We derive the explicit solution of the problem of time-optimal control (TOC) by a common magnetic fields for two independent spin-1/2 particles. Our approach is based on the Pontryagin Maximum Princple (PMP) and a novel symmetry reduction technique. We experimentally implement the optimal control via a home-built zero and ultralow filed NMR spectrometer. This is the first analytical solution and experimental demonstration of time-optimal control in such a system and it provides a route to achieve time optimal control in more general quantum systems.

Photonic entanglement is central resource to quantum information sciences, such as quantum communication and quantum computation. The entangled photons generated in conventional spontaneous parametric down-conversion usually yield THz bandwidth which becomes very dim in many applications call for narrow-band entanglement sources. Here we demonstrate the polarization-entanglement photon source with counterpropagating phase matching, which results in an inherent bandwidth of 7.1 GHz at telecom wavelength. The entanglement is measured to violate the Bell inequality by up to 18.5 standard deviations, with Clauser–Horne–Shimony–Holt S-parameter of 2.720±0.039. The quantum state tomography further characterizes the entanglement, with fidelity F=(95.71±0.61)%.