Utilizing the dissipative Gross-Pitaevskii equation,we investigated the splitting dynamics of triply quantized vortices at finite temperature.Through linear perturbation analysis,we determined the excitation modes of ...Utilizing the dissipative Gross-Pitaevskii equation,we investigated the splitting dynamics of triply quantized vortices at finite temperature.Through linear perturbation analysis,we determined the excitation modes of these vortices across various dissipation parameters.We identified three unstable modes with p=2-,3-and 4-fold rotational symmetries,revealing a significant dynamic transition of the most unstable mode.That is,as the dissipation parameter increases the most unstable mode transitions from the p=2 mode to the p=3 mode.Throughout the entire range of dissipation parameters,the p=4 unstable mode is never the dominant mode.Subsequently,we performed nonlinear numerical simulations of the vortex splitting process.Under random perturbations we confirmed the dynamical transition,and under specific perturbations we confirmed the instability of the p=4 mode.Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.展开更多
We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated...We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.展开更多
We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose...We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose–Einstein condensates are investigated,it is shown that the two structures can be manipulated by adjusting the parameters of the superposed Bessel optical lattices.The results show that the SOC interaction has an important effect on the two structures in the superposed Bessel optical lattices,and the SOC interaction can enhance the robustness of the structures.The Gaussian,toroidal and vortex superposition structures in the superposition lattice are presented,the interference processes in the steady state structures are analyzed,and the effects of SOC interactions on the Gaussian vortex and toroidal vortex structures are investigated,and the angular momentum of the vortex states can be increased by SOC interactions.展开更多
The Josephson effect,an important quantum supercurrent phenomenon,has been extensively studied in superconductors and superfluids.In this paper,we investigate the rich physics of one-dimensional Josephson junctions in...The Josephson effect,an important quantum supercurrent phenomenon,has been extensively studied in superconductors and superfluids.In this paper,we investigate the rich physics of one-dimensional Josephson junctions in a red-detuned optical lattice with sodium(Na)quantum gas.A one-dimensional Josephson array is formed by setting up an optical lattice using a red-detuned laser.By characterizing the dependence of Josephson oscillations of the lattice depth,we experimentally demonstrate the Josephson current.The lattice depth is controlled by altering the lattice power,and our observations are consistent with theoretical predictions.These findings offer valuable insights into quantum coherent transport and the intricate dynamics inherent to superfluidity.展开更多
As an important component of light hydrocarbon compounds,alkylbenzene compounds lack indicators to indicate the source of organic matter of light oils and condensates.Forty-one oil samples from the Tarim Basin and Bei...As an important component of light hydrocarbon compounds,alkylbenzene compounds lack indicators to indicate the source of organic matter of light oils and condensates.Forty-one oil samples from the Tarim Basin and Beibuwan Basin were analyzed by comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry(GC×GC-TOFMS).The concentration distributions of thirteen light hydrocarbon compounds with organic matter source and sedimentary environment indication were studied.There is no significant difference in the concentrations of 1-methylpropylbenzene(MPB)in all studied oils.However,the concentrations of 2-MPB in the Tarim swamp oils are higher than that in the Beibuwan lacustrine oils and Tarim marine oils.Based on the significant concentration difference of 1-and 2-MPB in all studied oils,1-/2-MPB(MPBr)was proposed as an indicator to identify the source of organic matter in crude oils.The MPBr values greater than 1.5 indicate that the crude oil mainly comes from lower aquatic organisms,bacteria,and algae.The MPBr values greater than 1.0 and less than 1.5 indicate that crude oil was derived from the combined contributions of lower aquatic organisms,bacteria and algae,and terrestrial higher plants.The MPBr values less than 1.0 suggest that the crude oil was mainly derived from terrigenous higher plants.The MPBr values in crude oils basically are not or slightly affected by depositional environment and secondary alteration.The MPBr values can be used to infer the organic matter origin in sediments,especially for the lack of biomarkers of light oils and condensates.展开更多
Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensat...Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.展开更多
We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the st...We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.展开更多
This paper introduces a novel numerical method based on an energy-minimizing normalized residual network(EMNorm Res Net)to compute the ground-state solution of Bose-Einstein condensates at zero or low temperatures.Sta...This paper introduces a novel numerical method based on an energy-minimizing normalized residual network(EMNorm Res Net)to compute the ground-state solution of Bose-Einstein condensates at zero or low temperatures.Starting from the three-dimensional Gross-Pitaevskii equation(GPE),we reduce it to the 1D and 2D GPEs because of the radial symmetry and cylindrical symmetry.The ground-state solution is formulated by minimizing the energy functional under constraints,which is directly solved using the EM-Norm Res Net approach.The paper provides detailed solutions for the ground states in 1D,2D(with radial symmetry),and 3D(with cylindrical symmetry).We use the Thomas-Fermi approximation as the target function to pre-train the neural network.Then,the formal network is trained using the energy minimization method.In contrast to traditional numerical methods,our neural network approach introduces two key innovations:(i)a novel normalization technique designed for high-dimensional systems within an energy-based loss function;(ii)improved training efficiency and model robustness by incorporating gradient stabilization techniques into residual networks.Extensive numerical experiments validate the method's accuracy across different spatial dimensions.展开更多
