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arXiv:2607.28231

Quantum Arago-Fresnel interference of displaced spin states of photons

Yan Zhang, Xiang Liu, Hou Ian

quant-phphysics.opticsSubmitted Jul 30, 2026• Announced Jul 31, 2026• 0 citations
v1 · Jul 30, 2026v2 · Sep 22, 2026
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Abstract

The four laws by Arago and Fresnel distinguish the coplanarity of two light beams to determine their capacity of interference, laying the historic milestone for conceptualizing the polarization of light. Equipped with modern descriptions of non-classical states, we re-investigate the macroscopic Arago-Fresnel interference producible by photon helicities. To this end, we compute the Stokes parameter of a polarized beam combined from a regular coherent state (displaced from the vacuum) and a displaced single-photon spin state (displaced from either a left- or right-spin state of photon). The spin orientation, together with its relative asymmetry with respect to the polarizing orientation of the displacing coherent state, produces distinguishing parameter dependences and thus distict interference fringes. Conversely, this quantum interferometry establishes a purely optical method to determine the spin of an unknown incident photon.

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The four laws by Arago and Fresnel distinguish the coplanarity of two light beams to determine their capacity of interference, laying the historic milestone for conceptualizing the polarization of light. Equipped with modern descriptions of non-classical states, we re-investigate the macroscopic Arago-Fresnel interference producible by photon helicities. To this end, we compute the Stokes parameter of a polarized beam combined from a regular coherent state (displaced from the vacuum) and a displaced single-photon spin state (displaced from either a left- or right-spin state of photon). The spin orientation, together with its relative asymmetry with respect to the polarizing orientation of the displacing coherent state, produces distinguishing parameter dependences and thus distict interference fringes. Conversely, this quantum interferometry establishes a purely optical method to determine the spin of an unknown incident photon.
The mathematical representation of each of the four interference laws of Fresnel and Arago is presented. Each of the laws is characterized by a unique Stokes vector. These vectors are arrived at by a matrix analysis of the, interference experiments of Fresnel and Arago in which only polarizers are used. The historical motivation that led Stokes to introduce the parameters that now bear his name is noted. The similarity in the approach taken by Stokes to represent the fundamental properties of the classical optical field in terms of observables is compared with Heisenberg's approach to the formulation of quantum mechanics. The mathematical statements that characterize unpolarized light are developed. These statements are then used to determine the Stokes vectors that describe each of the four interference laws of Fresnel and Arago. In a final section of the paper the mathematical apparatus developed here is used to describe Young's interference experiment with unpolarized light.
This thesis concerns the role of polarization, coherence, and geometric phase in both quantum and classical light interference.In the quantum domain, the thesis analyzes vector-light interference in a doubleslit geometry for single-photon and multiphoton states.Using a coherence Stokes formalism, a unified description of polarization modulation, geometric phase, and wave-particle duality is established.Single-photon interference is shown to exhibit a fundamental complementarity relation that directly links the geometric phase at the observation screen to which-path information at the slits.This framework is further extended to higher-order interference of multimode N00N states, where Nth-order polarization modulation and geometric-phase accumulation scale linearly with photon number and lead to new higher-order vector-light complementarity relations.In the classical domain, the thesis explores beam and pulse shaping enabled by polarization gratings.Spatial polarization gratings are shown to provide control over the profiles, coherence, diffraction orders, and polarization of partially coherent and partially polarized pulsed beams.The analysis is further extended to ultrafast pulse shaping, where spectral polarization gratings generate multiple temporally shifted pulses with distinct polarization states.Furthermore, a novel Poincaré pulse in the spatiospectral domain is presented.
We report that the true intrinsic degree of freedom of the photon is neither the polarization nor the spin. It describes a local property in momentum space and is represented in the local representation by the Pauli matrices. This result is achieved by treating the transversality condition on the vector wavefunction as a nonholonomic quantum constraint. We find that the quantum constraint makes it possible to generalize the Stokes parameters to characterize the polarization of a general state. Unexpectedly, the generalized Stokes parameters are specified in a momentum-space local reference system that is fixed by another degree of freedom, called Stratton vector. Only constant Stokes parameters in one particular local reference system can convey the intrinsic degree of freedom of the photon. We show that the optical rotation is one of such processes that change the Stratton vector with the intrinsic quantum number remaining fixed. Changing the Stratton vector of the eigenstate of the helicity will give rise to a Berry's phase.
Any polarization state of light occupies intrinsic quantum uncertainties due to the noncommutative behavior of the Stokes operators, which are manifested as unavoidable quantum fluctuations in the corresponding classical Stokes parameters.In this thesis, we explore such quantum polarization uncertainties exhibited by vectorial light fields in Young's seminal double-slit interference experiment.As a main result, by adopting a proper Stokes operator representation of double-slit interference, we establish general quantum polarization uncertainty relations for the Stokes parameters in the observation plane.The relations show how the lower bounds of the polarization uncertainties are periodically varying across the observation screen and how they are affected by the polarization and coherence properties of the light at the two slits.We also present various noncommutative, interlinked connections between coherence and polarization in the slit plane which have not been considered earlier in the literature.Our work sets the fundamental precision limits imposed by quantum physics for characterizing any polarization state in double-slit interference, which could find use in photonic applications exploiting polarimetric and interferometric techniques for high-resolution quantum-enhanced sensing.
The dual wave–particle nature of light and the degree of polarization are fundamental concepts in quantum physics and optical science, but their exact relation has not been explored within a full vector-light quantum framework that accounts for interferometric polarization modulation. Here, we consider vector-light quantum complementarity in double-pinhole photon interference and derive a general link between the degree of polarization and wave–particle duality of light. The relation leads to an interpretation for the degree of polarization as a measure describing the complementarity strength between photon path predictability and so-called Stokes visibility, the latter taking into account both intensity and polarization variations in the observation plane. It also unifies results advanced in classical studies by showing that the degree of polarization can be viewed as the ability of a light beam to exhibit intensity and polarization-state fringes. The framework we establish thus provides novel aspects and deeper insights into the role of the degree of polarization in quantum-light complementarity and photon interference.
We present a study of the imaging of the interference of spatial-helical modes of single photons. This work includes a mathematical treatment that accounts for the direction of propagation and spatial mode degrees of freedom in the situation where light travels through an interferometer that prepares the light in distinct spatial modes and makes them interfere. We present results of the interference at the single photon level of the spatialhelical modes with topological charge 1 and 0. The results are consistent with the expectation that each photon carries the entire spatial mode information.