Many-body quantum chaos, localization, and multiphoton entanglement in optical synthetic frequency dimension

Generation and control of entanglement are fundamental tasks in quantum information. In this paper, we propose a novel approach to generating controllable frequency-entangled photons using the concept of synthetic frequency dimension in an optical system. This system consists of a ring resonator made of tailored third-order nonlinear media to induce photon-photon interactions and a periodic modulator to manipulate coupling between different frequency modes. We show that this system provides a unique platform for the exploration of distinct few- or many-body quantum phases including chaos, localization, and integrability in a highly integrable photonics platform. In particular, we develop a proposal to calculate the spectral form factor, which characterizes the degree of chaos in the system and differentiates between these phases based on observable measurements. Then, the switching of the quench dynamics from an intermediate phase between integrable and chaotic to the Stark many-body phase can generate and sustain stable frequency-entangled multiphoton states. This work is the first to explore rich and controllable quantum phases beyond single-particle physics in a synthetic dimension.