We present a flexible manipulation and control of solitons via Bose-Einstein condensates.In the presence of Rashba spin-orbit coupling and repulsive interactions within a harmonic potential,our investigation reveals t...We present a flexible manipulation and control of solitons via Bose-Einstein condensates.In the presence of Rashba spin-orbit coupling and repulsive interactions within a harmonic potential,our investigation reveals the numerical local solutions within the system.By manipulating the strength of repulsive interactions and adjusting spin-orbit coupling while maintaining a zero-frequency rotation,diverse soliton structures emerge within the system.These include plane-wave solitons,two distinct types of stripe solitons,and odd petal solitons with both single and double layers.The stability of these solitons is intricately dependent on the varying strength of spin-orbit coupling.Specifically,stripe solitons can maintain a stable existence within regions characterized by enhanced spin-orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions.When rotational frequency is introduced to the system,solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation.The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin-orbit coupling.As a result,the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.展开更多
Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems.We further extend the region of existence of spin solitons in the nonlinearity coefficient space...Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems.We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose-Einstein condensate.Six types of spin soliton solutions can be obtained,and they exist in different regions.Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise.The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons.These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.展开更多
Atomic interaction leads to dephasing and damping of Bloch oscillations(BOs)in optical lattices,which limits observation and applications of BOs.How to obtain persistent BOs is particularly important.Here,the nonlinea...Atomic interaction leads to dephasing and damping of Bloch oscillations(BOs)in optical lattices,which limits observation and applications of BOs.How to obtain persistent BOs is particularly important.Here,the nonlinear Bloch dynamics of the Bose-Einstein condensate with two-body and three-body interactions in deep optical lattices is studied.The damping rate induced by interactions is obtained.The damping induced by two-body interaction plays a dominant role,while the damping induced by three-body interaction is weak.However,when the two-body and three-body interactions satisfy a threshold,long-lived coherent BOs are observed.Furthermore,the Bloch dynamics with periodical modulation of linear force is studied.The frequencies of linear force corresponding to resonance and pseudoresonance are obtained,and rich dynamical phenomena,i.e.,stable and strong BOs,drifting and dispersion of wave packet,are predicted.The controllable Bloch dynamics is provided with the periodic modulation of the linear force.展开更多
By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu J...By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.展开更多
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 dispersio...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.展开更多
The stability of Bose Einstein condensates （BECs） loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the sh...The stability of Bose Einstein condensates （BECs） loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs, The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.展开更多
The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied.For a system with asteady current,we construct the general solution of the 1st-order equation.From the boundedness condition of thegener...The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied.For a system with asteady current,we construct the general solution of the 1st-order equation.From the boundedness condition of thegeneral solution, we obtain the Melnikov function predicting the onset of chaos.The unpredictability of the system's dis-tribution of atom density is also theoretically analyzed.For a ^(23)Na system meeting the perturbation oondition,numericalsimulations show the existence of chaos,which is in accordance with our analytical results.Numerical simulations of a^(87)Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system.The casewithout a current is also investigated.展开更多
The corrosion behaviors of pure titanium and its weldment welded by tungsten inert gas （TIG） welding in simulated desulfurized flue gas condensates in thermal power plant chimney were investigated using potentiodyna...The corrosion behaviors of pure titanium and its weldment welded by tungsten inert gas （TIG） welding in simulated desulfurized flue gas condensates in thermal power plant chimney were investigated using potentiodynamic polarization, electrochemical impedance spectroscopy （EIS） and immersion tests. The effects of heat input and shielding gases on the corrosion behavior of the welded titanium were also studied. Grain coarsening and Widmanst^itten structure were found in both the fusion zone and the heat-affected zone. The welded titanium exhibited active-passive behavior in the simulated condensates. Both the polarization curves and EIS measurements confirmed that TIG welding process with different parameters had few effects on the corrosion behavior. It was proved that the microstructure changes were not the key material factors affecting the corrosion behavior of pure titanium under the test conditions, while the oxide film had remarkable effect on improving the corrosion resistance.展开更多
