  Recent progress in coherent quantum interactions between free-electron pulses
and laser-induced near-field light have revolutionized electron wavepacket
shaping. Building on these advancements, we numerically explore the potential
of sequential interactions between slow electrons and localized dipolar
plasmons in a sequential phase-locked interaction scheme. Taking advantage of
the prolonged interaction time between slow electrons and optical near-fields,
we aim to explore the effect of plasmon dynamics on the free-electron
wavepacket modulation. Our results demonstrate that the initial optical phase
of the localized dipolar plasmon at the starting point of the interaction,
along with the phase offset between the interaction zones, can serve as control
parameters in manipulating the transverse and longitudinal recoil of the
electron wavefunction. Moreover, it is shown that the polarization state of
light is an additional control knop for tailoring the longitudinal and
transverse recoils. We show that a sequential phase-locking method can be
employed to precisely manipulate the longitudinal and transverse recoil of the
electron wavepacket, leading to selective acceleration or deceleration of the
electron energy along specific diffraction angles. These findings have
important implications for the development of novel techniques for ultrafast
electron-light interferometry, shaping the electron wave packet, and quantum
information processing.
