Designing Nonlinear Photonic Crystals for High-Dimensional Quantum State Engineering
This work addresses the challenge of controlling quantum states in optics, offering a novel method for quantum state engineering with potential applications in quantum systems like superfluids and superconductors.
The authors tackled the problem of generating high-dimensional quantum states by proposing a physically-constrained, differentiable approach for designing nonlinear photonic crystals and pump beams, demonstrating the generation of maximally entangled states in the spatial degree of freedom both theoretically and experimentally.
We propose a novel, physically-constrained and differentiable approach for the generation of D-dimensional qudit states via spontaneous parametric down-conversion (SPDC) in quantum optics. We circumvent any limitations imposed by the inherently stochastic nature of the physical process and incorporate a set of stochastic dynamical equations governing its evolution under the SPDC Hamiltonian. We demonstrate the effectiveness of our model through the design of structured nonlinear photonic crystals (NLPCs) and shaped pump beams; and show, theoretically and experimentally, how to generate maximally entangled states in the spatial degree of freedom. The learning of NLPC structures offers a promising new avenue for shaping and controlling arbitrary quantum states and enables all-optical coherent control of the generated states. We believe that this approach can readily be extended from bulky crystals to thin Metasurfaces and potentially applied to other quantum systems sharing a similar Hamiltonian structures, such as superfluids and superconductors.