New scattering zones in quantum speckle propagation

Quantum speckles exhibit significantly richer behavior than their classical counterparts due to their higher dimensionality. A simple example is the far-field speckle pattern in 1D light scattering: classical light forms 1D speckles defined by the numerical aperture, whereas biphoton scattering depends in addition on the photon correlation length, forming 2D elliptical speckles. To date, the behavior of quantum speckles for shorter propagation distances has not been considered. We remedy this here by considering the paraxial evolution of two-photon entanglement at arbitrary propagation distances from an isotropic scatterer. We show, theoretically, numerically, and experimentally, that the two length scales of the biphoton introduce a new Fresnel regime between the conventional near and far fields. Further, we show that the quantum near field is characterized by speckles with a square shape that remain constant during propagation. In contrast, the intermediate regime can be engineered to have a constant speckle size along the sum coordinate but a linearly expanding speckle size along the difference coordinate, with a speckle shape that transitions from square to elliptical. The results merge quantum coherence with scattering statistics and suggest new regimes of operation for correlation-based quantum sensing and imaging.