Laser-induced Quantum Shaping Of Single Free-Electron Wavefunction And Its Particle-to-wave Transition

In order to realize a laser-driven micro-accelerator,we need to overcome the quan-tum effects that become significant on the order of micrometers,as well as the interac-tion of strong light field and matter.In order to study this problem,we refer to the pro-cess of electron transition from classical behavior to quantum behavior in free electron lasers,and draw on the processing of strong fields in laser-induced near-field electron microscopy.Free electron laser(FEL)is a device that makes relativistic electrons move in a periodically changing magnetic field(oscillator)and generates radiation for the os-cillation induced by Lorentz force.We can use the pure classical theory to describe the dynamic behavior of electrons in the actual FEL system and the electrons are treated as charged point particles in the magnetic field;while from the perspective of Compton scattering,when the quantum recoil of the interacting electrons is large enough and the width ?p of electron momentum is small enough,the momentum of the electron can produce an observable "quantization"distribution.The behavior of the electron needs to be described by quantum mechanics,and it is called a quantum free electron laser.The coupling of nanomaterials to the laser field can excite local strong field at the surface of the material,which is called near-field.When electrons couple with near-field light,the electrons can absorb/release multiple photons,similar to quantum FEL,producing "quantized" momentum/energy sideband distribution,the phenomenon is called Photon-induced near-field electron microscopy(PINEM)effect.In order to understand the particle-wave duality problem of electron uniformly,we treat electrons as wavepackets in the framework of quantum mechanics,and un-derstand the particle and wave properties as the electron behavior in the interaction process,which treats the interaction as a kind of measurement.Within the model of the inverse Smith-Purcell effect,we make the electrons interact with the near field induced by the incident laser on the grating,the quantum manipulation and bunching effect of a single free-electron wavefunction interacting with near-field is systematically inves-tigated by adjusting the wavelength of the incident light,the structural period of the grating,the size and phase of the initial wave packet.The particle behavior of electrons in the laser accelerator(such as dielectric laser accelerator)and the quantum behavior in ultrafast transmission electron microscopy(Such as PINEM effect)can be derived by the system.Through theoretical calculations,we define the ratio between the size of the elec-tron wave packet and the wavelength of the near-field light as the"decay parameter",which is used to measure the point particle behavior and wave behavior of electron ex-hibited during the coupling with near-field.At the same time,by adjusting the decay parameter,which means changing the size of the electron wave packet or the wave-length of the near-field light,the electrons interacting with the near-field light can re-alize the transition from particle to wave,specifically showing the wave-particle dual-ity.And we study the influence of the phase of the initial electron wavepacket on the final states together with the decay parameter to give three typical modes of the elec-tron behavior when coupling with near-field:classical point particle acceleration,the quantum PINEM effect and the unconventional momentum/energy sidebands with con-dition between the classical limit and quantum limit.We call the last one as anomalous photon-induced near-field electron microscopy(APINEM)effect.We use the Crank-Nicholson method to numerically calculate the evolution process of the electron wave function during the interaction,project the electronic state into the phase space to ob-tain the Wigner distribution of the wavepacket,and obtain two basic characteristics of the electron in the phase space:Quantum deformation of the wavepacket and quan-tum interference fringes between the momentum/energy spectrum sidebands.With the concept of quantum deformation and quantum interference,we understand APINEM effect as a kind of "transition" behavior between classical acceleration and quantum PINEM effect,so the classical acceleration and quantum PINEM effect of the electron coupled with near-field can be interpreted uniformly from the perspective of electron wavepacket.And according to the wavepacket shape in the phase space,we also s-tudy the behavior of single particle bunching,single particle anti-bundling and periodic bunching caused by free propagation.In periodic bunching we get the micro-bunch of the attosecond(10-18s)level,which is important for improving electron coherence for high-resolution electronic imaging and for studying electron luminescence.Therefore,with the image of wave-particle duality,we study the problem of elec-tron acceleration and electron quantum coherence regulation in a strong field environ-ment,propose the concept of decay parameter ?(L)to characterize the particle-to-wave transition of electron,and analyzes the quantum deformation and interference fringes induced by the interaction process through the Wigner distribution in phase space.With the concept of quantum interference,the three typical modes of electrons interacting with near-field are self-consistently linked,and the classical acceleration behavior is understood as the natural emergence in the quantum systems.