Motivated by recent experiments carried out by Spielman’s group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.

We present some general considerations on the properties of a two-component ultracold Fermi gas along the BEC-BCS crossover. It is shown that the interaction energy and the free energy can be written in terms of a single dimensionless function $h(\xi ,\tau )$, where $\xi =-{\left(k_F{a}_s\right)}^{-1}$ and $\tau =T∕T_F$. The function $h(\xi ,\tau )$ incorporates all the many-body physics and naturally occurs in other physical quantities as well. In particular, we show that the average rf-spectroscopy shift $\overline{\delta \omega }(\xi ,\tau )$ and the molecular fraction $f_c(\xi ,\tau )$ in the closed channel can be expressed in terms of $h(\xi ,\tau )$ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.

Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.

We investigate the ground state of interacting spin-$\frac{1}{2}$ fermions in three dimensions at a finite density ($\rho \sim k_F^3$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\lambda \equiv ({\lambda }_x,{\lambda }_y,{\lambda }_z)$, whose magnitude $\lambda$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $\left(k_F\right|a_s|\lesssim 1)$, the ground state in the absence of the gauge field ($\lambda =0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\lambda =0)$. For large gauge couplings $(\lambda /k_F\gg 1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—we call these bosons “rashbons.” In the absence of interactions ($a_s=0^{-}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\lambda }_T$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\lambda$ near ${\lambda }_T$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

Untwisting the Spin Spiral: Ultracold Fermi gases in the so-called unitary regime—where the diverging interactions between atoms make their thermodynamics universal—are an excellent test bed for an array of strongly interacting matter systems. The transport characteristics in this regime are particularly intriguing, and a discrepancy between two- and three-dimensional transport coefficients has been observed. Bardon et al. (p. 722 ) studied the demagnetization dynamics of a three-dimensional Fermi gas. The gas was initially polarized along a single direction and was noninteracting. An applied magnetic field gradient then caused a spin spiral to form; as the gas relaxed from this state, the authors extracted the diffusion coefficient and observed the buildup of interactions between the atoms.