Quantum field theory and inverse problems: Imaging with Entangled Photons

2025/06/04 by Matti Lassas, Lassas, Matti, Medet Nursultanov +5 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.03653

openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to uniquely determine the density of atoms from measurements of the source to solution map for a system of nonlocal partial differential equations, which describe the scattering of a two-photon state from the atoms. The required measurements involve correlating the outputs of a point detector with an integrating detector, thereby exploiting information about the entanglement of the photons.

Citations

• Dynamic One Photon Localization in a Discrete Model of Quantum Optics
• Nonlocal PDEs and quantum optics: band structure of periodic atomic sytems
• Nonlocal PDEs and Quantum Optics: Bound States and Resonances
• Kinetic equations for two-photon light in random media
• One-parameter semigroups for linear evolution equations

Cited by

• The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness
• Recovering asymptotics of potentials from the scattering of relativistic Schrödinger operators

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