Interaction of twisted light with free twisted atoms

Abstract

We investigate absorption and scattering of structured light by atoms, treating the photon and the atomic center of mass as spatially localized wave packets. We show that vortex photons can transfer orbital angular momentum (OAM) to the atomic center of mass with near-perfect efficiency in head-on collisions when the impact parameter $b$ is smaller than the atomic transverse coherence length $σ$, which ranges from nanometers to sub-micrometer scales. Larger offsets result in a shifted mean OAM and a finite variance, both controlled by the ratio $b/σ$. The wave-packet nature of light enables electronic transitions that violate standard selection rules, albeit with a clear hierarchy where the dipole transition dominates. For femtosecond pulses, the finite spatial coherence of the photon leads to measurable shaping of the resonant absorption lines. We demonstrate a transverse recoil of the atom in a vicinity of the photonic vortex, dubbed "the superkick", and its dual effect - "the selfkick" - when an initially twisted atomic packet experiences recoil upon absorbing a gaussian photon. These phenomena are within reach of experimental capabilities using structured light in combination with cold atomic beams and ions in Penning traps, providing a route to the controlled generation and manipulation of non-gaussian atomic packets.

Figures (13)

• Figure 1: Estimated probability distribution \ref{['estimated_dist']} of OAM in the evolved state of CM. Initial atomic packet width is $\sigma_\perp^{(\text{CM})} = 50$ nm, photonic packet width $\sigma_\perp^{\gamma} = 1$$\mu$m, transferred OAM at zero $b$ equals $\ell_0 = 3$ (indicated by red line). For $b = 10$ nm: $\langle \ell^{\text{(CM)}}\rangle = 2.72$, $\Delta \ell^{\text{(CM)}} = 0.47$. For $b = 200$ nm: $\langle \ell^{\text{(CM)}}\rangle = 0.40$, $\Delta \ell^{\text{(CM)}} = 0.53$.
• Figure 2: $n=1\to n=2$ transitions in hydrogen: the probabilities \ref{['prob_abs']} and cross sections \ref{['gen_sigma']} of absorption versus the average photon energy. $\left\langle \omega \right\rangle \equiv \sqrt{\left\langle k_z \right\rangle^2 + (2n_\gamma + |\ell_\gamma|+1)/(\sigma_\perp^\gamma)^2}$ for different values of the photon OAM $\ell_\gamma$. The photon packet \ref{['HG_LG_phot']} has $\lambda_i=1$, $\sigma^\gamma_z=10$$\mu$m, $\sigma^\gamma_\perp=1$$\mu$m, the radial and longitudinal indices are $n_\gamma=k_\gamma=0$. The CM wave function \ref{['HG_LG']} is gaussian with $\sigma^{\text{(CM)}}_\perp = \sigma^{\text{(CM)}}_z = 20$ nm, and it has a vanishing mean momentum, $\left\langle P_{iz} \right\rangle = 0$. Note that the transverse rms size of the photonic packet equals $\sigma_\perp^\gamma\sqrt{2n_\gamma+|\ell_\gamma|+1}$ rather than simply $\sigma_\perp^\gamma$.
• Figure 3: $n=1\to n=3$ transitions in hydrogen: the probabilities \ref{['prob_abs']} and cross sections \ref{['gen_sigma']} of absorption versus the average photon energy. The parameters of the wave packets are the same as in Fig. \ref{['n1_to_n2']}.
• Figure 4: Probability \ref{['prob_abs']} (blue points) and cross section \ref{['prob_sc']}(orange points) of the dipole transition $1s\to 2p, m_f=\lambda=1$ as a function of the photon OAM $\ell_\gamma$. The probability of transitions that violate the standard selection rule decreases exponentially with $\ell_\gamma$, while the cross section decreases only linearly.
• Figure 5: The asymmetry caused by the transverse photon coherence: the probability of the dipole transition $1s\to3p$ for different $\sigma^\gamma_\perp$. Both the packets are gaussian, $\sigma^\gamma_z = 10$$\mu$m, $\sigma^{\text{(CM)}}_z = \sigma^{\text{(CM)}}_\perp=5$ nm. The black vertical line indicates the transition frequency of $12.1$ eV.