Launching electrons to the centre of an optical field with a vortex phase profile via extreme-ultraviolet photoionization makes coherent imprinting of the spatial distribution of the vortex beam onto the electron wave packet possible.
Light has long been a favoured tool to trigger a desired response in matter, from the macro- to the microworld. Structuring light by shaping the direction of its electric field vector in space and time naturally shapes matter response. But is it possible to imprint macroscopic light patterns onto a microscopic object such as an electron? Writing in Nature Photonics, Giovanni De Ninno and co-workers provide evidence of such a possibility1.
Light fields are characterized by the behaviour of their polarization vector in space and time, providing rich opportunities for arranging this vector in unusual patterns. Vortex beams are an example of such global polarization shaping. For example, one can imagine a pattern in which light’s polarization vector gradually rotates around the circle, creating the overall patterns shown in Fig. 1a,b. Two quantities are introduced to describe such patterns: light’s spin angular momentum (SAM) and orbital angular momentum (OAM). Local rotation of the electric field vector in time, at every spatial point, is characterized by the SAM. Global rotation of the electric field vector in space, at any given time, is characterized by the OAM. The controlled interplay of the SAM and OAM can create a variety of patterns, such as those shown in Fig. 1a,b.
The findings by De Ninno and colleagues pose an intriguing question: can such patterns be transferred from a light wave to an electron ejected from an atom via the photoelectric effect? If the atom was the same size as the pattern of the light fields shown in Fig. 1a,b this would have been relatively easy — one could have put the atom in the centre of the vortex beam shown in Fig. 1a,b. The matter wave describing the ejected photoelectron would have faithfully reproduced the spatial structure of the vortex beam that triggered photoionization due to the local light–matter interaction, which is slightly different at every point. However, atoms are many thousands of times smaller than the polarization patterns in optical vortex beams. Electrons bound in each atom can only sense local fields at the atom’s position. For an electron, an attempt to sense the global light pattern may seem even more futile than our attempt to recognize the famous Nasca lines (Fig. 1c) at the ground level. Yet, against the odds, De Ninno and co-workers have achieved just this.
To record the pattern of the light polarization onto the electron, the light–matter interaction needs to be sensitive not only to the local field, but also to its gradient, which is the change of the field in space. Going back to our analogy with the Nasca lines, humans could create them by knowing exactly in which directions the lines had to go. For the light–matter interaction in the centre of the vortex beam, where the local field is zero, the sensitivity to the field gradients is especially high. Thus, if a cold atom is trapped exactly in the centre of the pattern, its electrons are best positioned to capture the structure of the vortex beam. This has been recently demonstrated by triggering bound electronic transitions within a cold atom trapped in the centre of a vortex2. But what if the atoms aren’t trapped and atomic gases are used instead, distributed across the entire interaction region?
Conceptually, the key to the successful transfer of the global light pattern onto the photoelectrons is to make sure that the useful signal carried by the relatively few electrons ejected from the centre of the vortex is not drowned out by the large signal originating from the vast spaces at the periphery of the vortex, where the field gradients are weak, thus making it difficult to sense the global pattern.
The trick used by De Ninno and colleagues is to combine the infrared (IR) vortex beam with an extreme-ultraviolet (XUV) beam focused right into the centre of the IR vortex. The XUV beam liberates the atomic electrons in the centre, launching the electron matter wave. Sufficiently tight focusing of the XUV light ensures that the signal carried by the electrons ejected from the centre of the vortex is not buried by the signal from the periphery. The interaction of the electron matter wave with the IR beam transfers the light pattern of the vortex onto the matter wave, imprinting light’s SAM and OAM onto the angular momentum of the departing electron. This pattern is later detected at a macroscopic distance from the interaction region by analysing the photoelectron angular distribution.
This analysis of the angular distribution, and how it changes as the pattern of the light vortex is changed, provided the smoking gun that both local and global angular momenta of light transfer onto a single photoelectron. When the local polarization of light co-rotates with the vortex, the photoelectron absorbing one IR photon in the centre of the vortex will change its energy by ћωIR, where ωIR is the carrier frequency of the IR laser beam, but feeling the field gradient, the photoelectron will grab two units of angular momentum. When the polarization of the IR light counter-rotates with the vortex, things are very different, especially in a focused IR beam: the tug-of-war between the two opposite rotations creates a strong, linearly polarized, longitudinal field that dominates the interaction with the IR field. Longitudinal fields are typical in focused beams, but in the light vortex with co-rotating SAM and OAM, the longitudinal field is absent3, enabling sensitivity to field gradients even in focused beams. This striking difference in the sensitivity to field gradients in focused beams is inevitably blurred by the photoelectron signal collected from the periphery of the vortex, where the electrons no longer sense the global pattern of the IR beam. Thus, comparing photoelectron angular distributions for co-rotating and counter-rotating SAM and OAM provides a quantitative measure of how well the light pattern of the vortex was imprinted onto the matter wave, with the experimentally detected signal reaching about 7–8% — a surprisingly large number.
Three-dimensional field patterns arising in focused vortex beams opens new opportunities for creating nontrivial chiral and topological patterns. One example could be new realizations of locally and globally chiral light — light in which the local pattern drawn by the electric field vector in time traces a three-dimensional chiral trajectory in every point in space4. In this case, the focused vortex beam will have to carry two colours — a fundamental and its second harmonic. Another example is a three-dimensional topological pattern referred to as the optical skyrmion5,6, where the quantized skyrmion number is formed by the field and its gradients. Since the work by De Ninno and colleagues shows that field gradients can be efficiently recorded, the skyrmion numbers can be imprinted onto chiral matter. In this case, the total absorption A of a three-colour skyrmionic field will be proportional to the skyrmion number S and a molecular-dependent chiral measure [Q12,x × Q13,y] · d23, giving A ~ S [Q12,x × Q13,y] · d23, and leading to quantized circular dichroism. Here the indices 1,2,3 label molecular states for which the transition frequencies are resonant with the colours of the skyrmion, d23 is the transition dipole moment, and Qij,x, Qij,y are the two vectors composed from the quadrupole tensor Qij,x = <i|xr|j>, Qij,y = <i|yr|j>, where i,j = 1,2,3 and r is the radius vector with components x,y,z.
The work of De Ninno and colleagues shows the potential of combining the local and global properties of light to control matter response at the macroscopic and microscopic scales, at the level of electrons, with chiral and topological matter being attractive candidates for exploring the nontrivial local and global properties of both light and matter.
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The author declares no competing interests.
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Smirnova, O. Nasca patterning in the microworld. Nat. Photonics 14, 527–528 (2020). https://doi.org/10.1038/s41566-020-0687-9