Classically tuning the quantum interference of two photons scattered by a macroscopic lossy sphere
Alessandro Ciattoni · Physical Review A · 2026
We investigate the quantum optical scattering of two-photon wave packets by a macroscopic lossy sphere by means of macroscopic quantum electrodynamics in the form of modified Langevin noise formalism. Building on our recently developed general scattering framework, we show that under the far-field approximation, the probability amplitudes for photon detection exhibit a direct correspondence to the classical electric field. This allows us to effectively map the quantum interference calculation for the spherical geometry onto a solvable classical electromagnetic problem, specifically by expressing the quantum-scattering amplitudes in terms of the classical Mie coefficients. The two ingoing photons with an arbitrary frequency-polarization spectrum impinge onto the sphere along two different directions and, as a consequence of matter losses, their scattering involves the three independent processes where two, one, and zero outgoing photons survive. Noncollinearity of ingoing photons causes the existence of two different quantum paths they can follow upon scattering, producing interference effects in the detection of the above three processes, which is governed by the wave-packet spectral symmetry. Furthermore, we demonstrate that the sphere's rotational and reflectional symmetries can be exploited to identify specific scattering geometries that enforce perfect constructive or destructive (Hong-Ou-Mandel) interference, both for symmetric and antisymmetric wave packets. To assess the impact of matter dispersion or losses on quantum interference effects accompanying photon detection, we analyze the scattering of narrow-band two-photon wave packets by high-index dielectric lossy spheres. We show that classical Mie resonance peaks, due to their Fano-like traits, yield very strong constructive and destructive interference effects, occurring when the wave packet carrier frequency matches the resonance frequency and side Fano dip frequency, respectively. In addition, we consider the overall scattering probabilities of two, one, and zero photons, and we prove that, at the Mie resonance frequencies, they exhibit quantum interference effects that are extremely sensitive to the spectral symmetry of the input wave packet, thus suggesting an efficient spectral technique assisted by matter losses to identify entanglement.