An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So fa...An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.展开更多
Along with all other quantum objects, an electron is partly a wave and partly a particle. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its traj...Along with all other quantum objects, an electron is partly a wave and partly a particle. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment. When an electron looks more like a particle it has no shape, “point particle”, according to the Standard Model, meaning that it interacts as if it is entirely located at a single point in space and does not spread out to fill a three-dimensional volume. Therefore, in the sense of particle-like interactions, an electron has no shape. In this paper, a new theory is proposed in which the electron has a structure and a shape. The central idea is that an electron is a frictionless vortex with conserved momentum made out of condensed vacuum generated in the Big Bang from massless virtual photons that acquire mass when moving in the vortex at the speed of light. Using Hydrodynamics laws and applying them on the superfluid vacuum the basic properties of the electron are described here forth. This study provides mathematical models to calculate the mass, kinetic energy, density, volume, time, charge, and particle-wave duality. Such mathematical formulations are presented to confirm the theory. We conclude that the shape of the electron is accessible to human imagination, knowing its shape helps to determine its properties and shed a light on how matter is made and to explain the interactions of sub-atomic particles.展开更多
Electron vortex beams(EVBs)have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics.Recently,a relativistic electron vortex beam(REVB)has ...Electron vortex beams(EVBs)have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics.Recently,a relativistic electron vortex beam(REVB)has been proposed[Phys.Rev.Lett.107174802(2011)].Compared with EVBs,except for orbital angular momentum,an REVB has intrinsic relativistic effect,i.e.,spin angular momentum and spin-orbit coupling.We study the electromagnetic field of an REVB analytically.We show that the electromagnetic field can be separated into two parts,one is only related to orbital quantum number,and the other is related to spin-orbit coupling effect.Exploiting this separation property,the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect.The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state;while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam.The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.展开更多
By numerically solving the time-dependent Schr?dinger equation and employing the analytical perturbative model,we investigated the chirp-induced electron vortex in the photoionization of hydrogen atoms by a pair of co...By numerically solving the time-dependent Schr?dinger equation and employing the analytical perturbative model,we investigated the chirp-induced electron vortex in the photoionization of hydrogen atoms by a pair of counter-rotating circularly polarized chirped attosecond extremely ultraviolet pulses.We demonstrated that single-photon ionization of hydrogen atoms generates photoelectron momentum distributions(PMDs)with distinct helical vortex structures either with or without a time delay between two counter-rotating circularly polarized laser pulses.These structures are highly sensitive to both the time delay between the pulses and their chirp parameters.Our analytical model reveals that the splitting of vortex spirals is caused by the sign changing of the chirp-induced frequency-dependent time delay.We showed that to obtain the counterpart of the PMD under a pair of counter-rotating circularly polarized chirped pulses,both chirp parameters and ordering of pulses need to be reversed.展开更多
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects...A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.展开更多
The nature and the origin of the fine structure are described. Based on the vortex model and hydrodynamics, a comprehensible interpretation of the fine structure constant is developed. The vacuum considered to have su...The nature and the origin of the fine structure are described. Based on the vortex model and hydrodynamics, a comprehensible interpretation of the fine structure constant is developed. The vacuum considered to have superfluid characteristics and elementary particles such as the electron and Hydrogen molecule are irrotational vortices of this superfluid. In such a vortex, the angular rotation ω is maintained, and the larger the radius, the slower the rotational speed. The fine structure value is derived from the ratio of the rotational speed of the boundaries of the vortex to the speed of the vortex eye in its center. Since the angular rotation is constant, the same value was derived from the ratio between the radius of the constant vortex core and the radius of the hall vortex. Therefore, the constancy of alpha is an expression of the constancy relation in the vortex structure.展开更多
Kinetic-scale magnetic holes(KSMHs)are structures characterized by a significant magnetic depression with a length scale on the order of the proton gyroradius.These structures have been investigated in recent studies ...Kinetic-scale magnetic holes(KSMHs)are structures characterized by a significant magnetic depression with a length scale on the order of the proton gyroradius.These structures have been investigated in recent studies in near-Earth space,and found to be closely related to energy conversion and particle acceleration,wave-particle interactions,magnetic reconnection,and turbulence at the kineticscale.However,there are still several major issues of the KSMHs that need further study—including(a)the source of these structures(locally generated in near-Earth space,or carried by the solar wind),(b)the environmental conditions leading to their generation,and(c)their spatio-temporal characteristics.In this study,KSMHs in near-Earth space are investigated statistically using data from the Magnetospheric Multiscale mission.Approximately 200,000 events were observed from September 2015 to March 2020.Occurrence rates of such structures in the solar wind,magnetosheath,and magnetotail were obtained.We find that KSMHs occur in the magnetosheath at rates far above their occurrence in the solar wind.This indicates that most of the structures are generated locally in the magnetosheath,rather than advected with the solar wind.Moreover,KSMHs occur in the downstream region of the quasi-parallel shock at rates significantly higher than in the downstream region of the quasi-perpendicular shock,indicating a relationship with the turbulent plasma environment.Close to the magnetopause,we find that the depths of KSMHs decrease as their temporal-scale increases.We also find that the spatial-scales of the KSMHs near the subsolar magnetosheath are smaller than those in the flanks.Furthermore,their global distribution shows a significant dawn-dusk asymmetry(duskside dominating)in the magnetotail.展开更多
基金This work is supported in part by the Key Research and Development Program from Ministry of Science and Technology of China(2022YFA1205000)National Natural Science Foundation of China(12274217 and 62105142)+1 种基金Natural Science Foundation of Jiangsu Province(BK20220068 and BK20212004)Fundamental Research Funds for Central Universities.
