dynamic classical model of a cavity that is bistable at the fundamental mode. We analyze the optical energy and the switching speed as a function of the cavity quality factors and mode volumes and identify the regime where only ten's of photons are required to perform the switching. An unusual trend in the switching speed is also observed, where the speed monotonically decreases as the cavity linewidth increases. This is ascribed to the increase in the switching gain with increasing cavity linewidth.
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Motivated by rapidly advancing capabilities for extensive nanoscale patterning of optical materials, I propose an approach to implementing photonic sequential logic that exploits circuit-scale phase coherence for efficient realizations of fundamental components such as a NAND-gate-with-fanout and a bistable latch. Kerr-nonlinear optical resonators are utilized in combination with interference effects to drive the binary logic. Quantum-optical input-output models are characterized numerically using design parameters that yield attojoule-scale energy separation between the latch states.