The dynamic evolution of a multi-level atom in the three-dimensional photonic crystal under an applied magnetic field is investigated.By combining the Zeeman effect with the photonic band gap effect,the dynamic quantu...The dynamic evolution of a multi-level atom in the three-dimensional photonic crystal under an applied magnetic field is investigated.By combining the Zeeman effect with the photonic band gap effect,the dynamic quantum superposition states and steady quantum coherent trapping states of the atom can be flexibly controlled.This paves the way for coherent manipulation of quantum states in the solid-state system,which has important applications in quantum information processing.展开更多
The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition princi...The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0). Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t). On the other hand, any physical experiment may bring errors so that the initial state (input state) may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution (GAAS) is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.展开更多
基金supported by the National Key Basic Research Special Foundation of China (Grant Nos. 2006CB921706 and 2010CB923200)the National Natural Science Foundation of China (Grant Nos. 10574160 and10725420)
文摘The dynamic evolution of a multi-level atom in the three-dimensional photonic crystal under an applied magnetic field is investigated.By combining the Zeeman effect with the photonic band gap effect,the dynamic quantum superposition states and steady quantum coherent trapping states of the atom can be flexibly controlled.This paves the way for coherent manipulation of quantum states in the solid-state system,which has important applications in quantum information processing.
基金supported by the National Natural Science Foundation of China(Grant Nos.11371012,11171197 and 11401359)the Innovation Fund Project for Graduate Program of Shaanxi Normal University(GrantNo.2013CXB012)+2 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.GK201301007 and GK201404001)the Science Foundation of Weinan Normal University(Grant No.14YKS006)the Foundation of Mathematics Subject of Shaanxi Province(Grant No.14SXZD009)
文摘The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0). Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t). On the other hand, any physical experiment may bring errors so that the initial state (input state) may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution (GAAS) is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.