Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method
Long Xiong1, Wei-Feng Zhuang1, and Ming Gong1,2*
1CAS Key Lab of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China 2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
Abstract：Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.
. [J]. 中国物理快报, 2022, 39(7): 73101-.
Long Xiong, Wei-Feng Zhuang, and Ming Gong. Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method. Chin. Phys. Lett., 2022, 39(7): 73101-.
2022, Vol. 39 
