Perfect Information Transfer And Perfect Population Transfer In Quantum Chains

In this paper, we explore the perfect information transfer in spin chains and the perfect population transfer in pulse-driven quantum chains.We study how to engineer parameters for perfect information transfer in neighbor-coupled spin chains. The 2N-dimension Hilbert space associated with quantum information transfer over the spin chain can be projected into an N+1-dimension subspace, so the Hamiltonian of the system will be reduced to a tridiagonal matrix in standard basis. The functional relation between the parameters of the spin chain and the eigenvalue spectrum of the Hamilto-nian, which can be determined by the perfect transfer conditions, are established. The task of finding all solutions to the parameters of perfect information transfer is accom-plished by solving polynomial equations.The results could be used to analyze structures of the chain or find particular chains with optimal properties.The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscilla-tions from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Groebner basis analysis technique is used to generalize o the results and get all analytical solutions for perfect population transfer. The explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.