We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textu...We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states： the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipole- dipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons （half skyrmions） can be generated in the presence of spin-orbit coupling.展开更多
In this paper, we present a method to solve difference differential equation（s）. As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions ar...In this paper, we present a method to solve difference differential equation（s）. As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation（s）.展开更多
We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and...We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. The many body physics of cold atom in harmonic potential is investigated in the frame of mean-field Gross-Pitaevskii equation. Then the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice.展开更多
We address the impact of imprinted fading optical lattices on the beam evolution of solitons in strongly nonlocal nonlinear media. The results show that the width of the soliton experiences a change with the increasin...We address the impact of imprinted fading optical lattices on the beam evolution of solitons in strongly nonlocal nonlinear media. The results show that the width of the soliton experiences a change with the increasing propagation distance, the critical power for the soliton varies with the lattice fading away, and the soliton breathing is affected by the initial lattice depth and the nonlocality degree.展开更多
We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1＋1 dimensional field theory.The related potential has infinite order corrections of exponential ...We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1＋1 dimensional field theory.The related potential has infinite order corrections of exponential pattern,and the coefficients for each order are determined.These coefficients can also be obtained by solving the equation of the fluctuations around the vacuum.At the lowest order,the kink lattice represents the Toda lattice.With higher order correction terms,the kink lattice can represent one kind of generic Toda lattice.With only two sites,the kink lattice is classically integrable.If the number of sites of the lattice is larger than two,the kink lattice is not integrable but is a near integrable system.We make use of Flaschka’s variables to study the Lax pair of the kink lattice.These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested.We also discuss the higher Hamiltonians for the deformed open Toda lattice,which has a similar result to the ordinary deformed Toda.展开更多
OVER three decades, since the wide applications of the soliton phenomena in almost all the physical fields, the theoretical, experimental and applied studies of the soliton have become an active research topic. The di...OVER three decades, since the wide applications of the soliton phenomena in almost all the physical fields, the theoretical, experimental and applied studies of the soliton have become an active research topic. The direct macro-observation of the soliton phenomana is one of the important problems. Since the observation of Wu et al. on the nonpropagating fluid solitons in 1984, the nonlinear systems on the vibratmg table have offered us a good experimental field. Some nonlinear excitations of the macro-monatomic lattice have been observed by Denardo et al. Ref. reported the observation of the localized structure of the granular sys-展开更多
We study the soliton mobility in nonlocal nonlinear media with an imprinted fading optical lattice. The results show that the transverse mobility of solitons varies with the lattice decay rate and the nonlocality degr...We study the soliton mobility in nonlocal nonlinear media with an imprinted fading optical lattice. The results show that the transverse mobility of solitons varies with the lattice decay rate and the nonlocality degree, which provides an opportunity for all-optical control of light.展开更多
We address the existence of surface solitons at an interface in a defocusing cubic medium with an imprinted one-dimensional （1D） composite Bessel optical lattice. This setting is composed of two Bessel lattices with...We address the existence of surface solitons at an interface in a defocusing cubic medium with an imprinted one-dimensional （1D） composite Bessel optical lattice. This setting is composed of two Bessel lattices with different orders and different modulation depths, separated beside both sides of an interface. Stability analysis and numerical propagation simulations prove that solitons supported by the model are dynamically stable in the entire domain of their existence. The order of lattice determines the shape of soliton, and the amplitude of soliton depends on the lattice modulation depth. The experimental realization of the scheme is also proposed. Our results may provide another effective way of controlling the shapes of surface solitons and thus their evolutions by introducing a new freedom degree.展开更多
We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first an...We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.展开更多
文摘We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states： the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipole- dipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons （half skyrmions） can be generated in the presence of spin-orbit coupling.
基金The project supported by the State Key Basic Research Program of China under Grant No 2004CB318000
文摘In this paper, we present a method to solve difference differential equation（s）. As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation（s）.
