A perfect attosecond experiment

Attosecond technology is revolutionizing ultrafast laser physics research, enabling experiments that provide unprecedented insight into the structure and time-dependent dynamics of electrons in atoms, molecules, and solids. In a new experiment, physicists from Waseda University (Japan), the National Research Council (Canada), and the Max Born Institute (Berlin) used attosecond technology to fully characterize the quantum mechanical wave function of an electron generated by photoionization , This work, published in Science, is the first example of a "perfect" experiment based on attosecond technology.

These non-catchy predictions of quantum mechanics are based on the fact that every measurement on a quantum mechanical system produces only one result from a large set of possible outcomes. The probability of obtaining a particular result is described by a probability distribution derived from the wave function - a fundamental object of quantum mechanics. The wave function itself can not be measured directly. However, it is possible to develop strategies according to which the wave function can be completely characterized by multiple measurements on a quantum mechanical system.

In a work (Villeneuve et al., "Coherent Imaging of Attosecond Electron Wave Packet"), which was published in Science, a new approach for the complete characterization of an atomic wave function with the help of novel ultrafast lasers, which only a few years ago were developed. In the measurements, the scientists characterize the wave function of an electron, which is generated after the interaction of a neon atom with a series of laser pulses.

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.

Figure 1: A) Ionization with the XUV pulse alone produces an electron in a state characterized by "s" and "d" rotational pulses. By measuring the electron angle distribution, the relative amplitude and phase between the two components is determined; B) XUV + IR ionization generates an electron in a "p" and "f" angular momentum state. Again the relative amplitude and phase is determined from the measurement of the electron angle distribution; C) The combined XUV alone and XUV + IR ionization generates electron wave functions containing both "s", "p", "d" and "f" contributions. The interferences between these angular momentum components change with the delay between the XUV pulse and the co-propagating IR pulse. The large contribution of the "f" component is clearly visible in the first and last picture; D) Measured electron pulse image at two time delays between XUV pulse and IR pulse (corresponding to the first and last image in C). The present experiment allows a complete determination of the relative amplitude and phase of all angular momentum components and therefore represents a "perfect" experiment.

In the experiment, the researchers used attosecond XUV pulses to ionize neon atoms. In the experiment, when only the attosecond pulse is fired, a combination of s and p electrons is generated whose amplitude and relative phase can be determined from the measured angular distribution (see Figure 1A). If, in addition to the attosecond pulse, a copy of the infrared laser pulse is used for ionization, the amplitude and relative phase of the p and f components can be obtained (see Figure 1B). Finally, if the attosecond pulses are generated by means of a two-color laser field (ie both with the mentioned infrared laser pulse and with a half-wavelength pulse copy) and used together with the infrared pulse, the ionization can be used to determine the amplitude and relative Phase of all four components (s, p, d and f) can be determined. The result of the experiment and the determined amplitudes and phases of all angular momentum components are shown in Figures 1C and 1D. The clearly visible sixfold structure is caused by the dominant contribution of the f orbital with m = 0 in XUV + IR ionization. By coherently superposing a contribution of the fully symmetric s orbital (generated only by the XUV pulse) and changing the delay between the XUV and IR pulses, up and down oscillation can be generated along the vertical laser polarization, which is the phase of the makes f-orbital visible.

This experiment is what atomic physicists consider a "complete" experiment because it allows a complete mathematical description of the wave function of the ionized electron. It is also the latest example of how attosecond technology is currently revolutionizing ultrafast laser physics. With the present work, this research has for the first time reached a state of perfection. (Text translation: Dr. Claus-Peter Schulz)

Original publication

Coherent imaging of an attosecond electron wave packet

D. M. Villeneuve, P. Hockett, M. J. J. Vrakking, H. Niikura

Science 365 (2017) 1150-1153