Quantum Manipulation Of Cold Atom In A Driven Optical Lattice

Optical lattice plays an important role in quantum simulation because it has a pure environment and controllable parameters,which has become a important experimental platform.Since the ultracold Bose and Fermi gas atoms have been experimentally loaded and trapped in a optical lattice potential well,the quantum control of the tunneling dynamics for ultracold atoms has becomes one of important research topics.The coherent modulation by using laser is the important method to realize the quantum control of atomic system,which has great significance in the study of classical-quantum correspondence and realization of the coherent control for atomic tunneling dynamics.And the related research is an effective way to deepen our understanding for the microscopic quantum world.In this paper,we focus on the coherent control of the tunneling dynamics of a few atoms in the periodically driven optical lattice system,such as the coherent control an open and depth-tilt-modulated one-dimensional(1D)optical lattice system,a opening driven planar four-well potential system and a driven one-dimensional triple-well potential system.It provides an important reference-value for the study of classical-quantum correspondence and coherent control of many-body transport in non-Hermitian system.The thesis have been divided into five chapters.In the first chapter,we give a brief introduction about the laser cooling and trapping of neutral atoms,and the corresponding progress of research,the Floquet theory,the coherent manipulation of atomic tunneling in periodic driving systems,the influence of chaos on quantum tunneling and the research progress of non-Hermitian systems are briefly introduced.In the second chapter,we report on the first direct investigation of quantumtransport and control of a classically chaotic open system which is a single atom held in an open and depth-tilt-modulated one-dimensional(1D)optical lattice.The area of chaotic region is demonstrated to decrease with the increase of damping of the classical open system.The corresponding non-Hermitian Hamiltonian is constructed,where the quantum decay rate positively correlating to the classical damping is qualitatively revealed.Under high-frequency approximation of the tilt modulation,we obtain a set of analytical solutions with the effective coupling being strengthened by the adjustable decay rate.The analytical and numerical results mean accordantly that we can enhance the tunneling rate to suppress the decoherence by increasing the decay rate to leave the chaotic region,which could be useful for qubit transport and control based on the classically chaotic open systems.In chapter three,we investigate the coherent control of tunneling dynamics for a single atom held in a open and driven planar four-well potential.The analytical quasi-energies are obtained and the parameter region of complete real quasi-energies is demonstrated,in which the area of parameter region will be amplified with the increase of the dc strength and the zero imaginary parts of the quasienergies are related to the coherent destruction of tunneling(CDT)effect.Furthermore,we obtain the non-Floquet solution with nonzero imaginary quasienergies.The analytical results mean that we can manipulate the decaying process,in which the lifetime of atom is adjustable in a wide range.The results are due to the competition between the dissipation effect and driving external field,and could be useful for designing adjusting scheme of quantum motion in a non-Hermitian system.In chapter four,we investigate the coherent control of quantum tunnelling for two bosons held in a driven triple-well potential.In the high-frequency region within resonance,the non-Floquet states with slowly varying populations are constructed by the linear superposition of Floquet solutions.For the non-resonance case with appropriate reduced parameters,we obtain another set of analytical solu-tions and their numerical correspondences,which exhibits the selective tunnelling effect of atoms.Applying the presented analytical results,a scheme to transport two bosons from the first well to the third is suggested by adjusting the driving parameters.In chapter five,a summary of our work and a outlook of this topic are given.