基金supported by the National Natural Science Foundation of China (10934010, 60978019 and 11104064)the National Basic Research Program of China (2009CB930701, 2010CB922904,2011CB921502 and 2012CB821300)+1 种基金the Research Grants Council of Hong Kong (11061160490 and 1386-N-HKU748/10)Zhang X F is also supported by the China Postdoctoral Science Foundation (2011M500032)
文摘We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. The many body physics of cold atom in harmonic potential is investigated in the frame of mean-field Gross-Pitaevskii equation. Then the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice.
基金Project supported by the Doctorial Start-up Fund of Hengyang Normal University, China (Grant No. 11B42)the Natural Science Foundation of Hunan Province, China (Grant No. 12JJ6001)the Construct Program of the Key Discipline in Hunan Province, China
文摘We address the impact of imprinted fading optical lattices on the beam evolution of solitons in strongly nonlocal nonlinear media. The results show that the width of the soliton experiences a change with the increasing propagation distance, the critical power for the soliton varies with the lattice fading away, and the soliton breathing is affected by the initial lattice depth and the nonlocality degree.
基金Supported by Shandong Provincial Natural Science Foundation(ZR2014AQ007)National Natural Science Foundation of China(11403015,U1531105)+1 种基金National Natural Science Foundation of China(11305235)S.He is supported by Max-Planck fellowship in Germany
文摘We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1＋1 dimensional field theory.The related potential has infinite order corrections of exponential pattern,and the coefficients for each order are determined.These coefficients can also be obtained by solving the equation of the fluctuations around the vacuum.At the lowest order,the kink lattice represents the Toda lattice.With higher order correction terms,the kink lattice can represent one kind of generic Toda lattice.With only two sites,the kink lattice is classically integrable.If the number of sites of the lattice is larger than two,the kink lattice is not integrable but is a near integrable system.We make use of Flaschka’s variables to study the Lax pair of the kink lattice.These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested.We also discuss the higher Hamiltonians for the deformed open Toda lattice,which has a similar result to the ordinary deformed Toda.
文摘OVER three decades, since the wide applications of the soliton phenomena in almost all the physical fields, the theoretical, experimental and applied studies of the soliton have become an active research topic. The direct macro-observation of the soliton phenomana is one of the important problems. Since the observation of Wu et al. on the nonpropagating fluid solitons in 1984, the nonlinear systems on the vibratmg table have offered us a good experimental field. Some nonlinear excitations of the macro-monatomic lattice have been observed by Denardo et al. Ref. reported the observation of the localized structure of the granular sys-
基金Project supported by the Natural Science Foundation of Hunan Province of China (Grant Nos.12JJ6001 and 13JJ4097)the Doctorial Start-up Fund of Hengyang Normal University of China (Grant No.11B42)the Construct Program of the Key Discipline in Hunan Province of China
文摘We study the soliton mobility in nonlocal nonlinear media with an imprinted fading optical lattice. The results show that the transverse mobility of solitons varies with the lattice decay rate and the nonlocality degree, which provides an opportunity for all-optical control of light.
基金Project supported by the National Natural Science Foundation of China(Grant No10704067)the Scientific Research Foundation of Education Bureau of Zhejiang Province of China(Grant No20060493)
文摘We address the existence of surface solitons at an interface in a defocusing cubic medium with an imprinted one-dimensional （1D） composite Bessel optical lattice. This setting is composed of two Bessel lattices with different orders and different modulation depths, separated beside both sides of an interface. Stability analysis and numerical propagation simulations prove that solitons supported by the model are dynamically stable in the entire domain of their existence. The order of lattice determines the shape of soliton, and the amplitude of soliton depends on the lattice modulation depth. The experimental realization of the scheme is also proposed. Our results may provide another effective way of controlling the shapes of surface solitons and thus their evolutions by introducing a new freedom degree.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12065022,12005173,11747018,and 11565021)the Natural Science Foundation of Gansu Province of China(Grant No.20JR10RA082)+1 种基金the China Postdoctoral Science Foundation(Grant No.2020M680318)the Scientific Research Foundation of NWNU(Grant No.NWNU-LKQN-16-3)。
文摘We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.
