Abstract
Recent developments in advanced electron microscopy aim at reaching subfemtosecond timescales, which would allow to study the dynamics of ultrafast elementary electronic processes at nanometer length scales. Spatio-temporal control of the quantum phase of free electron wave function with a time period shorter than the coherence time can be introduced with the help of ultrashort optical pulses. Until recently, only electron-photon interaction schemes involving nanostructures has been realised [1,2].
In this contribution, we present a novel scheme for quantum coherent control of the free electron wave function using inelastic scattering at the ponderomotive potential of optical fields. Two optical pulses of different frequencies can be used to generate optical travelling wave propagating parallel to the electron beam and synchronized with the electrons' velocity. Thus, electrons interact with an optical standing wave in their rest frame and their longitudinal momentum changes as a result of the action of the ponderomotive force. This effect is generalization of the Kapitza-Dirac effect [3,4] and under proper conditions can lead to coherent modulation of the phase of electron wave function. Up to now, inelastic scattering of electrons at the ponderomotive potential of travelling wave was performed in a classical regime of interaction, which resulted in electron spectrum broadening and attosecond electron pulses formation [5,6]. By modifying the previous experiment, it is possible to reach the coherent regime of the interaction and observe interference peaks in the electron energy spectra, which are separated by the difference between the energies of the two photons participating in the scattering and which can be manipulated by controlling the strength of the interaction. Electron energy spectrum modulation into discrete energy sidebands was observed very recently for 95 keV electron energies [7]; however, such experiment has not yet been performed at much lower electron energies in scanning electron microscope. Described all-optical scheme can be also used for electron wave function shaping, e. g. electron vortex beam generation. If one or both laser beams creating the optical traveling wave are optical vortices, their orbital angular momentum can be transferred to the electrons during the interaction, which would lead to the generation of electron vortex beams in the energy sidebands [8]. We will discuss our current experimental progress and possible development of this method.
[1] Feist, A., Echternkamp, K., Schauss, J. et al. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 521, 200-203 (2015).
[2] Vanacore, G.M., Madan, I., Berruto, G. et al. Attosecond coherent control of free-electron wave functions using semi-infinite light fields. Nat. Commun 9, 2694 (2018).
[3] Kapitza, P. L. and Dirac, P. A. M. The reflection of electrons from standing light waves. Proc. Camb. Phil. Soc. 29, 297-300 (1933).
[4] Freimund, D. L., Aflatooni, K. et Batelaan, H. Observation of the Kapitza-Dirac effect. Nature 413, 142-143 (2001).
[5] Kozák, M., Eckstein, T., Schönenberger, N. et al. Inelastic ponderomotive scattering of electrons at a high-intensity optical travelling wave in vacuum. Nat. Phys. 14, 121-125 (2018).
[6] Kozák, M. Ponderomotive generation and detection of attosecond free-electron pulse trains. Phys. Rev. Lett. 120, 103203 (2018).
[7] Tsarev, M., Thurner J. W. et Baum, P. Nonlinear-optical quantum control of free-electron matter waves. Nat. Phys. (2023). [Published: 2023-06-12]
[8] Kozák, M. Electron vortex beam generation via chiral light-induced inelastic ponderomotive scattering. ACS Photonics 8 (2), 431-435 (2021).