We investigate the matter rogue wave in Bose-Einstein Condensates with attractive interatomic interaction analytically and numerically. Our results show that the formation of rogue wave is mainly due to the accumulation of energy and atoms toward to its central part; Rogue wave is unstable and the decay rate of the atomic number can be effectively controlled by modulating the trapping frequency of external potential. The numerical simulation demonstrate that even a small periodic perturbation with small modulation frequency can induce the generation of a near-ideal matter rogue wave. We also give an experimental protocol to observe this phenomenon in Bose-Einstein Condensates.

We present theoretical analysis and numerical studies of the quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction in harmonic and anharmonic potentials, respectively. The exact quantized vortex and giant vortex solutions are constructed explicitly by similarity transformation. Their stability behavior has been examined by numerical simulation, which shows that a new series of stable vortex states (defined by radial and angular quantum numbers) can be supported by the spatiotemporally modulated interaction in this system. We find that there exist stable quantized vortices with large topological charges in repulsive condensates with spatiotemporally modulated interaction. We also give an experimental protocol to observe these vortex states in future experiments.

We show that double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit coupled Bose gases. It is found that the SU(3) spin-orbit coupling and spin-exchange interaction play important roles in determining the ground-state phase diagram. In the case of effective ferromagnetic spin interaction, the SU(3) spin-orbit coupling induces a three-fold degeneracy to the magnetized ground state, while in the antiferromagnetic spin interaction case, the SU(3) spin-orbit coupling breaks the ordinary phase rule of spinor Bose gases, and allows the spontaneous emergence of double-quantum spin vortices. This exotic topological defect is in stark contrast to the singly quantized spin vortices observed in existing experiments, and can be readily observed by the current magnetization-sensitive phase-contrast imaging technique.

The confinement induced resonance provides an indispensable tool for the realization of the low-dimensional strongly interacting quantum system. Here, we investigate the confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling. We find that the quasi-bound levels induced by the spin-orbit coupling and Raman coupling result in the Feshbach-type resonances. For sufficiently large Raman coupling, the bound states in one dimension exist only for sufficiently strong attractive interaction. Furthermore, the bound states in quasi-one dimension exist only for sufficient large ratio of the length scale of confinement to three dimensional s-wave scattering length. The Raman coupling substantially changes the confinement-induced resonance position. We give a proposal to realize confinement induced resonance through increasing Raman coupling strength in experiments.

Exploring physics and potential applications in vectorially structured light with propagation-invariant transverse structures has benefited many areas of modern optics and photonics. In this paper, we focus on non-eigen vector modes of paraxial light fields, and systemically investigate propagation variations and revivals of their transverse structures, including both amplitude and polarization profiles. We show that the deeper mechanism behind the evolution of the transverse structure is the variations and revivals of intramodal phases within spin-orbit coupled space and spatial-mode subspace, which originates from fractional Gouy phases, or rather, Geometric-phase difference between spatial modes under a same unitary transformation. This underlying principle, provides a general guideline for shaping vectorially structured light with custom propagation-evolution properties, and may also inspire many other new applications based on structured light.

The fragmentation of spin-orbit coupled spin-1 Bose gas with a weak interaction in external harmonic trap is explored by both exact diagonalization and mean-field theory. This fragmentation tendency, which originates from the total angular momentum conservation, is affected obviously by the spin-orbit coupling strength and the spin-dependent interaction. Strong spin-orbit interaction raises the inverse participation ratio, which describes the number of significantly occupied singleparticle states. As the spin-dependent interaction changes from anti-ferromagnetic to ferromagnetic, the peak values in the inverse participation ratio become lower. Without the confinement of the appointed total angular momentum, the condensate chooses a zero or finite total angular momentum ground state, which is determined by both the interaction and the spin-orbit coupling strength.

The Zitterbewegung effect in spin-orbit coupled spin-1 cold atoms is investigated in the presence of the Zeeman field and a harmonic trap. It is shown that the Zeeman field and the harmonic trap have significant effect on the Zitterbewegung oscillatory behaviors. The external Zeeman field could suppress or enhance the Zitterbewegung amplitude and change the frequencies of oscillation. A much slowly damping Zitterbewegung oscillation can be achieved by adjusting both the linear and quadratic Zeeman field. Multi-frequency Zitterbewegung oscillation can be induced by the applied Zeeman field. In the presence of the harmonic trap, the subpackets corresponding to different eigenenergies would always keep coherent, resulting in the persistent Zitterbewegung oscillations. The Zitterbewegung oscillation would display very complicated and irregular oscillation characteristics due to the coexistence of different frequencies of the Zitterbewegung oscillation. Numerical results show that, the Zitterbewegung effect is robust even in the presence of interaction between atoms.

The ring dark solitons in spin-1 23 Na and 87 Rb Bose-Einstein condensates are studied numerically in the framework of the time-dependent Gross-Pitaevskii equations. By simulating the phase engineering technique in real experiments, we explore the roles of the parameters characterizing the far-off resonant laser pulse which can be used to generate the ring dark solitons. The variations of these parameters have a dramatic effect on the lifetime and the decay profiles of the ring dark solitons. If only one ring dark soliton is generated in one component of the condensate, then ring dark solitons in other components are inclined to be induced, resulting in a coexistence state composed of interdependent ring dark solitons coming from different components of the condensate. Ring dark solitons in this coexistence state exhibit dynamical oscillations for hundreds of milliseconds. By studying the lifetime and decaying profiles of ring dark solitons, we explore the similarities and differences of 23 Na and 87 Rb condensates. In addition, taking into account the fact that the center of the ring may not coincide with that of the trap, we study the dynamics and decaying profiles of the off-centered ring dark solitons in the presence of the symmetry-breaking effect.