Studying magnetic circular vortex dichroism effect for photoionization of Rydberg atoms with vortex photons

TL;DR

This work introduces magnetic circular vortex dichroism (MCVD) as a spectroscopic observable in the photoionization of hydrogen-like Rydberg atoms by vortex photons carrying orbital angular momentum. Using a theoretical framework based on the first Born approximation, Bessel vortex states, and momentum-space wavefunctions, the authors derive transition amplitudes for plane-wave and vortex-photon excitations and compute differential cross sections with an azimuthally averaged vortex amplitude. They reveal that MCVD is highly sensitive to the atomic magnetic moment, exhibits strong angular-momentum selectivity, and shows energy- and TAM-dependent behavior that depends on the multipole order; notably, for |m_\gamma| ≥ 2 the MCVD saturates to ±1, reflecting pronounced chiral asymmetry. The results suggest that vortex beams can serve as powerful probes of Rydberg magnetism and angular-momentum–resolved dynamics, with practical implications for experimental investigations using polarized Rydberg targets and structured light.

Abstract

Rydberg atoms, renowned for their exceptional quantum properties, hold significant importance in quantum physics. The photoionization of Rydberg atoms serves as a critical tool for probing their unique characteristics. In this work, we investigate the photoionization dynamics of hydrogen-like Rydberg alkali atoms interacting with vortex photons-a class of structured light carrying intrinsic orbital angular momentum. This process gives rise to novel quantum phenomena distinct from conventional photoionization processes. Our results reveal that vortex photons exhibit exceptional sensitivity to the magnetic moments of Rydberg atoms, positioning them as a powerful spectroscopic tool for investigating Rydberg magnetism. It is also demonstrated that the initial photon energy must be carefully selected to observe significant experimental results. Furthermore, the photoionization process displays strong angular momentum selectivity, preferentially favoring configurations where the photon total angular momentum and atomic magnetic moment are aligned. This pronounced asymmetry directly manifests the chiral nature of the vortex photon-Rydberg atom collisions.

Figures (8)

• Figure 1: Transverse intensity profile of a Bessel vortex photon with $\omega =100$ eV, $\theta_{\vb k}=\pi/10$, $m_{\gamma}=1$, and $\Lambda_{\gamma}=-1$. All transverse distances are in nanometers.
• Figure 2: Momentum distribution of a monochromatic Bessel vortex state with topological charge $\bar{m}_{\gamma}=1$. The black circle of radius $\kappa$ indicates the distribution in momentum space. All momentum vectors lie on a circular cone. The phase factor of the plane wave components advances by $2\pi \bar{m}_{\gamma}$ around the circle (phases are color-coded). Here, $k_z$ is the longitudinal momentum and $\kappa$ is the fixed transverse momentum magnitude for all components.
• Figure 3: Geometry of a central collision between a vortex photon and a Rydberg atom. The polarized Rydberg atom is located within a weak, constant magnetic field. The incident vortex photon (represented by the blue cone with cone angle $\theta_k$) propagates along an axis collinear with the magnetic field direction. Here, $k_z$ and $\kappa$ denote the photon's longitudinal momentum and transverse momentum modulus, respectively. The atom is positioned directly on the singularity line of the vortex photon.
• Figure 4: MCVD in Rydberg atom photoionization with vortex photons. The principal and orbital quantum numbers are fixed at $n = l + 1 = 51$, while the magnetic quantum number varies from $10$ to $50$. Initial photon energy is chosen to be $100$ eV. Conical angle of vortex photon is $\theta_k=\pi/10$. Different lines corresponds to different cases with $m_{\gamma}$ ranging from $0$ to $\pm 3$. Label $(a,b)$ in the legends means we get MCVD from difference of two initial cases: $(m_{\gamma}=a,\Lambda_{\gamma}=b)$ and ($m_{\gamma}=-a,\Lambda_{\gamma}=-b)$.
• Figure 5: MCVD in CRA photoionization with vortex photons. Targets follow $n=l+1={m_l}+1$ with $n$ varying from $11$ to $51$. Initial photon energy is chosen to be $100$ eV. Conical angle of vortex photon is $\theta_k=\pi/10$. Different lines corresponds to different cases with $m_{\gamma}$ ranging from $0$ to $\pm 3$. Label $(a,b)$ in the legends means we get MCVD from difference of two initial cases: $(m_{\gamma}=a,\Lambda_{\gamma}=b)$ and ($m_{\gamma}=-a,\Lambda_{\gamma}=-b)$.