Study On Spin Faraday Wave And Spin Twist In Bose-Einstein Condensates

Bose Einstein condensate(BEC)has high tunability and macroscopic quantum properties,making them unique in the study of quantum simulations.Two component BECs have more abundant physical properties than single component BEC.With the increase of the highly tunable degree of freedom of interspecies interactions,novel quantum effects can be produced by controlling the intensity and type of intraspecies and interspecies interactions.This provides conditions for studying the microscopic physical mechanisms of quantum control.Parametric excitation is a fundamental excitation induced by small perturbation of the parameters of the BEC.The rich internal hyperfine structure of two component BECs enables the study of spin excitations.The optical lattice exhibits a lattice structure similar to that of solid materials.By tuning the parameters such as wavelength,polarization and phase of the laser,the atoms in different internal states can experience different lattice potentials when atoms are trapped in optical lattices.By tuning the interaction between atoms and the parameters of the optical lattice,we can control the quantum effect of the system.The innovations of this paper include: we investigate the formation of spin Faraday wave patterns with multiple rotational symmetries when two component BECs are periodically driven;we study the spin-twisted effect resulting from the twist between lattices and interlayer coupling when spin-dependent optical lattices show a double-well dispersion.The main works are as the following.1.We study parametric excitation and pattern formation in two component BECs trapped in a harmonic potential near the miscible-immiscible phase transition.By periodically modulating the atomic scattering lengths,spin-dependent wave patterns can be generated.In an elliptical condensate,the density oscillation along the longitudinal direction corresponds to spin Faraday waves where the modulation frequency and the spatial oscillation period are related to the velocity of spin sound.For a circular condensate,the generated spin Faraday waves exhibit an interesting l-fold rotational symmetry.The number of nodes along the radial and angular directions increases for larger modulation frequencies.2.A double-well dispersion model of the spin-dependent optical lattices was constructed.We explore the ground state of the two component BECs in the twisted-bilayer square optical lattices.The twist angle of the lattices and the strength of interlayer coupling can affect the distribution of spin states.When the optical lattices are twisted in the opposite direction,spin twist occurs,and as interlayer coupling increases,the two spin states overlap again.