An experimental proposal for realizing spin-orbit (SO) coupling of pseudospin 1 in the ground manifold ${}^{1}\mathrm{\ensuremath{\Sigma}}(\ensuremath{\upsilon}=0)$ of (bosonic) bialkali polar molecules is presented. The three spin components are composed of the ground rotational state and two substates from the first excited rotational level. Using hyperfine resolved Raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. The properties of Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar interactions are further explored. In addition to the SO-coupling-induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using SO-coupled rotating polar molecules with dipolar interactions.
An experimental proposal for realizing spin-orbit (SO) coupling of pseudospin 1 in the ground manifold 1\ensuremathΣ(\ensuremathυ=0) of (bosonic) bialkali polar molecules is presented. The three spin components are composed of the ground rotational state and two substates from the first excited rotational level. Using hyperfine resolved Raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. The properties of Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar interactions are further explored. In addition to the SO-coupling-induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using SO-coupled rotating polar molecules with dipolar interactions.
We propose a scheme to realize a pseudospin-1/2 model of the ${}^{1}\mathrm{\ensuremath{\Sigma}}(v=0)$ bialkali polar molecules with the spin states corresponding to two sublevels of the first excited rotational level. We show that the effective dipole-dipole interaction between two spin-1/2 molecules couples the rotational and orbital angular momenta and is highly tunable via a microwave field. We also investigate the ground-state properties of a spin-1/2 molecular condensate. A variety of nontrivial quantum phases, including the doubly quantized vortex states, are discovered. Our scheme can also be used to create spin-1 model of polar molecules. Thus we show that the ultracold gases of bialkali polar molecules provide a unique platform for studying the spinor condensates of rotating molecules.
We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. By employing the linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudospin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. 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 is formed.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
The recently realized spin-orbit-coupled quantum gases [Lin et al., Nature (London) 471, 83 (2011); Wang et al., Phys. Rev. Lett. 109, 095301 (2012); Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)] mark a breakthrough in the cold atom community. In these experiments, two hyperfine states are selected from a hyperfine manifold to mimic a pseudospin-1/2 spin-orbit-coupled system by the method of Raman dressing, which is applicable to both bosonic and fermionic gases. In this paper, we show that the method used in these experiments can be generalized to create any large pseudospin spin-orbit-coupled gas if more hyperfine states are coupled equally by the Raman lasers. As an example, we study, in detail, a quantum gas with three hyperfine states coupled by the Raman lasers and show, when the state-dependent energy shifts of the three states are comparable, triple-degenerate minima will appear at the bottom of the band dispersions, thus, realizing a spin-1 spin-orbit-coupled quantum gas. A novel feature of this three-minima regime is that there can be two different kinds of stripe phases with different wavelengths, which has an interesting connection to the ferromagnetic and polar phases of spin-1 spinor Bose-Einstein condensates without spin-orbit coupling.
The dissertation explores the effects of synthetic spin-orbit coupling on the behaviour of quantum gases in several different contexts. We first study realistic methods to create vortices in spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC). We propose two different methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the Raman lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We solve the Gross-Pitaevskii equation for several experimentally relevant regimes and find new interesting effects such as spatial separation of left- and right-moving spin-orbit-coupled condensates, and the appearance of unusual vortex arrangements. Next we consider cold atoms in an optical lattice with synthetic SOC in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model and derive the low-energy spin Hamiltonian which is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interaction. We find that the Hamiltonian supports a rich classical phase diagram with collinear, spiral and vortex phases. Next we study the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes controlled by the ratio of interaction and spin-orbit-coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero and for large λ, a partially magnetized state is dynamically stabilized. Motivated by an interesting stripe phase which appears in BEC with SOC [Li et al., Phys. Rev. Lett. 108, 225301 (2011)], we study the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions. We show that strong inter-spin interactions can lead to the appearance of magnetically ordered phases at temperatures above the superfluid transition. For the case of inter-spin attraction, we also discuss the possibility of a bosonic analogue of the Cooper-paired phase, however this state is not energetically favourable. We extend our calculations to a spin-orbit-coupled Bose gas to investigate the possibility of stripe ordering in the normal phase. However, within our approximations, we do not find an instability towards stripe formation. Finally, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This Hamiltonian can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature 471, 83 (2011)], or using the shaken lattice scheme of Parker et al. [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics 9, 769 (2013)]. By numerically comparing energies of various trial wave-functions, we show that, at low densities, the ground state is strongly correlated, in contrast to a typical mean-field BEC. The trial wave-function with the lowest energy is of Jastrow-type and it describes a state with finite, but strongly reduced, condensate fraction.
The experimental realization of emergent spin-orbit coupling through laser-induced Raman transitions in ultracold atoms paves the way for exploring novel superfluid physics and simulating exotic many-body phenomena. A recent proposal with the use of Laguerre-Gaussian lasers enables another fundamental type of coupling between spin and orbital angular momentum (SOAM) in ultracold atoms. We hereby study quantum phases of a realistic Bose-Einstein condensate (BEC) with this synthetic SOAM coupling in a disk-shaped geometry, respecting radial inhomogeneity of the Raman coupling. We find that the experimental system naturally resides in a strongly interacting regime in which the phase diagram significantly deviates from the single-particle picture. The interplay between SOAM coupling and interaction leads to rich structures in spin-resolved position and momentum distributions, including a stripe phase and various types of immiscible states. Our results would provide a guide for an experimental investigation of SOAM-coupled BECs.