We examine the internal structure of ground states a trapped Bose-Einstein condensate in which atoms have three hyperfine spins. determine set collective spin minimize interaction energy between atoms. also dynamics an initially polarized condensate. The time scale spin-mixing is predicted.

We present theoretical studies of a two-species Bose condensate. Using new numerical method, we have calculated ground state wave functions and show that, due to interspecies interactions, the condensate mixture displays novel behavior not found in pure compared our results with those Thomas-Fermi approximation (TFA) find that under broad range conditions TFA can be reliably used predict many qualitative features condensates. technique, modeled recent JILA experiment on dual spin-state...

We investigate theoretically the phase diagram of a spin-orbit coupled Bose gas in two-dimensional harmonic traps. show that at strong coupling single-particle spectrum decomposes into different manifolds separated by $\ensuremath{\hbar}{\ensuremath{\omega}}_{\ensuremath{\perp}}$, where ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is trapping frequency. For weakly interacting gas, quantum states with Skyrmion lattice patterns emerge spontaneously and preserve either parity symmetry or...

We study the spin-mixing dynamics of an $f=1$ spinor condensate. show that is sensitive to relative phase and particle number distribution among individual components condensate, find complex structures can develop in density profiles during time evolution. investigate different scales process their dependence on total number.

Motivated by the prospect of realizing a Fermi gas $^{40}$K atoms with synthetic non-Abelian gauge field, we investigate theoretically strongly interacting in presence Rashba spin-orbit coupling. As two-fold spin degeneracy is lifted interaction, bound pairs mixed singlet and triplet pairings (referred to as rashbons) emerge, leading an anisotropic superfluid. We show that this superfluidity can be probed via measuring momentum distribution single-particle spectral function trapped atomic...

We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Rosen correlation and fluctuation in one its quasispin components vanishes. show that an elongated condensate with large aspect ratio is most suitable such state.

We present a new theoretical treatment of the collective excitation spectrum two-species Bose-Einstein condensate confined in magnetic trap. show that interspecies interaction significantly modifies and gives rise to rich set phenomena. identify novel metastable state double under external perturbation there can be macroscopic quantum transition between this true ground system.

By means of variational methods and systematic numerical analysis, we demonstrate the existence metastable solitons in three dimensional (3D) free space, context binary atomic condensates combining contact self-attraction spin-orbit coupling, which can be engineered by available experimental techniques. Depending on relative strength intra- intercomponent attraction, stable feature a semivortex or mixed-mode structure. In spite fact that local cubic gives rise to supercritical collapse 3D,...

We investigate theoretically the condensate state and collective excitations of a two-component Bose gas in two-dimensional harmonic traps subject to isotropic Rashba spin-orbit coupling. In weakly interacting regime when inter-species interaction is larger than intra-species ($g_{\uparrow\downarrow}>g$), we find that ground has half-quantum-angular-momentum vortex configuration with spatial rotational symmetry skyrmion-type spin texture. Upon increasing interatomic beyond threshold $g_{c}$,...

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. find that a small perturbation in trapping potential can lead to dramatic changes condensate's density profile for sufficiently large interaction strengths and trap aspect ratios. By employing theory, we relate these oscillations previously-identified "roton-like" mode BECs. The same physics is responsible radial vortex states BECs have been predicted previously.

We demonstrate control of the collapse and expansion an 88Sr Bose-Einstein condensate using optical Feshbach resonance (OFR) near 1S0-3P1 intercombination transition at 689 nm. Significant changes in dynamics are caused by modifications scattering length up to +- ?10a_bg, where background is a_bg = -2a0 (1a0 0.053 nm). Changes monitored through size after a time-of-flight measurement. Because close zero, blue detuning OFR laser with respect photoassociative leads increased interaction energy...

Ultracold atoms confined to periodic potentials have proven be a powerful tool for quantum simulation of complex many-body systems. We confine fermions one-dimension realize the Tomonaga-Luttinger liquid model describing highly collective nature their low-energy excitations. use Bragg spectroscopy directly excite either spin or charge wave various strength repulsive interaction. observe that velocity and excitations shift in opposite directions with increasing interaction, hallmark...

