This repo contains the official implementation of the paper:

(If you use the code, please cite our paper.) We have introduced an algorithm for solving the inverse design problem of generating structured and entangled photon pairs in quantum optics, using tailored nonlinear interactions in the SPDC process. The SPDCinv algorithm extracts the optimal physical parameters which yield a desired quantum state or correlations between structured photon-pairs, that can then be used in future experiments. To ensure convergence to realizable results and to improve the predictive accuracy, our algorithm obeyed physical constraints through the integration of the time-unfolded propagation dynamics governing the interaction of the SPDC Hamiltonian.

We have shown how we can apply our algorithm to obtain the optimal nonlinear $\chi^{(2)}$ volume holograms (2D/3D) as well as different pump structures for generating the desired maximally-entangled states. Using this version, one can further obtain all-optical coherent control over the generated quantum states by actively changing the profile of the pump beam.

This work can readily be extended to the spectral-temporal domain, by allowing non-periodic volume holograms along the propagation axis -- making it possible to shape the joint spectral amplitude of the photon pairs. Furthermore, one can easily adopt our approach for other optical systems, such as: nonlinear waveguides and resonators, $\chi^{(3)}$ effects (e.g. spontaneous four wave mixing), spatial solitons, fiber optics communication systems, and even higher-order coincidence probabilities. Moreover, the algorithm can be upgraded to include passive optical elements such as beam-splitters, holograms, and mode sorters, thereby providing greater flexibility for generating and manipulating quantum optical states. The SPDCinv algorithm can incorporate decoherence mechanisms arising from non-perturbative high-order photon pair generation in the high gain regime. Other decoherence effects due to losses such as absorption and scattering can be incorporated into the model in the future. Finally, the current scheme can be adapted to other quantum systems sharing a similar Hamiltonian structure, such as superfluids and superconductors.

To understand and determine the variables of interaction and learning hyperparameters, see src/spdc_inv/experiments/experiment.py and read the documentation there (we will go into more detail here soon.)

Before you run the code, please run the following line from the bash: export PYTHONPATH="${PYTHONPATH}:/home/jupyter/src" Later, run experiment.py by: python src/spdc_inv/experiments/experiment.py