文摘An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.
文摘Along with all other quantum objects, an electron is partly a wave and partly a particle. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment. When an electron looks more like a particle it has no shape, “point particle”, according to the Standard Model, meaning that it interacts as if it is entirely located at a single point in space and does not spread out to fill a three-dimensional volume. Therefore, in the sense of particle-like interactions, an electron has no shape. In this paper, a new theory is proposed in which the electron has a structure and a shape. The central idea is that an electron is a frictionless vortex with conserved momentum made out of condensed vacuum generated in the Big Bang from massless virtual photons that acquire mass when moving in the vortex at the speed of light. Using Hydrodynamics laws and applying them on the superfluid vacuum the basic properties of the electron are described here forth. This study provides mathematical models to calculate the mass, kinetic energy, density, volume, time, charge, and particle-wave duality. Such mathematical formulations are presented to confirm the theory. We conclude that the shape of the electron is accessible to human imagination, knowing its shape helps to determine its properties and shed a light on how matter is made and to explain the interactions of sub-atomic particles.
基金the National Natural Science Foundation of China(Grant Nos.11574085,91536218,and 11834003)the 111 Project,China(Grant No.B12024)+1 种基金the National Key Research and Development Program of China(Grant No.2017YFA0304201)the Innovation Program of Shanghai Municipal Education Commission,China(Grant No.2019-01-07-00-05-E00079)。
文摘Electron vortex beams(EVBs)have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics.Recently,a relativistic electron vortex beam(REVB)has been proposed[Phys.Rev.Lett.107174802(2011)].Compared with EVBs,except for orbital angular momentum,an REVB has intrinsic relativistic effect,i.e.,spin angular momentum and spin-orbit coupling.We study the electromagnetic field of an REVB analytically.We show that the electromagnetic field can be separated into two parts,one is only related to orbital quantum number,and the other is related to spin-orbit coupling effect.Exploiting this separation property,the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect.The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state;while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam.The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFE0134200)the National Natural Science Foundation of China(Grant Nos.12174147,91850114,11774131)+1 种基金the Natural Science Foundation of Jilin Province,China(Grant No.20220101016JC)the Open Research Fund of State Key Laboratory of Transient Optics and Photonics。
文摘By numerically solving the time-dependent Schr?dinger equation and employing the analytical perturbative model,we investigated the chirp-induced electron vortex in the photoionization of hydrogen atoms by a pair of counter-rotating circularly polarized chirped attosecond extremely ultraviolet pulses.We demonstrated that single-photon ionization of hydrogen atoms generates photoelectron momentum distributions(PMDs)with distinct helical vortex structures either with or without a time delay between two counter-rotating circularly polarized laser pulses.These structures are highly sensitive to both the time delay between the pulses and their chirp parameters.Our analytical model reveals that the splitting of vortex spirals is caused by the sign changing of the chirp-induced frequency-dependent time delay.We showed that to obtain the counterpart of the PMD under a pair of counter-rotating circularly polarized chirped pulses,both chirp parameters and ordering of pulses need to be reversed.
文摘A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength;furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.
文摘The nature and the origin of the fine structure are described. Based on the vortex model and hydrodynamics, a comprehensible interpretation of the fine structure constant is developed. The vacuum considered to have superfluid characteristics and elementary particles such as the electron and Hydrogen molecule are irrotational vortices of this superfluid. In such a vortex, the angular rotation ω is maintained, and the larger the radius, the slower the rotational speed. The fine structure value is derived from the ratio of the rotational speed of the boundaries of the vortex to the speed of the vortex eye in its center. Since the angular rotation is constant, the same value was derived from the ratio between the radius of the constant vortex core and the radius of the hall vortex. Therefore, the constancy of alpha is an expression of the constancy relation in the vortex structure.
基金the National Natural Science Foundation of China(grants 41731068,41774153,41941001,41961130382,41431072,and 41704169)Royal Society NAF\R1\191047the PRODEX program managed by ESA in collaboration with the Belgian Federal Science Policy Office.
文摘Kinetic-scale magnetic holes(KSMHs)are structures characterized by a significant magnetic depression with a length scale on the order of the proton gyroradius.These structures have been investigated in recent studies in near-Earth space,and found to be closely related to energy conversion and particle acceleration,wave-particle interactions,magnetic reconnection,and turbulence at the kineticscale.However,there are still several major issues of the KSMHs that need further study—including(a)the source of these structures(locally generated in near-Earth space,or carried by the solar wind),(b)the environmental conditions leading to their generation,and(c)their spatio-temporal characteristics.In this study,KSMHs in near-Earth space are investigated statistically using data from the Magnetospheric Multiscale mission.Approximately 200,000 events were observed from September 2015 to March 2020.Occurrence rates of such structures in the solar wind,magnetosheath,and magnetotail were obtained.We find that KSMHs occur in the magnetosheath at rates far above their occurrence in the solar wind.This indicates that most of the structures are generated locally in the magnetosheath,rather than advected with the solar wind.Moreover,KSMHs occur in the downstream region of the quasi-parallel shock at rates significantly higher than in the downstream region of the quasi-perpendicular shock,indicating a relationship with the turbulent plasma environment.Close to the magnetopause,we find that the depths of KSMHs decrease as their temporal-scale increases.We also find that the spatial-scales of the KSMHs near the subsolar magnetosheath are smaller than those in the flanks.Furthermore,their global distribution shows a significant dawn-dusk asymmetry(duskside dominating)in the magnetotail.
