We study harmonically trapped one-dimensional atoms subjected to an equal combination of Rashba and Dresselhaus spin-orbit coupling induced by Raman transition. We first examine the wave function and the degeneracy of the single-particle ground state, followed by a study of two weakly interacting bosons or fermions. For the two-particle ground state, we focus on the effects of the interaction on the degeneracy, the spin density profiles, and the density-density correlation functions. Finally we show how these studies help us to understand the many-body properties of the system.

We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudo-spin states of the atom. This gives rise to an effective coupling between atom's pseudo-spin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-orbit coupling modifies the Dicke superradiance phase transition boundary and the non-superradiant normal phase may become reentrant in some regimes.

Abstract: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.

We investigate the ground-state properties of a dual-species spin-1/2 Bose-Einstein condensate. One of the species is subjected to a pair of Raman laser beams that induces spin-orbit (SO) coupling, whereas the other species is not coupled to the Raman laser. In certain limits, analytical results can be obtained. It is clearly shown that, through the inter-species spin-exchange interaction, the second species also exhibits SO coupling. This mixture system displays a very rich phase diagram, with many of the phases not present in an SO coupled single-species condensate. Our work provides a new way of creating SO coupling in atomic quantum gases, and opens up a new avenue of research in SO coupled superfluid mixtures. From a practical point of view, the spin exchange-induced SO coupling may overcome the heating issue for certain atomic species when subjected to the Raman beams.

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We develop an analytical approach for calculating the scattering and bound states of two polaritons in a one-dimensional (1D) infinite array of coupled cavities, with each cavity coupled to a two-level system (TLS). In particular, we find that in such a system a contact interaction between two polaritons is induced by the nonlinearity of the Jaynes-Cummigs Hamiltonian. Using our approach we solve the two-polariton problem with zero center-of-mass momentum, and find 1D resonances. Our results are relevant to the transport of two polaritons, and are helpful for the investigation of many-body physics in a dilute gas of polaritons in a 1D cavity array.

We consider a mixture of spin-1/2 bosons and fermions, where only the bosons are subjected to the spin-orbit coupling induced by Raman beams. The fermions, although not directly coupled to the Raman lasers, acquire an effective spin-orbit coupling through the spin-exchange interaction between the two species. Our calculation shows that this is a promising way of obtaining spin-orbit coupled Fermi gas without Raman-induced heating, where the long-sought topological Fermi superfluids and topological bands can be realized. Conversely, we find that the presence of fermions not only provides a new way to create the supersolid stripe phase of the bosons, but more strikingly it can also greatly increase the spatial period of the bosonic density stripes, and hence makes this phase directly observable in experiment. This system provides a new and practical platform to explore the physics of spin-orbit coupling, which possesses a dynamic nature through the interaction between the two species.

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