Atomic wavefunctions probed through strong-field light--matter interaction

Strong-field light–matter interactions can encode the spatial properties of the electronic wavefunctions that contribute to the process1–4. In particular, the broadband harmonic spectra, measured for a series of molecular alignments, can be used to create a tomographic reconstruction of molecular orbitals5. Here, we present an extension of the tomography approach to systems that cannot be naturally aligned. We demonstrate this ability by probing the two-dimensional properties of atomic wavefunctions. By manipulating an electron–ion recollision process6, we are able to resolve the symmetry of the atomic wavefunction with high contrast. The basic route to spatially probe a molecular orbital involves four main steps5. First, the orbital axis is aligned in the laboratory frame7, this being accomplished by aligning the molecule. Second, an electron is ionized by a strong laser field through tunnelling ionization, after which the electron oscillates in the laser electric field and may recollide with the parent ion. Third, if the electron recollides, the recollision projects the ground state into the spatial frequencies that compose the free-electron wavefunction. The whole process, induced during less than one optical cycle, leads to the emission of extreme ultraviolet pulses with attosecond duration8. The projected ground state is therefore obtained from the broadband spectrum of the emitted pulses. In the final step, the molecule is aligned at different angles to the recolliding electron momentum, which permits tomographic reconstruction of the orbital. Despite its importance and generality, it has been impossible to extend this approach, known as orbital tomography, beyond simplemolecular orbitals such as theN2 highest occupiedmolecular orbital. There are two fundamental limitations. The first arises from the coupling between ionization and recollision. When the molecule is rotated, both the tunnelling and recollision probabilities can be very strongly modulated9,10. This couples the angle dependence of tunnelling, recollision and recombination in the harmonic spectrum. These processes must be disentangled before tomography can be extended beyond sigma orbitals (where tunnelling is relatively insensitive to angle). The second limitation arises from the requirement to fix the orbital in the laboratory frame—using molecular alignment. Tomography cannot resolve degenerate orbitals that are not fixed within a molecular structure, or molecules that are difficult to align. We overcome both limitations, generalizing tomography to atoms and by extension, to degenerate molecular orbitals. In addition, by removing the necessity to rotate the molecule, we remove the deleterious effects of tunnelling, without affecting its benefits. In fact, in the future aligning molecules will provide a new use. Alignment will enable a specific orbital to be selected for study from among a set of ionizing orbitals in complexmolecules.