Atomic form factor for twisted vortex photons interacting with atoms

Abstract

The relatively new atomic form factor for twisted (vortex) beams, which carry orbital angular momentum (OAM), is considered and compared to the conventional atomic form factor for plane wave beams that carry only spin angular momentum (SAM). Since the vortex symmetry of a twisted photon is more complex that that of a plane-wave, evaluation of the atomic form factor is also more complex for twisted photons. On the other hand, the twisted photon has additional parameters, including the OAM quantum number, ℓ, the nodal radial number, p, and the Rayleigh range, z R that determines the cone angle of the vortex. This Rayleigh range may be used as a variable parameter to control, in new ways, the interaction of twisted photons with matter. Here we address: i) normalization of the vortex atomic form factor, ii) displacement of target atoms away from the center of the beam vortex, and iii) formulation of transition probabilities for a variety of photon-atom processes. We attend to features related to new experiments that can test the range of validity and accuracy of calculations of these variations of the atomic form factor. Using the absolute square of the form factor for vortex beams, we introduce a vortex factor that can be directly measured.

Dynamic electron correlation in interactions of light with matter formulated inb⃗space

“…The twisted vortex beams are more complex than plane-wave beams; they may carry an orbital angular momentum not present in plane-wave beams. Moreover the asymptotic [18]. The maximum of the Gaussian envelope (shown here) of the beam intensity distribution is along the beam axis, and the envelope is cut off when its intensity falls by a factor of 1/e 2 0.135 of its maximum.…”

“…IV B below, we will address how a( b) may be used to describe interactions with beams that fall off with distance in the transverse direction from the beam axis, and thus have an explicit dependence on b. We also briefly address some aspects of twisted vortex beams of photons and electrons [18]. But next we show how a( b) may be used to to describe interactions of photons with atomic matter in such a way that one may apply previous formulations of electron dynamics to interactions of light with matter.…”

“…The paraxial approximation [15] used for twisted vortex photons in our previous paper [18] simplifies the scattering problem by decoupling beam trajectories from the x-y plane. In this approximation, particle and ray trajectories are approximated as parallel to the axis of the macroscopic beam [35], which is taken as the z-axis with b in the x-y plane (as is q for forward scattering).…”

“…This may also be applied to electron, proton, and some ion beams in the limit that Coulomb scattering of the incident charged projectile with the target can be ignored [36]. In the example of transfer of orbital angular momentum between the beam and the target [18], in this limit the direction of spin of an atom is reversed (like reversing the spin of a boat's propeller) by exchange of the direction of spin with the twisted photon, where the joint photonic-atomic spin axis is the beam axis, which differs in general from the axis of the photon's trajectory [37]. Mathematical descriptions of twisted vortex beams that avoid the paraxial approximation are available [38,39], but they are more complex both mathematically and conceptually.…”

“…I, for beams of twisted photons and electrons incident on atomic targets (see Fig. 1 [18]. Thus, at a fixed value of z R (and fixed w(0) at a fixed λ), Θ V (b) can be used to macroscopically control cross sections and reaction rates by choosing different Θ V (b) within the beam [40] to vary b.…”