Non-Markovian Dynamics in Fiber Delay-line Buffers

Abstract: We study the non-Markovian effect on a two-photon polarization entangled state, in which one photon from the pair is stored in a fiber delay-line buffer. We propose a model of a photonic qubit coupled to fiber birefringence and a fiber reservoir representing the environment. We analytically derive a non-Markovian probability function for the buffered photon and its paired photon. To verify the probability function, we perform full quantum state tomography of the photon pairs. The probability function fits well with the experimental data and physical values. Our results indicate that our quantum system operates slightly above the threshold for a non-Markovian transition. We observe a unique polarization dynamic of the buffered photon. We further exploit measures of quantum mutual information to study the quantumness of the photon pairs. Werner's well-known separability criterion occurs at a buffer time of about 0.9$\,$ms. Our results imply that quantum discord can surpass Werner's criterion, and hence, quantum bi-partite correlation can exist for buffer times greater than 0.9$\,$ms.