Spontaneous parametric down conversion (SPDC) is one of the most versatile techniques for the generation of correlated photon pairs, whose quantum state is essential for photon entanglement that underpins many quantum applications like secure communication, quantum metrology and lithography and quantum imaging. SPDC allows for choosing arbitrary momentum and energy correlations between the generated photons, operating robustly at room temperature, and utilising multiple simultaneously pumped SPDC sources with spatial and temporal coherence.

 There exists the quantum-classical correspondence between SPDC and sum frequency generation (SFG): In SPDC, the material absorbs a pump photon and generate a signal and idler photon pair. The corresponding SFG would happen when the exact signal and idler photon pair are absorbed by the same material to generate the exact pump photon. This correspondence can be used as a tool to better understand SPDC, particularly useful in simulation. 

In my PhD, I work with nanostructures like nanoresonators and metasurfaces as these subwavelength structures do not require phase matching for nonlinear processes and they exist high efficiency. Smaller components also allow denser integration of functional quantum devices. SPDC was demonstrated with a high-index contrast nanoparticle. This nanoparticle example specifically showcased the possibility to create spatially reconfigurable and highly indistinguishable quantum states in a miniaturised system by combining different nanostructures.

My PhD program currently focuses on the polarisation control of SPDC, and its classical counterpart SFG. The first project utilised SFG generated by nanoresonators to demonstrate the possibility to generate uniform far-field polarisation states across all propagation directions, to control he polarisation along the optical axis and to simultaneously tune the polarisation along the entire circumference of the Poincare sphere by solely modifying the excitation polarisation.  In my current project, I am utilising photonic inverse design algorithms to obtain optimised metasurfaces that generate entangled photons with desired polarisation in desired propagation direction. After the current project, I am planning to build on the developed approaches to design multi-functional metasurfaces that can simultaneously generate distinct photon states in several emission directions and at non-degenerate wavelengths.