We consider the intrinsic stability of vortex states a pure Bose-Einstein condensate confined in harmonic potential under effects coherent atom-atom interaction. find that stable vortices can be supported and controlled by changing interparticle interaction strength. At unstable regimes, will spontaneously disintegrate into with different angular momenta even without external perturbations, lifetime determined its imaginary excitation frequencies.

We have mapped out a detailed phase diagram that shows the ground state structure of spin-1 condensate with magnetic dipole-dipole interactions. show interplay between dipolar and spin-exchange interactions induces rich variety quantum phases exhibit spontaneous ordering in form intricate spin textures.

We consider a system of quantum degenerate spin-polarized fermions in harmonic trap at zero temperature, interacting via dipole-dipole forces. introduce variational Wigner function to describe the deformation and compression Fermi gas phase space use it examine stability system. emphasize important roles played by Fock exchange term dipolar interaction, which results nonspherical surface.

We examine theoretically the visualization of Majorana fermions in a two-dimensional trapped ultracold atomic Fermi gas with spin-orbit coupling. By increasing an external Zeeman field, transits from nontopological to topological superfluid, via mixed phase which both types superfluids coexist. show that zero-energy fermion, supported by superfluid and localized at vortex core, may be visible through (i) core density (ii) local states, are readily measurable experiment. present realistic...

Under the second-order degenerate perturbation theory, we show that physics of $N$ particles with arbitrary spin confined in a one dimensional trap strongly interacting regime can be described by super-exchange interaction. An effective spin-chain Hamiltonian (non-translational-invariant Sutherland model) constructed from this procedure. For spin-1/2 particles, model reduces to non-translational-invariant Heisenberg model, where transition between anti-ferromagnetic (AFM) and ferromagnetic...

By inducing a Raman transition using pair of Gaussian and Laguerre-Gaussian laser beams, we realize ^{87}Rb condensate whose orbital angular momentum (OAM) its internal spin states are coupled. varying the detuning coupling strength transition, experimentally map out ground-state phase diagram system for first time. The transitions between different phases feature discontinuous jump OAM polarization, hence order. We demonstrate hysteresis loop associated with such first-order transitions....

We propose a scheme to simulate topological physics within single degenerate cavity, whose modes are mapped lattice sites. A crucial ingredient of the is construct sharp boundary so that open condition can be implemented for this effective system. In doing so, properties system manifest themselves on edge states, which probed from spectrum an output cavity field. demonstrate with two examples: static Su-Schrieffer-Heeger chain and periodically driven Floquet insulator. Our work opens up new...

The interplay of interactions, symmetries, and gauge fields usually leads to intriguing quantum many-body phases. To explore the nature emerging phases, we study a Rabi triangle system as an elementary building block for synthesizing artificial magnetic field. We develop analytical approach rich phase diagram associated criticality. Of particular interest is emergence chiral-coherent phase, which breaks both ${\mathbb{Z}}_{2}$ chiral symmetry. In this photons flow unidirectionally chirality...

We map a quantum Rabi ring, consisting of N cavities arranged in ring geometry, into an effective magnetic model containing the XY exchange and Dzyaloshinskii-Moriya (DM) interactions. The analog latter is induced by artificial field, which modulates photon hopping between nearest-neighbor with phase. This mapping facilitates description understanding different phases optical through simple arguments competing For square geometry (N=4) rich phase diagram exhibits three superradiant denoted...

We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of stability. It plays same role sign scattering length in one-species condensate. predict that there is range interspecies interaction strength which sodium-rubidium mixture can be stable harmonic trap.

We investigate the properties of single vortices and vortex lattice in a rotating dipolar condensate. show that this system possess many novel features induced by long-range anisotropic interaction between particles. For example, when dipoles are polarized along rotation axis, may display crater-like structure; orthogonal to cores takes an elliptical shape no longer possesses hexagonal symmetry.

We study the Feshbach resonance assisted stimulated adiabatic passage of an effective coupling field for creating stable molecules from atomic Bose condensate. By exploring properties coherent population trapping state, we show that, contrary to previous belief, mean-field shifts need not limit conversion efficiency as long one chooses route that compensates collision phase and avoids dynamical unstable regime.