New Families of Soliton and Periodic Solutions of Bose-Einstein Condensation in Linear Magnetic Field and Time-Dependent Laser Field

By using a new generally projective Riccati equation method and with the help of symbolic computation,we consider a nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. As a result,some new soliton solutions, rational function solution, and periodic solutions are obtained.

A Rotating Bose-Einstein Condensation in a Toroidal Trap

We have studied the ground state configurations of a rotating Bose-Einstein condensation in a toroidal trap as the radius of the central Ganssian potentiaJ expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the ganssian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.

Dynamic Analysis for Bose-Einstein Condensation in Quantum Cavity

For the two-level atoms system interacting with single-mode active field in a quantum cavity, the dynamics of the Bose-Einstein Condensation (BEC) is analyzed using an ordinary method suggested by authors to solve the system of Schrodinger representation in the Heisenberg representation. The wave function of the atoms is given. The stability factor determining the BEC and the selection rules of the quantum transition are solved.

Envelope Periodic Solutions to Bose-Einstein Condensation in Linear Magnetic Field and Time-Dependent Laser Field

In this paper, by applying the extended 3acobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose-Einstein condensation in linear magnetic field and time-dependent laser field are obtained.

Classical-field description of Bose-Einstein condensation of parallel light in a nonlinear optical cavity

We study the Bose–Einstein condensation of parallel light in a two-dimensional nonlinear optical cavity,where the massive photons are converted into photon molecules(p-molecules).We extend the classical-field method to provide a description of the two-component system,and we also derive a coupled density equation which can be used to describe the conversion relation between photons and p-molecules.Furthermore,we obtain the chemical potential of the system,and we also find that the system can transform from the mixed photon and p-molecule condensate phase into a pure p-molecule condensate phase.Additionally,we investigate the collective excitation of the system.We also discuss the problem how the spontaneous decay of an atom is influenced by both the phase transition and collective excitation of the coupling system.

Temperature dependence of the energy-level shift induced by the Bose-Einstein condensation of photons

We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose-Einstein condensation of photons. It is found that below the critical temperature Tc, the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.

All-Optical Production of Quantum Degeneracy and Molecular Bose-Einstein Condensation of ~6Li

We achieve a highly degenerate and strongly interacting Fermi gas in a mixture of the two lowest hyperfine states of 6 Li by direct evaporative cooling in a high power crossed optical dipole trap. The trap is loaded from a large atom number magneto-optical trap realized by a laser system of Z5-W intracavity-frequency-doubled light output at 671 nm. With this system, we also demonstrate the production of a molecular Bose-Einstein condensate （reBEC） of 6Li2, and observe the anisotropic expansion of Fermi gases in the so-called BEC-Bardeen-Cooper-Schrieffer crossover regime.

Influence on the Lifetime of ^(87)Rb Bose-Einstein Condensation for Far-Detuning Single-Frequency Lasers with Different Phase Noises

We study the influence of the phase noises of far detuning single frequency lasers on the lifetime of Bose-Einstein condensation（BEC）of^（87）Rb in an optical dipole trap.As a comparison,we shine a continuous-wave singlefrequency Ti：sapphire laser,an external-cavity diode laser and a phase-locked diode laser on BEC.We measure the heating and lifetime of BEC in two different hyperfine states：｜F=2,m_F=2〉and｜F=1,m_F=1〉.Due to the narrow linewidth and small phase noise,the continuous-wave single-frequency Ti：sapphire laser has less influence on the lifetime of^（87）Rb BEC than the external-cavity diode laser.To reduce the phase noise of the external-cavity diode laser,we use an optical phase-locked loop for the external-cavity diode laser to be locked on a Ti：sapphire laser.The lifetime of BEC is increased when applfying the phase-Jocked diode laser in contrast with the external-cavity diode laser.

Bose-Einstein condensation on an atom chip

This paper reports an experiment of creating Bose-Einstein condensate （BEC） on an atom chip. The chip-based Z-wire current with a homogeneous bias magnetic field creates a tight magnetic trap, which allows for a fast production of BEC. After a 4.17-s forced radio frequency evaporative cooling, a condensate with about 3000 atoms appears. The transition temperature is about 300 nK. This compact system is quite robust, allowing for versatile extensions and further studying of BEC.

A Method for Determining the Phase Transition Point of the Bose-Einstein Condensation by Judging the Fitting Errors

In this paper, We demonstrate an approach to determine the phase transition point and critical temperature of Bose-Einstein condensation. During the fitting sequence of time-of-flight images, for just one picture we take four kinds of different calculations instead of only one. By calculating the quantitative least-square errors, which have always been neglected before, we find out that this value can act as a criterion to judge the status of atom clouds. Using this criterion, we can not only discriminate the status around the phase transition point, but can also find the critical point precisely. Also with this method, we can achieve the totally automatical running of calculating programs without human＇s judgments.

Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation

The BEG of charged pions is investigated in the framework of O（4） linear sigma model. By using Cornwall- Jackiw-Tomboufis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The critical temperature and phase diagram of BEG are discussed in the non-chiral limit at Hartree approximation.

