Quantum Coherence in Reflected and Refracted Beams: A Van Cittert-Zernike Approach

TL;DR

The paper develops a quantum van Cittert–Zernike framework to track how coherence and polarization of light evolve when beams are reflected and refracted at a dielectric interface, revealing polarization coupling from interface-induced angular-spectrum rotations as a natural beam-splitting mechanism. By modeling two thermal Gaussian beams and using a four-point correlation formalism with Fresnel propagation, it demonstrates that incidence angle and propagation distance can controllably modify multiphoton correlations, including regimes where sub-Poissonian statistics emerge via post-selection without traditional light–matter interactions. A key finding is that certain second-order correlations can be tuned to vanish or reveal enhanced cross-correlations, with a collimation-dependent scaling law $w_0/lambda$ governing far-field thermalization. These results extend the quantum van Cittert–Zernike theorem to interface-driven settings, offering a decoherence-avoiding route to quantum state control with potential applications in quantum information and metrology.

Abstract

Recent advances in quantum optics have highlighted the critical role of spatial propagation in controlling the quantum coherence of light beams. However, the evolution of quantum coherence for light beams undergoing fundamental optical processes at dielectric interfaces remains unexplored. Furthermore, manipulating multiphoton correlations typically requires complex interactions that challenge few-photon level implementation. Here, we introduce a quantum van Cittert-Zernike theorem for light beams, describing how their coherence-polarization properties are influenced by reflection and refraction, as well as how these properties evolve upon subsequent propagation. Our work demonstrates that the quantum statistics of photonic systems can be controllably modified through the inherent polarization coupling arising from reflection and refraction at an interface, without relying on conventional light-matter interactions. Our approach reveals regimes where thermal light can exhibit sub-Poissonian statistics with fluctuations below the shot-noise level through post-selected measurements, and this statistical property can be tuned by the incident angle. Remarkably, this quantum statistical modification is governed by a scaling law linking beam collimation to far-field thermalization. Our work establishes a robust, decoherence-avoiding mechanism for quantum state control, advancing the fundamental understanding of coherence in quantum optics and opening new avenues for applications in quantum information and metrology.

Figures (4)

• Figure 1: The proposed setup for investigating quantum van Cittert-Zernike theorem for reflection and refraction of light beams. In this setup, both the incident blue and yellow beams are Gaussian beams. The inset shows the intensity distribution of their transverse cross-section. The incident beams interact with a dielectric medium of refractive index $n=1.5$, whose reflection coefficients ($r_p$, $r_s$) and transmission coefficients ($t_p$, $t_s$) are illustrated in an accompanying plot. After reflection and refraction, the Gaussian beams propagate to a screen located at a distance of $\Delta_Z$. Two detectors are symmetrically placed on the screen with a horizontal separation of $\Delta_Y$ and are positioned at a vertical height of $\Delta_X$ from the base of the screen.
• Figure 2: The second-order coherence as functions of $\Delta_Y/\Delta_X$ for various post-selected measurements in the far field with $\theta=60^{\circ}$ and $\Delta_X/\Delta_Z=0.5$. We choose a waist radius of $w_0$=14mm and a wavelength of $\lambda$=8.5mm for the incident Gaussian beam, parameters that are experimentally accessible according to Ref. iyer2010compact. Other parameters are the same as those in Fig. 1.
• Figure 3: (a)The second-order coherence $|g^{(2),out}|$ and (b) the coherence $g^{out,HH}$ as functions of $\theta$ for various post-selected measurements in the far-field with $\Delta_X/\Delta_Z=\Delta_Y/\Delta_Z=0.5$. Other parameters are the same as those in Fig. 1.
• Figure 4: The VVVV component of the second-order coherence, $|g^{(2),out}_{VVVV}|$, is plotted as a function of $\Delta_Z$ and $w_0/\lambda$ in the far field, with $\theta=60^{\circ}$ and $\Delta_X/\Delta_Z=\Delta_Y/\Delta_Z=0.5$. A key finding is that $|g^{(2),out}_{VVVV}|$ is independent of the specific value of the waist radius $w_0$, depending only on the ratio $w_0/\lambda$. Other parameters are the same as in Fig. 1.