| To faithfully characterize the quantum system, classical computer will consume exponential growth of computing resources with the increasing of the system size. In reaction to this problem, Feynman et al. propose the concept of quantum simulation, that is to say, according to the principle of quantum mechanics we build a computer to simulate the quantum system. For now, the application of quantum simulation has extend to many domains of physics, such as condensed matter physics, high energy physics, cosmology, quantum chemistry and atomic physics. With the long decoherence time and mature experimental technology, nuclear magnetic resonance (NMR) is one of the earliest physical system to implement quantum computing and quantum simulation. During the doctorate study period, my research focus on the quantum simulation of Heisenberg model based on NMR. This doctor thesis mainly involves the following parts.In chapter 1,1 present the concept of quantum computer and quantum simulation. Then, some potential physical system are illustrated.In chapter 2, I introduce the basic principle of NMR and explain how to realize quantum computing and quantum simulation with NMR.In chapter 3,1 show how to prepare quantum entangled states via global controls in closed linear Ising spin chains with nearest-neighbor couplings. Entanglement is one of the most intriguing features of quantum physics, which stays at the heart of applications such as quantum computation, quantum teleportation,and quantum cryptography, so preparation of the entangled states is of significance in many-particle physics. However, it is difficult to prepare entangled states by addressing individual qubits in large-qubit systems. One of the practical way is to use control fields that act globally on all the spins. In experiment, we prepare two important types of entangled states in a three-spin system, i.e., GHZ and W states.In chapter 4,I present how to experimentally measure the ground-state geometric phase of the three-spin XY model with NMR simulator. The experimental results indi-cate that the geometric phase could be used as a fingerprint of the ground-state quantum phase transition of many-body system, with no need for the system to undergo the tran-sition. This work will contribute to an improved understanding of geometric phase and QPT in quantum systems.In chapter 5, I introduce how to observe the Lee-Yang Zeros in ferromagnetic Ising system in experiment, which has been regarded as impossible since Lee-Yang Zeros occur only at an imaginary magnetic field, i.e., it is unphysical. By measuring the co- herence of a probe spin coupled to a many-body system, it is experimentally feasible to observe the Lee-Yang Zeros. we have directly observed the Lee-Yang zeros with NMR simulator for the first time. We also demonstrated the feasibility of using probe spin coherence to determine the thermodynamic properties of the baths and, more generally, to access thermodynamics on the complex plane of physical parameters.Chapter 5 is a summary and expectation. |
