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arXiv 1609.05929quant-phcs.SYeess.SY
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腔体非线性光学的模型降维：一种准主成分方法

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

School of Electrical Engineering and Telecommunications, UNSW Australia（新南威尔士大学电气工程与电信学院）

Zhan Shi, Hendra I. Nurdin

备注：
33 pages (with 17 pages of appendices), 5 figures. Closer to published version. Published in Journal of Physics D
发表信息：
J. Phys. D: Appl. Phys. 49, 465501 (2016)
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AI总结：

本文提出一种准主成分方法，用于降维腔体非线性光学模型，以高效模拟光子逻辑门。通过识别重要子空间，构建更小维度的近似模型，实现对光子逻辑门性能的准确分析。

摘要：

Kerr非线性腔体显示光学阈值特性，已被提议用于实现超低功率光子逻辑门。在超低光子数极限下，量子输入-输出模型对于研究不可避免的量子涨落对逻辑门性能的影响至关重要。然而，作为量子非谐振子，Kerr腔具有无限维的希尔伯特空间，由振子的费曼态张成。这给模拟和分析由多个Kerr非线性组成光子逻辑门和电路带来了挑战。为了模拟，通常将振子的希尔伯特空间截断为有限数量的费曼态的张成。本文开发了一种准主成分方法，以识别Kerr腔希尔伯特空间的重要子空间，并利用该方法在更小的希尔伯特空间上构建近似降维模型。使用这种方法，我们发现一个希尔伯特空间维数为15的降维模型，当由输入相干场在两个能级之间切换时，可以接近传统截断费曼态模型（维数75）的平均传输和反射输出场的幅度。对于相同的输入，降维模型也能够接近Kerr腔基于的AND和NOT门以及由完整75维模型模拟得到的NAND锁存器的平均输出场幅度。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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