Bose-Einstein Condensation of Confined Magnons in Nanostructures

A number of diverse kinds of magnetic experiments are shown to lead to the observation of a Bose-Einstein condensation of magnons in some nanostructures, especially in Fe and in Co/Pt. The experiments include 1) the measurement of magnetic aftereffect, 2) measurements of Néel’s fluctuation field, including an estimate of activation volume, 3) the measurement of the energy gap which provides a lower limit on the BEC temperature, 4) using Lagrange multipliers in the quantum thermodynamics of magnons, and 5) the observation of a visible anomaly in the Bloch T3/2 law for the temperature dependence of magnetization of nanostructured ferromagnets.

Bose-Einstein Condensation of Photons and Photon Pairs

We investigate the Bose-Einstein condensation of photons and photon pairs in a two-dimension optical microcavity. We find that in the paraxial approximation, the mixed gas of photons and photon pairs is formally equivalent to a two dimension system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phase. We also discuss the quantum phase transition of the system and obtain the critical point analytically. Moreover, we find that the quantum phase transition of the system can be interpreted as second harmonic generation.

Variational Monte Carlo analysis of Bose-Einstein condensation in a two-dimensional trap

The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas-Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.

Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

The critical temperature of Bose-Einstein condensation at minimum momentum state for weakly interacting Bose gases in a power-law potential and the deviation of the critical temperature from ideal bose gas are studied.The effect of interaction on the critical temperature is ascribed to the ratiaoα/I_(c),whereαis the scattering length for s wave andI_(c) is de Broglie wavelength at critical temperature.Asα/I_(c)<<1/(2p)^(2),the interaction is negligible.The presented deviation of the critical temperature for three dimensional harmonI_(c) potential is well in agreement with recent measurement of critical temperature for ^(87)Rb bose gas trapped in a harmonI_(c) well.

Numerical Study of Vortex Interactions in Bose-Einstein Condensation

The dynamics and interaction of quantized vortices in Bose-Einstein condensates(BECs)are investigated by using the two-dimensional Gross-Pitaevskii equation(GPE)with/without an angular momentum rotation term.If all vortices have the same winding number,they would rotate around the trap center but never collide.In contrast,if the winding numbers are different,their interaction highly depends on the initial distance between vortex centers.The analytical results are presented to describe the dynamics of the vortex centers when β=0.While if β≠0,there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs.Finally,the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.

Facile synthesis of hierarchical NaX zeolite from natural kaolinite for efficient Knoevenagel condensation

Zeolite catalysts have found extensive applications in the synthesis of various fine chemicals.However,the micropores of zeolites impose diffusion limitations on bulky molecules,greatly reducing the catalytic efficiency.Herein,we explore an economic and environmentally friendly method for synthesizing hierarchical NaX zeolite that exhibits improved catalytic performance in the Knoevenagel condensation reaction for producing the useful fine chemical 2-cyano-3-phenylacrylate.The synthesis was achieved via a low-temperature activation of kaolinite and subsequent in-situ transformation strategy without any template or seed.Systematic characterizations reveal that the synthesized NaX zeolite has both intercrystalline and intra-crystalline mesopores,smaller crystal size,and larger external specific surface area compared to commercial NaX zeolite.Detailed mechanism investigations show that the inter-crystalline mesopores are generated by stacking smaller crystals formed from in-situ crystallization of the depolymerized kaolinite,and the intra-crystalline mesopores are inherited from the pores in the depolymerized kaolinite.This synthesis strategy provides an energy-saving and effective way to construct hierarchical zeolites,which may gain wide applications in fine chemical manufacturing.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose-Einstein condensate

Manipulating nonlinear excitations,including solitons and vortices,is an essential topic in quantum many-body physics.A new progress in this direction is a protocol proposed in[Phys.Rev.Res.2043256(2020)]to produce dark solitons in a one-dimensional atomic Bose–Einstein condensate(BEC)by quenching inter-atomic interaction.Motivated by this work,we generalize the protocol to a two-dimensional BEC and investigate the generic scenario of its post-quench dynamics.For an isotropic disk trap with a hard-wall boundary,we find that successive inward-moving ring dark solitons(RDSs)can be induced from the edge,and the number of RDSs can be controlled by tuning the ratio of the after-and before-quench interaction strength across different critical values.The role of the quench played on the profiles of the density,phase,and sound velocity is also investigated.Due to the snake instability,the RDSs then become vortex–antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction.By tuning the geometry of the box traps,demonstrated as polygonal ones,more subtle dynamics of solitons and vortices are enabled.Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in near future cold-atom experiments.

Effects of drive imbalance on the particle emission from a Bose-Einstein condensate in a one-dimensional lattice

Time-periodic driving has been an effective tool in the field of nonequilibrium quantum dynamics,which enables precise control of the particle interactions.We investigate the collective emission of particles from a Bose-Einstein condensate in a one-dimensional lattice with periodic drives that are separate in modulation amplitudes and relative phases.In addition to the enhancement of particle emission,we find that amplitude imbalances lead to energy shift and band broadening,while typical relative phases may give rise to similar gaps.These results offer insights into the specific manipulations of nonequilibrium quantum systems with tone-varying drives.

Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations

Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications.In this work,we investigate the collective particle emission from a Bose-Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions.We give the regimes for discrete modes,and find that the emission can be distinctly suppressed.The configuration induces a broad band,but few particles are ejected due to the interference of the matter waves.We further qualitatively model the emission process and demonstrate the short-time behaviors.This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices,and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.