Measuring the phase of the scattering amplitude with vortex beams

Abstract

We show that colliding vortex beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the plane wave scattering amplitude changes with the scattering angle. Since vortex beams are coherent superpositions of plane waves with different momenta, their scattering amplitude receives contributions from plane wave amplitudes with distinct kinematics. These contributions interfere, leading to the measurement of their phase difference. Although interference exists for any generic wave packet collision, we show that using vortex beams dramatically enhances sensitivity to the phase in comparison with non-vortex beams. Since the overall phase is inaccessible in a plane wave collision, this measurement would be of great importance for a number of topics in hadronic physics, for example, meson production in the resonance region, physics of nucleon resonances, and small angle elastic hadron scattering.Comment: 18 pages, 5 figures; v2: introduction rewritten and expanded, matches the published versio

Electron vortices: Beams with orbital angular momentum

“…the larger helicity tending to accompany the larger transverse momentum, which may fall within a range determined by the transverse momentum of the incident vortex (Ivanov, 2012b). This result may be applied to generate vortex-entangled particles or di↵erent species by collision, or additionally opens up the possibility of applying vortex states to high energy particle physics through colliding high energy vortex electrons with protons or other particles.…”

“…Theoretical estimates suggest that a shift of 0.02 nm may be induced in a 300 kV electron vortex beams using a moderately strong laser pulse, so experimental observation is challenging but feasible. Ivanov (2012b) considered the case for electron-photon interactions and demonstrated the entanglement arising from conservation of the sum of the helicity shown in Eq. (80) below for particle-particle collisions also applies in the case of electron-photon interactions.…”

“…There are also plans to use inverse Compton scattering of laser light by electron vortex beams to generate structured X-ray beams In addition to the dynamics of the interactions of freely propagating vortices and anti-vortices, collisions between electrons and other particles carrying orbital angular momentum may also be considered (Ivanov and Serbo, 2011;Ivanov, 2012b;Jentschura and Serbo, 2011;Seipt et al, 2014), with implications for generating high energy vortices of various species. In such two-particle scattering situations, there are several possible outcomes -the particles may be scattered to a range of final states, including plane-plane or vortex-plane wave states (Ivanov and Serbo, 2011;Jentschura and Serbo, 2011), or vortexvortex entangled states (Ivanov, 2012b). In high energy electron-particle scattering, due to the scattering geometry, such collision processes are suitably described by consideration of the orbital helicity of each particle, i.e.…”

Scattering of wave packets with phases

“…Vortex electrons with the kinetic energy of 200 − 300 keV can be focused to a spot of anÅngström size [21], their OAM can be as high as = 200 [22], their magnetic moment increases proportionally to [13], and this brings about new effects in the electromagnetic radiation [23,24]. Such photons and electrons were also proved useful for optical manipulation [14], for probing phase of a transition amplitude, for creating pairs entangled in their OAM [25][26][27][28][29][30], etc.…”

“…That is why the higher values of the asymmetry favor the case with σ 1 ∼ σ 2 , in accordance with the ref. [29].…”