We report a new method to determine the orientation of individual nitrogen-vacancy (NV) centers in a bulk diamond and use them to realize a calibration-free vector magnetometer with nano-scale resolution. Optical vortex beam is used for optical excitation and scanning the NV center in a [111]-oriented diamond. The scanning fluorescence patterns of NV center with different orientations are completely different. Thus the orientation information of each NV center in the lattice can be known directly without any calibration process. Further, we use three different-oriented NV centers to form a 1

Harnessing the dynamics of complex quantum systems is an area of much interest and a quantum simulator has emerged as a promising platform to probe exotic topological phases. Since the flexibility offered by various controllable quantum systems has helped gain insight into the quantum simulation of such complicated problems, an analog quantum simulator has recently shown its feasibility to tackle the problems of exploring topological phases. However, digital quantum simulation and the detection of topological phases still remain elusive. Here, we develop and experimentally realize the digital quantum simulation of topological phases with a solid-state quantum simulator at room temperature. Distinct from previous works dealing with static topological phases, the topological phases emulated here are Floquet topological phases. Furthermore, we also illustrate the procedure of digitally simulating a quantum quench and observing the nonequilibrium dynamics of Floquet topological phases. Using a quantum quench, the 0- and π -energy topological invariants are unambiguously detected through measuring time-averaged spin polarizations. We believe our experiment opens up a new avenue to digitally simulate and detect Floquet topological phases with fast-developed programmable quantum simulators.

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