An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for...An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.展开更多
The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. W...The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.展开更多
We study the formation of vortices in a dipolar Bose-Einstein condensate in a synthetic magnetic field by numerically solving the Gross-Pitaevskii equation. The formation process depends on the dipole strength, the ro...We study the formation of vortices in a dipolar Bose-Einstein condensate in a synthetic magnetic field by numerically solving the Gross-Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.展开更多
We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mappin...We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.展开更多
基金provided by the Guangdong Basic and Applied Basic Research Foundation of China(Grant Nos.2024A1515012552,2022A1515011938,2022A1515012425)the National Natural Science Foundation of China(Grant No.12005088)the support received from Lingnan Normal University(Grant Nos.YL20200203,ZL1930)。
文摘Utilizing the dissipative Gross-Pitaevskii equation,we investigated the splitting dynamics of triply quantized vortices at finite temperature.Through linear perturbation analysis,we determined the excitation modes of these vortices across various dissipation parameters.We identified three unstable modes with p=2-,3-and 4-fold rotational symmetries,revealing a significant dynamic transition of the most unstable mode.That is,as the dissipation parameter increases the most unstable mode transitions from the p=2 mode to the p=3 mode.Throughout the entire range of dissipation parameters,the p=4 unstable mode is never the dominant mode.Subsequently,we performed nonlinear numerical simulations of the vortex splitting process.Under random perturbations we confirmed the dynamical transition,and under specific perturbations we confirmed the instability of the p=4 mode.Our findings on the finite temperature dependence of the splitting dynamics of triply quantized vortices are expected to be verifiable in experiments.
基金Projects supported by the Natural Science Foundation of Hunan Province(2016JJ6020)the Scientific Research Fund of Hunan Provincial Education Department(18A436)the Scientific Research Fund of Hunan First normal University(XYS13N16)。
文摘We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.
基金supported by the Longdong University Doctoral Fund Program Projects(Grant Nos.XYBYZK2227,XYBYZK2219).
文摘We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices.The static and rotational structures are formed in the presence of a spin-orbit coupling(SOC)interaction in the atomic in Bose–Einstein condensates are investigated,it is shown that the two structures can be manipulated by adjusting the parameters of the superposed Bessel optical lattices.The results show that the SOC interaction has an important effect on the two structures in the superposed Bessel optical lattices,and the SOC interaction can enhance the robustness of the structures.The Gaussian,toroidal and vortex superposition structures in the superposition lattice are presented,the interference processes in the steady state structures are analyzed,and the effects of SOC interactions on the Gaussian vortex and toroidal vortex structures are investigated,and the angular momentum of the vortex states can be increased by SOC interactions.
基金Project supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302103)the National Natural Science Foundation of China(Grant Nos.62325505,62020106014,62175140,62475138,92165106,12104276)the Shanxi Province Graduate Student Research Innovation Project(Grant No.2024KY105)。
文摘The Josephson effect,an important quantum supercurrent phenomenon,has been extensively studied in superconductors and superfluids.In this paper,we investigate the rich physics of one-dimensional Josephson junctions in a red-detuned optical lattice with sodium(Na)quantum gas.A one-dimensional Josephson array is formed by setting up an optical lattice using a red-detuned laser.By characterizing the dependence of Josephson oscillations of the lattice depth,we experimentally demonstrate the Josephson current.The lattice depth is controlled by altering the lattice power,and our observations are consistent with theoretical predictions.These findings offer valuable insights into quantum coherent transport and the intricate dynamics inherent to superfluidity.
基金supported by Doctor's Scientific Research Initiation Project of Yan'an University(YAU202213093)National Nature Science Foundation of China(Grant No.41503029).
文摘As an important component of light hydrocarbon compounds,alkylbenzene compounds lack indicators to indicate the source of organic matter of light oils and condensates.Forty-one oil samples from the Tarim Basin and Beibuwan Basin were analyzed by comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry(GC×GC-TOFMS).The concentration distributions of thirteen light hydrocarbon compounds with organic matter source and sedimentary environment indication were studied.There is no significant difference in the concentrations of 1-methylpropylbenzene(MPB)in all studied oils.However,the concentrations of 2-MPB in the Tarim swamp oils are higher than that in the Beibuwan lacustrine oils and Tarim marine oils.Based on the significant concentration difference of 1-and 2-MPB in all studied oils,1-/2-MPB(MPBr)was proposed as an indicator to identify the source of organic matter in crude oils.The MPBr values greater than 1.5 indicate that the crude oil mainly comes from lower aquatic organisms,bacteria,and algae.The MPBr values greater than 1.0 and less than 1.5 indicate that crude oil was derived from the combined contributions of lower aquatic organisms,bacteria and algae,and terrestrial higher plants.The MPBr values less than 1.0 suggest that the crude oil was mainly derived from terrigenous higher plants.The MPBr values in crude oils basically are not or slightly affected by depositional environment and secondary alteration.The MPBr values can be used to infer the organic matter origin in sediments,especially for the lack of biomarkers of light oils and condensates.
