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We explore a new way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a {\pi} phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half- skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba-type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in a good agreement with the numerical results., Comment: 13 pages, 9 figures

Recently, the terahertz (THz) photon-assisted tunneling (PAT) through a two-level InAs quantum dot (QD) has been successfully realized in experiment [Phys. Rev. Lett. {\bf 109}, 077401 (2012)]. The Coulomb interaction in this device is comparable with the energy difference between the two energy levels. We theoretically explore the effects of Coulomb interaction on the PAT processes and show that the main peaks of the experiment can be well derived by our model analysis. Furthermore, we find additional peaks, which were not addressed in the InAs QD experiment and may be further identified in experiments. In particular, we show that, to observe the interesting photon-induced excited state resonance in InAs QD, the Coulomb interaction should be larger than THz photon frequency., Comment: 6 pages, 4 figures

Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin-orbit coupling on a deep square optical lattice using spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase. It suggests the emergence of a new state in the phase diagram. Such features of the spin excitation spectra provide further insights into the exploration of the exotic spin phases., Comment: 8pages, 4 figures

We investigate the superfluidity of attractive Fermi gas in a square optical lattice with spin-orbit coupling (SOC). We show that the system displays a variety of new filling-dependent features. At half filling, a quantum phase transition from a semimetal to a superfluid is found for large SOC. Close to half filling where the emerging Dirac cones governs the behaviors of the system, SOC tends to suppress the BCS superfluidity. Conversely, SOC can significantly enhance both the pairing gap and condensate fraction and lead to a new BCS-BEC crossover for small fillings. Moreover, we demonstrate that the superfluid fraction also exhibits many interesting phenomena compared with the spin-orbit coupled Fermi gas without lattice., Comment: references updated and typos corrected

We analytically and numerically investigate the ground state of the spin-orbit coupled spin-1 Bose-Einstein condensates in an external parabolic potential. When the spin-orbit coupling strength $\kappa$ is comparable with that of the trapping potential, the density distribution centers of different components of the spinor condensate deviate evidently from the trap center in the plane wave and stripe phases. When $\kappa\gg1$, the magnitude of this deviation decreases as $\kappa$ is getting larger and larger. Correspondingly, periphery half-skyrmions textures arise. This deviation can be reflected by the non-uniform magnetic moment in the $z$ direction, $\mathcal{F}_z$. With the manipulation of the external trap, the local magnitude of $\mathcal{F}_z$ can be increased evidently. This kind of increase of $\mathcal{F}_z$ is also observed in the square vortex lattice phase of the condensate., Comment: 7pages,8 figures

We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when the strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.