Modulational Instability of Trapped Two-Component Bose-Einstein Condensates

The modulational instability of two-component Bose-Einstein condensates(BECs)under an external parabolic potential is discussed.Based on the trapped two-component Gross-Pitaevskill equations,a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis.It is shown that a modulational unstable time scale exists for trapped two-component BECs.The modulational properties-which are determined by the wave number,external trapping parameter,intraand inter-species atomic interactions-are modified significantly.The analytical results are confirmed by direct numerical simulation.Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Periodically modulated interaction effect on transport of Bose–Einstein condensates in lattice with local defects

We theoretically investigate the periodically modulated interaction effect on the propagation properties of a traveling plane wave in a Bose–Einstein condensate(BEC) trapped in a deep annular lattice with local defects both analytically and numerically. By using the two-mode ansatz and the tight-binding approximation, a critical condition for the system preserving the superfluidity is obtained analytically and confirmed numerically. We find that the coupled effects of periodic modulated atomic interactions, the quasi-momentum of the plane wave, and the defect can control the superfluidity of the system. Particularly, when we consider the periodic modulation in the system with single defect, the critical condition for the system entering the superfluid regime depends on both the defect and the momentum of the plane wave. This is different from the case for the system without the periodic modulation, where the critical condition is only determined by the defect. The modulation and quasi-momentum of the plane wave can enhance the system entering the superfluid regime. Interestingly, when the modulated amplitude/frequency, the defect strength, and the quasi-momentum of the plane wave satisfy a certain condition, the system will always be in the superfluid region. This engineering provides a possible means for studying the periodic modulation effect on propagation properties and the corresponding dynamics of BECs in disordered optical lattices.

Collapses-revivals phenomena induced by weak magnetic flux in diamond chain

We investigate the quantum dynamical behaviors of bosons in a diamond chain with weak magnetic flux(WMF),including Landau–Zener tunnelling,Bloch oscillations,localization phenomenon,and collapses-revivals phenomena.We observed that collapses-revivals phenomena can occur in diamond chain with WMF and cannot exist in the strong magnetic flux case as the previous study(Chang N N and Xue J K,2018,Chin.Phys.B 27105203).Induced by WMF,the energy band for the system varies from gapless to gapped structure.The position of the extrema of probability amplitude for ground state can also be altered by WMF within a single diamond plaquette.As a consequence,the transitions between different dynamical behaviors of bosons in diamond chain can be manipulated by WMF,depending on its initial configurations.

Tunneling dynamics of bosons in the diamond lattice chain

We analyze the effect of tilting and artificial magnetic flux, on the energy bands structure for the system and the corresponding tunneling dynamics for bosons with various initial configurations in the diamond lattice chain, where intriguing and significant phenomena occur, including Landau–Zener tunneling, Bloch oscillations, and localization phenomenon.Both vertical tilting and artificial magnetic flux may alter the structure of energy levels（dispersion structure or flat band）,and enforce the occurrence of Landau–Zener tunneling, which scans the whole of the Bloch bands. We find that, transitions among Landau–Zener tunneling, Bloch oscillations, and localization phenomenon, are not only closely related to the energy bands structure, but also depends on the initial configuration of bosons in the diamond lattice chain. As a consequence,Landau–Zener tunneling, Bloch oscillations, and localization phenonmenon of bosons always counteract and are complementary with each other in the diamond lattice chain.

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.

Direct electron acceleration by chirped laser pulse in a cylindrical plasma channel

We study the dynamics of single electron in an inhomogeneous cylindrical plasma channel during the direct acceleration by linearly polarized chirped laser pulse.By adjusting the parameters of the chirped laser pulse and the plasma channel,we obtain the energy gain,trajectory,dephasing rate and unstable threshold of electron oscillation in the channel.The influences of the chirped factor and inhomogeneous plasma density distribution on the electron dynamics are discussed in depth.We find that the nonlinearly chirped laser pulse and the inhomogeneous plasma channel have strong coupled influence on the electron dynamics.The electron energy gain can be enhanced,the instability threshold of the electron oscillation can be lowered,and the acceleration length can be shortened by chirped laser,while the inhomogeneity of the plasma channel can reduce the amplitude of the chirped laser.

