In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum distribution and momentum-resolved radio-frequency spectroscopy, we observe the change of fermion population in different helicity branches consistent with a finite temperature calculation, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system.

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.

In this letter we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. Dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region, as a function of spin-orbit coupling parameters as well as oscillation amplitude. Anharmonic properties beyond effective-mass approximation are revealed, such as amplitude-dependent frequency and finite oscillation frequency at place with divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates magnetic nonzero-momentum condensate from nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a bench mark for recently developed theoretical approaches.Many interesting quantum phases can emerge in solid state materials when electrons are placed in a strong magnetic field or possess strong spin-orbit (SO) coupling, such as the fractional quantum Hall effect [1] and the topological insulator [2]. In cold atom systems, albeit neutral atoms have neither charges nor SO coupling, the recent exciting experimental progress demonstrates that artificial gauge potentials can be synthesized in laboratory by laser control technique [3][4][5][6][7][8][9][10]. Synthetic gauge potential is becoming a powerful tool for simulating real materials with cold atoms. Moreover, the system of SO coupled bosons does not have an analogy in conventional condensed matter systems, and can exhibit many novel phases [11] such as striped superfluid phase [12,13] and half vortex phase [14][15][16][17].Collective excitations play an important role in studying physical properties of trapped atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases. Collective dipole oscillation is a center-of-mass motion of all atoms. For a conventional condensate, the dipole oscillation is trivial: the frequency is just the harmonictrap frequency, independent of oscillation amplitude and interatomic interaction. This is known as Kohn theorem [18,19]. For a SO coupled condensate, however, it was found [4] that the dipole-oscillation frequency deviates from the trap frequency and the experimental data thereby can be explained by effective-mass approximation. Recently, much theoretical effort has been taken to understand dynamics of a SO coupled BEC [20][21][22][23][24][25], and many predicted unconventional properties remain to be experimentally explored. In particular, the so-called sum-rule approach predicts [25] a unique feature of SO coupled condensate: spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillatio...

This review focuses on recent developments in synthetic spin-orbit (SO) coupling in ultracold atomic gases. Two types of SO coupling are discussed. One is Raman process induced coupling between spin and motion along one of the spatial directions and the other is Rashba SO coupling. We emphasize their common features in both single-particle and two-body physics and the consequences of both in many-body physics. For instance, single particle ground state degeneracy leads to novel features of superfluidity and a richer phase diagram; increased low-energy density-of-state enhances interaction effects; the absence of Galilean invariance and spin-momentum locking gives rise to intriguing behaviours of superfluid critical velocity and novel quantum dynamics; and the mixing of two-body singlet and triplet states yields a novel fermion pairing structure and topological superfluids. With these examples, we show that investigating SO coupling in cold atom systems can, enrich our understanding of basic phenomena such as superfluidity, provide a good platform for simulating condensed matter states such as topological superfluids and more importantly, result in novel quantum systems such as SO coupled unitary Fermi gas and high spin quantum gases. Finally we also point out major challenges and some possible future directions.

We apply the fermion functional renormalization-group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended s wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter-Fermi-surface Josephson scattering generated by the antiferromagnetic correlation.