Oba Junpei, Kajita Seiji, Soeda Akihito
Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi, 480-1192, Japan.
Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan.
Sci Rep. 2024 Feb 8;14(1):3208. doi: 10.1038/s41598-024-53246-2.
Photons are elementary particles of light in quantum mechanics, whose dynamics can be difficult to gain detailed insights, especially in complex systems. Simulation is a promising tool to resolve this issue, but it must address the curse of dimensionality, namely, that the number of bases increases exponentially in the number of photons. Here we mitigate this dimensionality scaling by focusing on optical systems composed of linear optical objects, modeled as an ensemble of two-level atoms. We decompose the time evolutionary operator on multiple photons into a group of time evolution operators acting on a single photon. Since the dimension of a single-photon time evolution operator is exponentially smaller than that of a multi-photon one in the number of photons, the decomposition enables the multi-photon simulations to be performed at a much lower computational cost. We apply this method to basic single- and multi-photon phenomena, such as Hong-Ou-Mandel interference and violation of the Bell-CHSH inequality, and confirm that the calculated properties are quantitatively comparable to the experimental results. Furthermore, our method visualizes the spatial propagation of photons hence provides insights that aid experiment designs for quantum-enabled technologies.
在量子力学中，光子是光的基本粒子，其动力学特性可能难以深入理解，尤其是在复杂系统中。模拟是解决这一问题的一种很有前景的工具，但它必须应对维度灾难，即基的数量随光子数量呈指数增长。在此，我们通过关注由线性光学对象组成的光学系统（建模为二能级原子的集合）来减轻这种维度缩放。我们将多光子上的时间演化算符分解为作用于单个光子的一组时间演化算符。由于单光子时间演化算符的维度在光子数量上比多光子的指数级小得多，这种分解使得多光子模拟能够以低得多的计算成本进行。我们将此方法应用于基本的单光子和多光子现象，如Hong-Ou-Mandel干涉和贝尔-CHSH不等式的违背，并确认计算出的特性在数量上与实验结果相当。此外，我们的方法可视化了光子的空间传播，从而为量子技术的实验设计提供了有助于深入理解的见解。
