arXiv subjects

Takumi Jinushi

Publications and source records attributed to Takumi Jinushi.

2 recordsLinked to original sources

arXiv2026

Algebraic Characterization of Biphoton Spatial-Mode Entanglement in Higher-Order Laguerre--Gaussian-Pumped SPDC

High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre--Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.

quant-ph↗

arXiv2026

Quantum Gouy phase singularities in a propagating biphoton state

Phase singularities are topological defects around which the phase winds by an integer multiple of $2π$. In entangled multiphoton states, they can emerge nonlocally in the joint wavefunction rather than in the field of either subsystem alone. Here we show that the quantum Gouy phase generates nonlocal phase singularities (NPSs) in the two-dimensional longitudinal propagation space of entangled photon pairs. We consider photon pairs produced via spontaneous parametric down-conversion pumped by a Laguerre--Gaussian beam, with the signal and idler photons propagating independently over different longitudinal distances. The accumulated radial-mode-dependent Gouy phases induce destructive interference among biphoton spatial-mode components, producing isolated intensity nulls with quantized phase winding. For a pump with radial mode number $p$, the NPS topological charges have magnitude $p$, whereas their propagation positions and charge signs are governed by the Rayleigh ranges of the pump and phase-matching functions. We further identify the radial-mode structure required for their formation, showing that separable biphoton states cannot support isolated longitudinal NPSs. Our results extend nonlocal singular optics from transverse spatial correlations to longitudinal propagation dynamics and establish propagation distance as a coordinate space for topological structures in entangled photon pairs.

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