Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dime...Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.展开更多
We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation.We put forward a...We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation.We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature,on transverse trapping frequency,on atom number in the condensate,and on length of the system.Different from the usual calculation method for the three dimension system,our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation.With little approximation,our theoretical calculation results agree with the experimental ones.Comparing with the usual calculation method,our theory is helpful to deduce the inter-particle interactions in damping phenomenon.展开更多
In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3,...In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3, spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 21） Bose-Einstein condensation in harmonic potential trap is smaller.展开更多
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 equiv...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.展开更多
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 ...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.展开更多
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used ...Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.展开更多
A novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations.For fermions system,the results in the limit where the reached temper...A novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations.For fermions system,the results in the limit where the reached temperature T is small and where there is no constraint for the reached temperature T compared to the Fermi energy εf at a given density ρ are given,respectively.Quadrupole and multiplicity fluctuation relations are derived in terms of T/εf.We compared the two set results in the limit when T is much smaller compared to Fermi energy εf and they are consistent,as expected.The classical limit is also obtained for high temperatures and low densities.For bosons system,quadrupole and multiplicity fluctuations using Landau's theory of fluctuations near the critical point for a Bose-Einstein condensate(BEC) at a given density ρ are derived.As an example,we apply our approach to heavy ion collisions using the Constrained Molecular Dynamics model(CoMD) which includes the fermionic statistics.The multiplicity fluctuation quenching for fermions is found in the model and confirmed by experimental data.To reproduce the available experimental data better,we propose a modification of the collision term in the approach to include the possibility of α-α collisions.The relevant Bose-Einstein factor in the collision term is properly taken into account.This approach increases the yields of bosons relative to fermions closer to data.Boson fluctuations become larger than one as expected.展开更多
Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure fa...Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.展开更多
Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time...Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.展开更多
We present three families of exact matter-wave soliton solutions for an effective one-dimension twocomponent Bose-Einstein condensates(BECs) with tunable interactions,harmonic potential and gain or loss term. We inves...We present three families of exact matter-wave soliton solutions for an effective one-dimension twocomponent Bose-Einstein condensates(BECs) with tunable interactions,harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons,bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential,and kinklike modulated harmonic trap potential.Through the Feshbach resonance,these dynamics can be realized in experiments by suitable control of time-dependent trap parameters,atomic interactions,and interaction with thermal cloud.展开更多
The rogue waves with a controllable center are reported for the nonlinear Schroedinger equation in terms of rational-like functions by using a direct method. The position of these solutions can be controlled by choosi...The rogue waves with a controllable center are reported for the nonlinear Schroedinger equation in terms of rational-like functions by using a direct method. The position of these solutions can be controlled by choosing different center parameters and this may describe the possible formation mechanisms for optical, oceanic, and matter rogue wave phenomenon in optical fibres, the deep ocean, Bose-Einstein condensates respectively.展开更多
Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation r...Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.展开更多
Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-tw...Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.展开更多
We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency.The precise position information of an a...We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency.The precise position information of an atom is observed on the resonance absorption and dispersion distribution spectrum of a weak probe field.Single and multiple localization peaks are observed in specific directions of the corresponding wave numbers and phase of the standing wave fields.The strength of space-independent Rabi frequency reduces the position uncertainty in the localized peaks without disturbing the probability of the atom.In a hot atomic medium the localized probability of an atom is reduced which depends upon the temperature of that medium.Our results provide useful applications in the development of laser cooling,atom nanolithography and Bose-Einstein condensation.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11201239)the Singapore A*STAR SERC PSF(Grant No.1321202067)
文摘Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.
