Stochastic Processes in Quantum Optics

Lue Bouten

Quoc Khoa Doan

K. Wódkiewicz

Ryogo Kubo, T. Takagahara, Eiichi Hanamura

J Procházka

Abstract Both the corpuscular theory of light and the theory of stochastic processes are well known in the literature. However, they are not systematically used together for description of optical phenomena. There are optical phenomena, such as the well-known three-polarizer experiment or other phenomena related to polarization of light, which have never been quantitatively and qualitatively explained using the concept of quantum of light (photon). The situation changed in 2022 when stochastic memoryless and independent (IM) process formulated within the framework of the theory of stochastic processes was introduced. It is suitable for determination of probability (density) functions characterizing interaction (transmission or reflection) of individual photons with optical elements on the basis of experimental data. The process has memoryless (Markov) property, and it is assumed that the interactions of individual photons with an optical system are independent. Formulae needed for analysis of data in the context of polarization of light are derived. An example analysis of the three-polarizer experiment is performed and numerical result of the probability (density) functions are determined. These original results were missing in the literature. The results imply that the possibilities of the corpuscular theory of light to describe optical phenomena can be significantly extended with the help of stochastic IM process and the theory of stochastic processes in general.

Ying Oon Tan

Previously [J. Mod. Optics, 51, 1093, (2004)], we introduced an alternative stochastic mechanics in the form of a stochastic differential equation with a stochastic process defined by the set of Bohmian momentum time histories from an ensemble of particles. We showed that the alternative stochastic mechanics with a purely random process characterized by an n‐th order joint probability density in the form of products of delta functions is equivalent to quantum mechanics. In this paper, we show that, for a particular non‐purely random process, the alternative stochastic mechanics is not equivalent to quantum mechanics. Hence, the alternative stochastic mechanics is generally not equivalent to quantum mechanics.