基金supported by NSFC under Grant No.12272403Beijing Training Program of Innovation under Grant No.S202410019024。
文摘Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.
基金supported by the National Natural Science Foundation of China(Grant No.62275075)the Natural Science Foundation of Hubei Soliton Research Association(Grant No.2025HBSRA09)+1 种基金joint supported by Hubei Provincial Natural Science Foundation and Xianning of China(Grant Nos.2025AFD401 and 2025AFD405)Israel Science Foundation(Grant No.1695/22).
文摘We propose a theoretical framework,based on the two-component Gross-Pitaevskii equation(GPE),for the investigation of vortex solitons(VSs)in hybrid atomic-molecular Bose-Einstein condensates under the action of the stimulated Raman-induced photoassociation and square-optical-lattice potential.Stationary solutions of the coupled GPE system are obtained by means of the imaginary-time integration,while the temporal dynamics are simulated using the fourth-order Runge-Kutta algorithm.The analysis reveals stable rhombus-shaped VS shapes with topological charges m=1 and 2 of the atomic component.The stability domains and spatial structure of these VSs are governed by three key parameters:the parametric-coupling strength(χ),atomicmolecular interaction strength(g_(12)),and the optical-lattice potential depth(V_(0)).By varyingχand g_(12),we demonstrate a structural transition where four-core rhombus-shaped VSs evolve into eight-core square-shaped modes,highlighting the nontrivial nonlinear dynamics of the system.This work establishes a connection between interactions of cold atoms and topologically structured matter waves in hybrid quantum systems.
基金supported by the National Natural Science Foundation of China(Grant No.11971411)。
文摘This paper introduces a novel numerical method based on an energy-minimizing normalized residual network(EMNorm Res Net)to compute the ground-state solution of Bose-Einstein condensates at zero or low temperatures.Starting from the three-dimensional Gross-Pitaevskii equation(GPE),we reduce it to the 1D and 2D GPEs because of the radial symmetry and cylindrical symmetry.The ground-state solution is formulated by minimizing the energy functional under constraints,which is directly solved using the EM-Norm Res Net approach.The paper provides detailed solutions for the ground states in 1D,2D(with radial symmetry),and 3D(with cylindrical symmetry).We use the Thomas-Fermi approximation as the target function to pre-train the neural network.Then,the formal network is trained using the energy minimization method.In contrast to traditional numerical methods,our neural network approach introduces two key innovations:(i)a novel normalization technique designed for high-dimensional systems within an energy-based loss function;(ii)improved training efficiency and model robustness by incorporating gradient stabilization techniques into residual networks.Extensive numerical experiments validate the method's accuracy across different spatial dimensions.
基金the Natural Science Foundation of Zhejiang Province of China(Grant No.LZ22A050002)the National Natural Science Foundation of China(Grant Nos.12074343 and 11835011)Muhammad Idrees acknowledges support from the postdoctoral fellowship of Zhejiang Normal University(Grant No.YS304123952).
文摘We present a flexible manipulation and control of solitons via Bose-Einstein condensates.In the presence of Rashba spin-orbit coupling and repulsive interactions within a harmonic potential,our investigation reveals the numerical local solutions within the system.By manipulating the strength of repulsive interactions and adjusting spin-orbit coupling while maintaining a zero-frequency rotation,diverse soliton structures emerge within the system.These include plane-wave solitons,two distinct types of stripe solitons,and odd petal solitons with both single and double layers.The stability of these solitons is intricately dependent on the varying strength of spin-orbit coupling.Specifically,stripe solitons can maintain a stable existence within regions characterized by enhanced spin-orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions.When rotational frequency is introduced to the system,solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation.The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin-orbit coupling.As a result,the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.
基金supported by the National Natural Science Foundation of China(Contract Nos.12375005 and 12235007)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2018KJXX-094).
