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Kerr nonlinear cavities displaying optical thresholding have been proposedfor the realization of ultra-low power photonic logic gates. In the ultra-lowphoton number regime, corresponding to energy levels in the attojoule scale,quantum input-output models become important to study the effect of unavoidablequantum fluctuations on the performance of such logic gates. However, being aquantum anharmonic oscillator, a Kerr-cavity has an infinite dimensionalHilbert space spanned by the Fock states of the oscillator. This poses achallenge to simulate and analyze photonic logic gates and circuits composed ofmultiple Kerr nonlinearities. For simulation, the Hilbert of the oscillator istypically truncated to the span of only a finite number of Fock states. Thispaper develops a quasi-principal components approach to identify importantsubspaces of a Kerr-cavity Hilbert space and exploits it to construct anapproximate reduced model of the Kerr-cavity on a smaller Hilbert space. Usingthis approach, we find a reduced dimension model with a Hilbert space dimensionof 15 that can closely match the magnitudes of the mean transmitted andreflected output fields of a conventional truncated Fock state model ofdimension 75, when driven by an input coherent field that switches between twolevels. For the same input, the reduced model also closely matches themagnitudes of the mean output fields of Kerr-cavity-based AND and NOT gates anda NAND latch obtained from simulation of the full 75 dimension model.

Model reduction of cavity nonlinear optics for photonic logic: A quasi-principal components approach