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.

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.Introduction.-Strong spin-orbit (SO) interaction is the key to realizing such remarkable states of electronic matter as topological band insulators [1, 2] and Weyl semimetals [3]. SO coupled Mott insulators can also realize the Kitaev model [4] which may enable the study of Majorana fermions in a condensed matter setting and provide a platform for topological quantum computation [5]. This has motivated parallel experimental advances in ultracold atomic gases, where Raman processes can be used to create tunable SO coupling, or more general nonabelian gauge fields [6][7][8], thus paving the way to investigating SO coupling and its emergent consequences for atomic fermions as well as bosons.Experiments [6][7][8][9] and theory [10-15] on such SO coupled bosons have, so far, mainly focused on Bose-Einstein condensation in weakly interacting gases in the absence of a lattice. However, as theory [16][17][18] and experiments [19] in the absence of SO interaction have shown, tuning the lattice depth for bosons in an optical lattice can lead to a strongly interacting regime, accompanied by a suppression of the condensate density and finally a quantum phase transition into a featureless Mott insulator [20]. By contrast, the physics of SO coupled atoms in a strongly interacting regime and in an optical lattice, both of which are expected to lead to unique phenomena, remains a relatively unexplored frontier [21].One of the most significant results in this Letter is our discovery that tuning SO coupling and interparticle interactions for 'spinful' bosons at a filling of one boson per site, leads to Mott insulating states with a

5We investigate the ground state of interacting spin-1 2 fermions in 3D at a finite density (ρ ∼ k 3 F ) 6 in the presence of a uniform non-Abelian gauge field. The gauge field configuration (GFC) described 7 by a vector λ ≡ (λx, λy, λz), whose magnitude λ determines the gauge coupling strength, generates 8 a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel 9 described by a small negative scattering length (kF |as| 1), the ground state in the absence of the 10 gauge field (λ = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. 11With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS 12 ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction

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 h͑ , ͒, where =−͑k F a s ͒ −1 and = T / T F . The function h͑ , ͒ 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 ␦͑ , ͒ and the molecular fraction f c ͑ , ͒ in the closed channel can be expressed in terms of h͑ , ͒ and thus have identical temperature dependence. The conclusions should have testable consequences in future experiments.

Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with s-wave symmetry, i.e., without relative angular momentum.We report measurements of two new physical quantities, the "p-wave contacts", and present evidence that they encode the universal aspects of p-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of 40 K, in which s-wave interactions are suppressed by polarising the sample, while p-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive p-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant p-wave quantum gas. 1 arXiv:1505.08151v4 [cond-mat.quant-gas] 13 Apr 2016 A fundamental question provoked by observation of natural systems is how macroscopic and collective properties depend on microscopic few-body interactions. Ultracold neutral atoms provide a model system in which to explore this question, since in certain conditions,few-body interactions can be tuned and characterised precisely. Over the last decade, a direct link has been made in these systems between thermodynamic properties and the underlying isotropic (s-wave) interactions. At the centre stage is a quantity called the "contact" [1][2][3][4][5][6], which describes how the energy of a system changes when the interaction strength is changed. Surprisingly, the contact is also the pivot of a set of universal relations, that constrain numerous microscopic properties, including the two-particle correlation function at short range. These relations apply regardless of temperature, density, or interaction strength [1-3, 5], to fermions and bosons [7][8][9], and in one-, two-, and three-dimensional systems [7,[10][11][12]. Contact relations have also been extended to Coulomb gases [13] and neutron-proton interactions [14]. Despite the breadth of this discussion, measurements of the contact have so far been restricted to systems with s-wave interactions.In general, the relative wave function of any pair of particles can be decomposed into components with angular momentum equal to an integer multiple of quanta. In a spinpolarised Fermi gas, quantum statistics forbids short-range interactions with even values of . Therefore, the first allowed scattering channel has = 1 (p-wave), which is typically weak due to the centrifugal barrier (see Fig. 1): the scattering cross section decreases with the square of...