Generation of a Plasma Waveguide with Slow-Wave Structure

Using the particle-in-cell simulations,we report an efficient scheme to generate a slow wave structure in the electron density of a plasma waveguide,based on the array laser-plasma interaction.The spatial distribution of the electron density of the plasma waveguide is modulated via effective control of the super-Gaussian index and array pattern code of the lasers.A complete overview of the holding time,and the bearable laser’s intensity of the electron density structure of the plasma waveguide,is obtained.In addition,the holding time of the slow wave structure of the plasma waveguide is also controlled by adjusting the frequency of the array laser beam.Finally,effects due to ion motion are discussed in detail.

Cyclotron dynamics of neutral atoms in optical lattices with additional magnetic field and harmonic trap potential

We analytically and numerically discuss the stability and dynamics of neutral atoms in a two-dimensional optical lattice subjected to an additional harmonic trap potential and artificial magnetic field.The harmonic trap potential plays a key role in modifying the equilibrium state properties of the system and stabilizing the cyclotron orbits of the condensate.Meanwhile,the presence of the harmonic trap potential and lattice potential results in rich cyclotron dynamics of the condensate.The coupling effects of lattice potential,artificial magnetic field,and harmonic trap potential lead to single periodic,multi-periodic or quasi-periodic cyclotron orbits of the condensate.So we can control the cyclotron dynamics of neutral atoms in optical lattice by manipulating the strength of harmonic confinement,artificial magnetic field,and initial conditions.Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in optical lattices exposed to the artificial gauge magnetic field and harmonic trap potential.

Laser-driven relativistic electron dynamics in a cylindrical plasma channel

The energy and trajectory of the electron, which is irradiated by a high-power laser pulse in a cylindrical plasma channel with a uniform positive charge and a uniform negative current, have been analyzed in terms of a single-electron model of direct laser acceleration. We find that the energy and trajectory of the electron strongly depend on the positive charge density, the negative current density, and the intensity of the laser pulse. The electron can be accelerated significantly only when the positive charge density, the negative current density, and the intensity of the laser pulse are in suitable ranges due to the dephasing rate between the wave and electron motion. Particularly, when their values satisfy a critical condition. the electron can stay in phase with the laser and gain the largest energy from the laser. With the enhancement of the electron energy, strong modulations of the relativistic factor cause a considerable enhancement of the electron transverse oscillations across the channel, which makes the electron trajectory become essentially three-dimensional, even if it is flat at the early stage of the acceleration.

Sound Wave of Spin-Orbit Coupled Bose-Einstein Condensates in Optical Lattice

We study the phonon mode excitation of spin–orbit （SO） coupled Bose–Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode, i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

We investigate the matter-wave sohtons in a spin-orbit-coupled spin-1 Bose-Einstein condensate us- ing a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled three- component Gross-Pitaevskii equations, we derive a single nonlinear SehrSdinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright sohtons when the spin-orbit coupling is weak, with the solitons depending onthe atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Bose–Einstein condensates with tunable spin–orbit coupling in the two-dimensional harmonic potential: The ground-state phases, stability phase diagram and collapse dynamics

We study the ground-state phases,the stability phase diagram and collapse dynamics of Bose–Einstein condensates(BECs)with tunable spin–orbit(SO)coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation.Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling(RC),which can be realized experimentally.Through the high-frequency approximation,an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained,which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength.Using the variational method,the phase transition boundary and collapse boundary of the system are obtained analytically,where the phase transition between the spin-nonpolarized phase with zero momentum(zero momentum phase)and spin-polarized phase with non-zero momentum(plane wave phase)can be manipulated by the external driving and sensitive to the strong external trapping potential.Particularly,it is revealed that the collapsed BECs can be stabilized by periodic driving of RC,and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed.In addition,we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength,which also depends on the RC,SO coupling strength and external trapping potential.Finally,the variational approximation is confirmed by numerical simulation of Gross–Pitaevskii equation.Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases,collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential,which can be realized easily in current experiments.