Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations

We show that the wave function of a one dimensional spinor gas with contact $s$-wave interaction, either bosonic or fermionic, can be mapped to the direct product of the wave function of a spinless Fermi gas with short-range $p$-wave interaction and that of a spin system governed by spin parity projection operators. Applying this mapping to strongly interacting spinor gases, we obtain a generalized spin chain model that captures both the static and dynamics properties of the system. Using this spin chain model, we investigate the breathing mode frequency and the quench dynamics of strongly interacting harmonically trapped spinor gases.Comment: 5 pages of main text + 5 pages of Supplemental Materia

Photon-Induced Spin-Orbit Coupling in Ultracold Atoms inside Optical Cavity

We consider an atom inside a ring cavity, where a plane-wave cavity field together with an external coherent laser beam induces a two-photon Raman transition between two hyperfine ground states of the atom. This cavity-assisted Raman transition induces effective coupling between atom's internal degrees of freedom and its center-of-mass motion. In~the meantime, atomic dynamics exerts a back-action to cavity photons. We investigate the properties of this system by adopting a mean-field and a full quantum approach, and show that the interplay between the atomic dynamics and the cavity field gives rise to intriguing nonlinear phenomena.Comment: 12 pages, 5 figures, and published versio

Multi-stability in an optomechanical system with two-component Bose-Einstein condensate

We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudo-spin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center- of-mass motion, the atomic collective spin and the cavity field leads to a strong nonlinearity, resulting in multi- stable behavior in both matter wave and light wave at the few-photon level.Comment: 4 pages, 3 figure