Quantum Control For Ultracold Atom-molecule Slow Light And Spinor Bose-einstein Condensates

We summarize the Bose-Einstein condensation (BEC) and slow light with the quantum statetransfer and quantum storage in ultracold atomic sample. We study the process of scalar-orspinor-molecule BEC formation by using photoassociation(PA) magnetic Feshback resonance (FR)technology. Because of the long-rang and anisotropic interactions for ultracold polar molecules, ultracoldpolar molecules not only would enable explorations of a large class of many-body physics phenomena butalso could be used for quantum information processing.In the second chapter of this thesis, we propose to use a quantized version of coherent two-colorphotoassociation to realize a hybrid atom-molecule quantum device for storage and retrieve of opticalinformation. This may indicate a hybrid atom-molecule quantum device for storage and retrieve of opticalinformation.In the third chapter of this thesis, we also show that the group velocity of the light field dependsexplicitly on whether the atoms are bosons or fermions, as well as on the existence or absence of a pairinggap in the case of Fermi atom-molecule slow light system, so that the measurement of the group velocityrealizes a nondestructive diagnosis of the atomic state and the pairing gap.In the fourth chapter of this thesis, we study the theory of several aspects of the dynamics ofcoherent atom-molecule conversion in spin-one Bose-Einstein condensates. Specifically, we discuss how,for a suitable dark-state condition, the interplay of spin-exchange collisions and photo association leads tothe stable creation of an atom-molecule pair from three initial spin-zero atoms. This process involves two two-body interactions and can be intuitively viewed as an effective three-body recombination. Weinvestigate the relative roles of photoassociation and of the initial magnetization in the “resonant” case,where the dark-state condition is perfectly satisfied. We also consider the “nonresonant” case, where thatcondition is satisfied either only approximately—the so-called adiabatic case—or not at all. In the adiabaticcase, we derive an effective nonrigid pendulum model that allows one to conveniently discuss the onset ofan antiferromagnetic instability in an “atom-molecule pendulum,” as well as large-amplitude pairoscillations and atom-molecule entanglement.In the fifth chapter of this thesis, we propose an experimental scheme to create spin-orbitcoupling in spin-3Cr atoms using Raman processes. By employing the linear Zeeman effect and opticalStark shift, two spin states within the ground electronic manifold are selected, which results in apseudospin-1/2model. We show that, in addition to the stripe structures induced by the spin-orbit coupling,the magnetic dipole-dipole interaction gives rise to the vortex phase, in which a spontaneous spin vortex isformed. Compared to its spin-3counterpart， the pseudo spin-1/2Cr condensate has the advantage of muchsimple form of contact interaction, such that the spin vortex is readily observable. Finally, we point out thatour scheme should also apply to the Dy atom, which has an even larger dipole moment.