The evolution of quantum mechanics in the first decades of the last century forced scientists to accept that matter behaves on the microscopic scale according to physical rules that are fundamentally different from those in the macroscopic world. In the microscopic world, concepts such as the uncertainty principle play a role that describes the accuracy with which certain properties of small particles, e.g. their place and their speed, can measure at the same time. In addition, quantum mechanics introduces the wave-particle dualism, which states that the behavior of small particles can sometimes be better understood by wave properties.
Electrons are elementary particles responsible for such everyday things as electricity. They are e.g. characterized by their (negative) unit charge. In addition, they also have an angular momentum. This is a vector that describes the rotation of the electron around the center of an atom. Slow rotation or rotation near the positively charged nucleus corresponds to a low angular momentum, while rapid rotation or rotation far from the nucleus results in a high angular momentum. The rules of quantum mechanics state that the angular momentum can only assume certain values. Consequently, angular momentum states are denoted by "s", "p", "d" and "f", which corresponds to the angular momentum quantum numbers l = 0-3. In addition to the magnitude of the angular momentum, the projection of the angular momentum vector onto a selected axis in the laboratory system (e.g., the polarization axis of the laser used in the experiment), characterized by the magnetic quantum number m, plays a role in the outcome and interpretation of laboratory experiments.
In the paper, scientists describe how you have succeeded in fully characterizing the wave functions of an ionized electron that contains contributions of the angular momentum to a value of l = 3 (i.e., s, p, d, and f contributions). Each of these angular momentum states is contained in the wave function with a certain amplitude and phase. These amplitudes and phases are now determined by a series of interference experiments. Here, the wave nature of the quantum mechanical particle is utilized. As with two intersecting water waves that either amplify or cancel out, interference between different parts of a quantum mechanical wave function can increase or decrease the probability of detecting a particle at a particular location or velocity. By conducting a series of interference experiments with different conditions, the pairwise interference between the s and d contributions of the wave function, the p and f contributions, and finally between all four components can be observed (see Figure 1). Accordingly, a precise and complete mathematical expression for the wave function of the ionized electron was obtained.
A key component of the success of this unique achievement was the use of attosecond laser pulses (1 as = 10-18 s). Attosecond pulses are the shortest laser pulses that can be generated in state-of-the-art laser laboratories. They are generated in a process called "high-harmonic generation". For this purpose, an atomic noble gas is exposed to an intense infrared (IR) laser pulse, which typically has a duration of a few femtoseconds (1 fs = 10-15 s). If the intensity of the infrared laser is high enough, the laser field can pull electrons out of the atom, which are then accelerated in the oscillating electric field of the infrared laser. Some of the accelerated electrons then collide with the atom from which they were removed. In this case, the electron can be taken up by the atom. All of the energy applied for ionization and acceleration of the electron is then released in the form of a high energy light particle (i.e., a photon in the extreme ultraviolet (XUV) or soft X-ray region of the electromagnetic spectrum). Since the various steps of high harmonic generation occur on a time scale that is short compared to the duration of one optical oscillation of the infrared laser (typically a few femtoseconds), this XUV / X-ray light appears in the form of a short attosecond pulse.