Hydrogen atoms under the microscope

Direct observation of node structures in electronic states of the hydrogen atom

In order to describe the microscopic properties of matter and their interactions with the environment, quantum mechanics uses wavefunctions whose structure and time dependence are described by the Schrödinger equation. In atoms, using electronic wave functions, i.a. Describe charge distributions whose magnitude is far removed from our everyday experience. The experimental observation of the charge distribution is complicated by the fact that the process of measurement itself has effects on the wave function and each measurement selectively detects only one manifestation of the possible states. Physicists therefore use calculations of charge distributions that are possible with textbook knowledge. Better said, until today this was so. Under the leadership of MBI scientists, an international team of researchers has succeeded in developing a microscope that allows the wave function of excited hydrogen atoms to be increased by a factor of more than twenty thousand. Thus, the node structures of the electronic states of the hydrogen atom can be visualized on a two-dimensional detector. The results of the work represent the realization of a three-decade-old idea and were published in Physical Review Letters (PRL 110, 213001 (2013) and on physicsworld.com.

The development of quantum mechanics in the first half of the last century had a significant impact on the scientific understanding of the world. Quantum mechanics extended the world view based on classical Newtonian mechanics to a description of the micro-world, whose properties could not be explained by classical approaches. These properties include e.g. the particle-wave-duality, the interference and entanglement of particle properties, the Heisenberg uncertainty principle and the Pauli exclusion principle. Of central importance in quantum mechanics is the concept of wave function, which allows a mathematical solution of the time-dependent Schrödinger equation. According to the Copenhagen interpretation, the wave function describes the likelihood of measurement results resulting from a quantum mechanical system, such as a. the energy of a system or the position and momentum of its components. The wave function thus allows the description of non-classical phenomena on the microscale, which are observed by measurements on the macroscale. The measurement corresponds to viewing one or more of the innumerable possible manifestations of the wave function.

Despite their tremendous impact on modern electronics and photonics, quantum mechanics and its potential still pose great intellectual challenges. Again and again, new experiments were inspired to illustrate the fascinating predictions of the theory. For example, Haroche and Wineland received the Nobel Prize in 2012 for their work on measuring and controlling single quantum systems in interference-free quantum experiments, paving the way for more accurate optical clocks and possibly even for the future realization of a quantum computer. Using short laser pulses, coherent overlays of stationary quantum mechanical states (waves) of the electrons moving on periodic orbits around atomic nuclei can be observed in experiments. The wave function of each of these electronic stationary states is a standing wave, which has a node pattern in which the quantum numbers of the respective states are reflected. To observe such nodal patterns, raster tunneling techniques have been applied to surfaces. In addition, recent laser ionization experiments have enabled the generation of extreme UV light which encodes the initial wave function of an atom or molecule at rest.

Fig. (left) two-dimensional projection of electrons from the excitation of hydrogen atoms to four electronic states, given with quantum numbers (n1, n2, m) and with (from top to bottom) 0, 1, 2 and 3 nodes in their wave function for the parabolic coordinate ξ = r+z; (right) Comparison of the experimentally measured radial distribution (solid lines) with results from quantum mechanical calculations (dashed lines), which shows that the node structure of the quantum mechanical wave function was measured in the experiment.

About 30 years ago Russian theorists presented an alternative experimental method to measure the properties of wave functions. They proposed to conduct experiments to investigate the laser ionization of atomic hydrogen in a static electric field. They predicted that the projection of electrons on a two-dimensional detector (placed perpendicular to the static electric field) allows the measurement of interference patterns, which directly reflects the nodal structure of the electronic wave function. This fact is due to the special property of hydrogen, which contains as the only naturally occurring atom only one electron. Because of this peculiarity, the wave functions of hydrogen can be represented as the product of exactly two wave functions, which describe how the wave function changes as a function of two so-called "parabolic coordinates". It is essential that the shape of the two parabolic wave functions is constant, independent of the strength of the static electric field, and thus remains throughout the journey of the electron from the ionization site to the two-dimensional detector (in our experiment about half a meter !!).

Translating the coherent idea into experimental reality was anything but easy. Since hydrogen atoms are not chemically stable, they first had to be prepared by laser dissociation of a suitable precursor molecule (hydrogen disulfide). Then the hydrogen atoms had to be excited into corresponding electronic states, which in turn required two additional laser sources to be tuned exactly. Finally, when the electrons were excited, an extremely delicate electrostatic lens had to be used to increase the physical dimensions of the atom to within a millimeter scale on which they could then be observed with the naked eye on a two-dimensional imager and captured by a camera system , The most important results are shown in the figure below. The figure shows the raw camera data from four measurements in which the hydrogen atom was excited to states with 0, 1, 2, and 3 knots in the wave function for the parabolic coordinate ξ = r+z. As the experimentally determined projections on the two-dimensional detector show, the nodes can be easily detected via the measurements. The experimental setup here serves as a microscope, which allows us, at a magnification of about twenty thousand, to look very deeply into a hydrogen atom.

Beyond the pure proof of more than 30 years old theoretical consideration, the intricacies of quantum mechanics are beautifully demonstrated in our experiment. Moreover, our results should serve as a fertile field for further research, for example, exposing hydrogen atoms to both electric and magnetic fields simultaneously. The simplest atom in nature still has a lot of exciting physics to offer.

Original publication

Hydrogen atoms under magnification: Direct observation of the nodal structure of Stark states

A. S. Stodolna, A. Rouzée, F. Lépine, S. Cohen, F. Robicheaux, A. Gijsbertsen, J. H. Jungmann, Ch. Bordas, M. J. J. Varkking

Physical Review Letters 110 (2013) 213001/1-5


Further information:


Aneta Stodolna, (030) 6392 1470, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
Prof. Dr. Marc Vrakking, (030) 6392 1200, MBI