Spin texturing in a parabolically confined quantum wire with Rashba and Dresselhaus spin–orbit interactions

In this study, we investigate theoretically the effect of spin–orbit coupling on the energy level spectrum and spin texturing of a quantum wire with a parabolic confining potential subjected to the perpendicular magnetic field. Highly accurate numerical calculations have been carried out using a finite element method. Our results reveal that the interplay between the spin–orbit interaction and the effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps. Competing effects between external field and spin–orbit interactions introduce complex features in spin texturing owing to the couplings in energy subbands. We obtain that spatial modulation of the spin density along the wire width can be considerably modified by the spin–orbit coupling strength, magnetic field and charge carrier concentration.     

Spin–orbit-coupled spin-1 Bose–Einstein condensates confined in radially periodic potential

We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radiallyperiodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, wefirst demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex canbe observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbitcoupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-functionphase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase ofthe ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength cancontrol the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.     

Dark Soliton of Polariton Condensates under Nonresonant PT-Symmetric Pumping

A quantum system in complex potentials obeying parity-time(PT) symmetry could exhibit all real spectra,starting out in non-Hermitian quantum mechanics. The key physics behind a PT-symmetric system consists of the balanced gain and loss of the complex potential. We plan to include the nonequilibrium nature(i.e., the intrinsic kinds of gain and loss of a system) to a PT-symmetric many-body quantum system, with an emphasis on the combined effects of non-Hermitian due to nonequilibrium nature and PT symmetry in determining the properties of a system. To this end, we investigate the static and dynamical properties of a dark soliton of a polariton Bose–Einstein condensate under the PT-symmetric non-resonant pumping by solving the drivendissipative Gross–Pitaevskii equation both analytically and numerically. We derive the equation of motion for the center of mass of the dark soliton's center analytically with the help of the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and PT-symmetry affects the properties of the dark soliton; i.e., the soliton relaxes by blending with the background at a finite time. Further numerical solutions are in excellent agreement with the analytical results.     

Enhancing von Neumann entropy by chaos in spin–orbit entanglement

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.     

Polaron and molecular states of a spin–orbit coupled impurity in a spinless Fermi sea

We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling(SOC)coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spinselected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass(c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Bose–Einstein condensates under a non-Hermitian spin–orbit coupling

We study the properties of Bose–Einstein condensates under a non-Hermitian spin–orbit coupling(SOC), induced by a dissipative two-photon Raman process. We focus on the dynamics of the condensate at short times, when the impact of decoherence induced by quantum jumps is negligible and the dynamics is coherently driven by a non-Hermitian Hamiltonian. Given the significantly modified single-particle physics by dissipative SOC, the interplay of non-Hermiticity and interaction leads to a quasi-steady-state phase diagram different from its Hermitian counterpart. In particular, we find that dissipation can induce a phase transition from the stripe phase to the plane-wave phase. We further map out the phase diagram with respect to the dissipation and interaction strengths, and finally investigate the stability of quasi-steady states through the time-dependent dissipative Gross–Pitaevskii equation. Our results are readily accessible based on standard experiments with synthetic spin–orbit couplings.     

Superfluidity of Bose Einstein condensates in ultracold atomic gases

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose–Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters,such as interaction strength and density. The new superfluid, Bose–Einstein condensate(BEC), offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin–orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spin–orbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross–Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.     

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice, with the nearest- neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define ＂half-time＂ as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.     

Composite solitons in SU(3) spin–orbit-coupling Bose gases

We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases.     

线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响

利用变分近似及基于Gross-Pitaevskii方程的直接数值模拟方法,研究了自旋-轨道耦合玻色-爱因斯坦凝聚体中线性塞曼劈裂对亮孤子动力学的影响,发现线性塞曼劈裂将导致体系具有两个携带有限动量的静态孤子,以及它们在微扰下存在一个零能的Goldstone激发模和一个频率与线性塞曼劈裂有关的谐振激发模.同时给出了描述孤子运动的质心坐标表达式,发现线性塞曼劈裂明显影响孤子的运动速度和振荡周期.     

Self-deflection of bright soliton in a separate bright-dark screening soliton pair based on higher-order space charge field

Based on the interaction of the separate soliton pair, the self-deflection of the bright screening soliton in a bright-dark pair is studied by taking the higher order space charge field into account. Both numerical and analytical methods are adopted to obtain the result that the higher order of space charge field can enhance the deflection process of the bright soliton and varying the peak intensity of the dark soliton can influence the self-deflection strongly. The expression of the deflection distance with the dark soliton's peak intensity is derived, and some corresponding properties of the self-deflection process are figured out.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Nonautonomous deformed solitons in a Bose-Einstein condensate

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.     

Bright soliton dynamics in Fourier synthesized optical lattice

We consider the dynamics of bright solitons in one dimensional Bose Einstein condensate with spin orbit coupling and trapped by an optical lattice potential. We mainly focus on the effects of the spin orbit coupling, Rabi coupling and detuning parameter on the soliton dynamics. The solution of the coupled Gross Pitaevskii equation is performed with the help of the variational and numerical methods for various parameters. The population imbalance and the center of mass motion show different dynamic behaviors depending on the parameters. We also obtain traveling bright solitons related with a given finite initial momentum.     

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrdinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter , which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈2≠1) while it has no effects on the wave central position.Moreover, the precise expressions of a nonautonomous black soliton's (∈2≠1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.     

Hamiltonian Two-Body System in Special Relativity

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of “predictive relativistic mechanics”, founded on the equal-time condition. The center of mass is rather a center of energy. Individual energies are separately conserved and the meaning of their positivity is discussed in terms of world-lines. Several results derived decades ago under restrictive assumptions are extended to the general case. Relative motion has a structure similar to that of a nonrelativistic one-body motion in a stationary external potential, but its evolution parameter is generally not a linear function of the center-of-mass time, unless the relative motion is circular (in this latter case the motion is periodic in the center-of-mass time). Finally the case of an extreme mass ratio is investigated. When this ratio tends to zero the heavy body coincides with the center of mass provided that a certain first integral, related to the binding energy, is not too large.     

A Self-Damping Phenomenon in the Motion of the Soliton

The properties of the soliton's acceleration in a constant applied field are studied numerically. The results indicate that its acceleration varies in waves rather than maintains constant in time, and it is not proportional to the applied field. The motion of the soliton appears to be a self-damping phenomenon.     

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, X(t), and its width, l(t), we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width l(t) oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necessary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and phi4 systems, which are seen to exhibit the same qualitative behavior. Our results show features similar to those obtained in recent experimental work on dissipation induced symmetry breaking.