Dynamical Quantum Simulation Based On Nitrogen-vacancy Center In Diamond

Quantum simulation is to imitate the target quantum system with a controllable quantum system,in order to study the target quantum system.Simulating quantum sys-tems is known to be a difficult computational problem for classical computers,hence quantum simulation is an important research method for studying quantum systems.A number of quantum systems,such as ultra-cold atoms,trapped ions,superconducting circuits,liquid NMR and solid-state spin systems have been proposed as quantum sim-ulators,and promise to have applications in the study of many research areas,including condensed-matter physics,high-energy physics,atomic physics,quantum chemistry,and cosmology.This thesis focuses on the use of diamond nitrogen-vacancy color center system to simulate topological phases,in order to study their topological properties through their non-trivial quench dynamics.First,the fundamentals and experimental techniques of diamond NV center are introduced,as well as the general theory of dynamical classifica-tion of topological quantum phases.In the main part of this thesis,we describe a series of research based on a home-built optically detected magnetic resonance experimental setup,in the following aspects:1.Using the electron spin of diamond NV center as a single qubit system,we simulate a 2-dimensional quantum anomalous Hall model in momentum space.Firstly,we experimentally demonstrate the correspondence between non-trial bulk topology and dynamical spin-texture field emerging on momentum space band-inversion surfaces,namely the bulk-surface correspondence,and classify topological phase accordingly.After that,we demonstrate the universality of this dynamical topological characterization method by applying to different quench axis and higher topological number.Finally,we study the robustness of this method in the presence of dephasing effect.2.We use the electron and nuclear spin of NV center as a two qubit system,to simulate a 3-dimensional chiral topological insulator,which has not been ob-served experimentally in condensed-matter systems.First,we observe the bulk-surface correspondence and characterize the topological phase,and we introduce a symmetry-breaking term to observe the symmetry protection of topological phase.Then we detect topological charges by dynamical means and character-ize the topological phase directly.When reducing the quench field,we observe the moving of dynamical topological charges,and a emergent topological transi-tion.Finally,we study the robustness of this method in the presence of dephasing effect.3.We explore some experimental techniques for NV center at low temperature,in-cluding using dynamical decoupling sequence to detect and control weakly cou-pled carbon nuclear spins,and high fidelity readout methods based on nuclear spin ancilla and spin-to-charge conversion.These experimental techniques lay the foundation for the future realization of many-qubit simulators based on NV center.