Preservation and destruction of the purity of two-photon states in the interaction with a classical nanoscatterer

The optical resonances supported by nanostructures offer the possibility to enhance the interaction between matter and quantum states of light. On the other hand, due to abrupt changes in the optical response the quantum states of light can be significantly affected by the interaction. In this work, we provide a framework to study the scattering of quantum states of light (with information encoded in their helicity) by a nanostructure. We analyze the purity of the scattered output quantum state and find that the purity of the incident state can be lost when it interacts with the optical resonances of the nanostructure. To explain the loss of quantum purity, we develop a physical picture based on time delays and frequency shifts between the output two-photon modes. The framework and analysis proposed in this work establish a tool to address the interaction between quantum light and nanoenvironments.