基金Supported by National Natural Science Foundation of China under Grant No.10864006the Key Research Project of Xinjiang Higher Education,China under Grant No.XJED2010141the Key Discipline of Theoretical Physics of Xinjiang,China and the Postgraduate Scientific and Technological Innovation Project of Xinjiang Normal University,China under Grant No.20111202
文摘We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation.We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature,on transverse trapping frequency,on atom number in the condensate,and on length of the system.Different from the usual calculation method for the three dimension system,our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation.With little approximation,our theoretical calculation results agree with the experimental ones.Comparing with the usual calculation method,our theory is helpful to deduce the inter-particle interactions in damping phenomenon.
基金Supported by National Natural Science Foundation of China under Grant No.11275082
文摘In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional （11）） and quasi-two-dimensional （2D） Bose-Einstein condensation （BEC） in harmonic potential trap. The energ3, spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 21） Bose-Einstein condensation in harmonic potential trap is smaller.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10904096 and 10604024the Natural Science Foundation of Beijing under Grant No.1092009
文摘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.
基金Supported by the National Natural Science Foundation under Grant No. 11047010
文摘Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.
文摘A novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations.For fermions system,the results in the limit where the reached temperature T is small and where there is no constraint for the reached temperature T compared to the Fermi energy εf at a given density ρ are given,respectively.Quadrupole and multiplicity fluctuation relations are derived in terms of T/εf.We compared the two set results in the limit when T is much smaller compared to Fermi energy εf and they are consistent,as expected.The classical limit is also obtained for high temperatures and low densities.For bosons system,quadrupole and multiplicity fluctuations using Landau's theory of fluctuations near the critical point for a Bose-Einstein condensate(BEC) at a given density ρ are derived.As an example,we apply our approach to heavy ion collisions using the Constrained Molecular Dynamics model(CoMD) which includes the fermionic statistics.The multiplicity fluctuation quenching for fermions is found in the model and confirmed by experimental data.To reproduce the available experimental data better,we propose a modification of the collision term in the approach to include the possibility of α-α collisions.The relevant Bose-Einstein factor in the collision term is properly taken into account.This approach increases the yields of bosons relative to fermions closer to data.Boson fluctuations become larger than one as expected.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11004200 and 11274315
文摘Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.
基金Supported by the National Natural Science Foundation of China under Grant No.11105057the Foundation of Hubei University of Education under Grant No.2009B013the Project of Excellent Teacher Team of Hubei University of Education under Grant No.2012KB302
文摘Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11041003 and 60802087the Natural Science Foundation of Jiangsu Province under Grant No.BK2004119
文摘We present three families of exact matter-wave soliton solutions for an effective one-dimension twocomponent Bose-Einstein condensates(BECs) with tunable interactions,harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons,bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential,and kinklike modulated harmonic trap potential.Through the Feshbach resonance,these dynamics can be realized in experiments by suitable control of time-dependent trap parameters,atomic interactions,and interaction with thermal cloud.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10971109,10971211K.C.Wong Magna Fund in Ningbo UniversityProgram for New Century Excellent Talents in University under Grant No.NCET-08-0515
文摘The rogue waves with a controllable center are reported for the nonlinear Schroedinger equation in terms of rational-like functions by using a direct method. The position of these solutions can be controlled by choosing different center parameters and this may describe the possible formation mechanisms for optical, oceanic, and matter rogue wave phenomenon in optical fibres, the deep ocean, Bose-Einstein condensates respectively.
文摘Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.
基金Supported by National Natural Science Foundation of China under Grant No.61361002the Applied Fundamental Research Projects of Yunnan Province under Grant No.2013FZ121
文摘Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.
文摘We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency.The precise position information of an atom is observed on the resonance absorption and dispersion distribution spectrum of a weak probe field.Single and multiple localization peaks are observed in specific directions of the corresponding wave numbers and phase of the standing wave fields.The strength of space-independent Rabi frequency reduces the position uncertainty in the localized peaks without disturbing the probability of the atom.In a hot atomic medium the localized probability of an atom is reduced which depends upon the temperature of that medium.Our results provide useful applications in the development of laser cooling,atom nanolithography and Bose-Einstein condensation.