文摘Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems.We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose-Einstein condensate.Six types of spin soliton solutions can be obtained,and they exist in different regions.Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise.The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons.These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12264045,12164042,11764039,11847304,and 11865014)the Natural Science Foundation of Gansu Province (Grant No.17JR5RA07620JR5RA526)+2 种基金the Scientific Research Project of Gansu Higher Education (Grant No.2016A-005)the Innovation Capability Enhancement Project of Gansu Higher Education (Grant Nos.2020A146 and 2019A-014)the Creation of Science and Technology of Northwest Normal University (Grant No.NWNULKQN-18-33)。
文摘Atomic interaction leads to dephasing and damping of Bloch oscillations(BOs)in optical lattices,which limits observation and applications of BOs.How to obtain persistent BOs is particularly important.Here,the nonlinear Bloch dynamics of the Bose-Einstein condensate with two-body and three-body interactions in deep optical lattices is studied.The damping rate induced by interactions is obtained.The damping induced by two-body interaction plays a dominant role,while the damping induced by three-body interaction is weak.However,when the two-body and three-body interactions satisfy a threshold,long-lived coherent BOs are observed.Furthermore,the Bloch dynamics with periodical modulation of linear force is studied.The frequencies of linear force corresponding to resonance and pseudoresonance are obtained,and rich dynamical phenomena,i.e.,stable and strong BOs,drifting and dispersion of wave packet,are predicted.The controllable Bloch dynamics is provided with the periodic modulation of the linear force.
基金The project supported by National Natural Science Foundation of China under Grant No, 10475113
文摘By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11764039,11847304,11865014,11475027,11274255 and 11305132the Natural Science Foundation of Gansu Province under Grant No 17JR5RA076the Scientific Research Project of Gansu Higher Education under Grant No 2016A-005
文摘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.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10475066 and 10774120）, and by the Natural Science Foundation of Gansu Province, China （Grant No 3ZS051-A25-013） and by Creation of Science and Technology of Northwest Normal University, China （Grant No NWNU-KJCXGC-03-17）.
文摘The stability of Bose Einstein condensates （BECs） loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs, The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.
基金National Natural Science Foundation of China under Grant No. 10125521the 973 National Major State Basic Research and Development of China under Grant No. 62000077400+1 种基金the CAS Knowledge Innovation Project under Grant No. KJCX2-SW-N02the Fund of Education Ministry of China under Grant No. 20010284036
文摘The spatial chaos of Bose-Einstein condensates in a cigar-shaped trap is studied.For a system with asteady current,we construct the general solution of the 1st-order equation.From the boundedness condition of thegeneral solution, we obtain the Melnikov function predicting the onset of chaos.The unpredictability of the system's dis-tribution of atom density is also theoretically analyzed.For a ^(23)Na system meeting the perturbation oondition,numericalsimulations show the existence of chaos,which is in accordance with our analytical results.Numerical simulations of a^(87)Rb system dissatisfying the perturbation condition also demonstrate that there exists chaos in the system.The casewithout a current is also investigated.
基金supported by the National Natural Science Foundation of China (No.51131008)
文摘The corrosion behaviors of pure titanium and its weldment welded by tungsten inert gas （TIG） welding in simulated desulfurized flue gas condensates in thermal power plant chimney were investigated using potentiodynamic polarization, electrochemical impedance spectroscopy （EIS） and immersion tests. The effects of heat input and shielding gases on the corrosion behavior of the welded titanium were also studied. Grain coarsening and Widmanst^itten structure were found in both the fusion zone and the heat-affected zone. The welded titanium exhibited active-passive behavior in the simulated condensates. Both the polarization curves and EIS measurements confirmed that TIG welding process with different parameters had few effects on the corrosion behavior. It was proved that the microstructure changes were not the key material factors affecting the corrosion behavior of pure titanium under the test conditions, while the oxide film had remarkable effect on improving the corrosion resistance.
基金supported by National Natural Science Foundation of China under Grant No.10474022
文摘An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10774120 and 10975114)the Natural Science Foundation of Gansu Province of China (Grant No. 1010RJZA012)the Science Foundation for Creation of Scienceand Technology of Northwest Normal University of China (Grant Nos. NWNU-KJCXGC-03-17 and NWNU-KJCXGC-03-48)
文摘The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.
基金supported by the National Natural Science Foundation of China(Grant No.11274039)the National Basic Research Program of China(Grant No.2013CB922002)the Fundamental Research Funds for the Central Universities of China
文摘We study the formation of vortices in a dipolar Bose-Einstein condensate in a synthetic magnetic field by numerically solving the Gross-Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.
基金Project supported by the National Natural Science Foundation of China（Grant Nos 10575087 and 10302018）, and the Natural Science Foundation of Zhejiang Province, China （Grant No Y605056）.
文摘We present several families of exact solutions to a system of coupled nonlinear Schrodinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.
