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Physical Review Research

Vector-light interference with a multimode N00N state

Elvis Pillinen, Tero Setälä, Andreas Norrman

Published Jan 20, 2026• 0 citations
Publisher

Abstract

Multimode N00N states stand out as an excellent platform to explore higher-order quantum interference phenomena, with benefits in quantum-enhanced estimation of multiple parameters beyond classical limits. Here, we investigate higher-order polarization properties, geometric phase features, and associated wave-particle duality structures in double-slit vector-light interference involving a multimode N00N state. We particularly show that the interferometric polarization modulation and the accompanied geometric phase accumulation are N times faster for the multimode N00N state than for one-photon or classical light. We also formulate N th -order extensions of the three wave-particle duality relations established for a single vector-light photon: the two via distinguishabilities and visibilities [A. Norrman , ], and the one via the geometric phase and which-path information ratio [E. Pillinen , ]. Our work contributes to the broader fundamental understanding of how vectorial quantum light acts in higher-order interference, with possible opportunities in precision metrology outside scalar-field regimes.

DOI
10.1103/zq23-n1ql

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Multimode N00N states stand out as an excellent platform to explore higher-order quantum interference phenomena, with benefits in quantum-enhanced estimation of multiple parameters beyond classical limits. Here, we investigate higher-order polarization properties, geometric phase features, and associated wave-particle duality structures in double-slit vector-light interference involving a multimode N00N state. We particularly show that the interferometric polarization modulation and the accompanied geometric phase accumulation are N times faster for the multimode N00N state than for one-photon or classical light. We also formulate N th -order extensions of the three wave-particle duality relations established for a single vector-light photon: the two via distinguishabilities and visibilities [A. Norrman , ], and the one via the geometric phase and which-path information ratio [E. Pillinen , ]. Our work contributes to the broader fundamental understanding of how vectorial quantum light acts in higher-order interference, with possible opportunities in precision metrology outside scalar-field regimes.
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.
The principle of complementarity relationship introduced by Niels Bohr in 1927 states that particle and wave behavior are two mutually exclusive properties for a quantum system.This relationship has taken the attention of researchers for decades due to its conceptual importance.This thesis contains a theoretical research work conducted on quantum complementarity of vectorial light fields and in the doublepinhole interference.Here we have adopted the classical Stokes parameters within a quantum framework and calculated the Stokes parameters in the observation plane in double-pinhole interference.Based on these calculations, we further evaluated visibility and distinguishability parameters for an arbitrary pure single-photon state and for a specific single-photon pure state, where the photon is x polarized at the first pinhole and y polarized at the second pinhole.We have then examined and interpreted the wave-particle duality for the mentioned two states.Finally, we performed mixed state calculation where fully unpolarized photon is incident on the two pinholes, but with the photon at one pinhole rotated by an angle of π/2.From the obtained results we concluded that a priori which path information (WPI) regarding the complementarity relations for the single photon pure vectorial quantum state couples not to the intensity visibility but to the total visibility.We further found that the vectorial quantum state gives rise to polarization modulation.From the results obtained for the mixed state calculations, we discovered that the last Stokes parameter has a non-zero value and it contributes to the polarization modulation.Thereby we further recommended to repeat the calculation for different mixed states other than what we have considered here to extend the exploration about the nature of polarization modulation.
We explore quantum correlations of general vector-light fields in multislit interference and show that the nnnth-order field-coherence matrix is directly linked with the reduced nnn-photon density matrix. The connection is utilized to examine photon wave-particle duality in the double-slit configuration, revealing that there is a hidden information-theoretic contribution that complements the standard inequality associated with such duality by transforming it into a strict equality, a triality identity. We also establish a general quantum complementarity relation among the field correlations and the particle correlations which holds for any number of slits, correlation orders, and vector-light states. The framework that we advance hence uncovers fundamental physics about quantum interference.
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.