A team from Laboratoire de chimie physique-matière et rayonnement (CNRS/UPMC), in collaboration with international teams(1), has performed an experiment illustrating the measurement problem in quantum mechanics, in analogy with the famous Schrödinger’s cat thought-experiment. Trying to measure whether an electron emitted by a molecule was initially localized around one specific atom or another, the scientists eventually showed the result depends on the way the molecule dissociates after it has lost the electron. Results are published online in Nature Communications.
In an article, famous since its publication in 1935, Erwin Schrödinger proposed a thought-experiment in which a cat was trapped in a chamber containing a radioactive mechanism that can randomly lead to the cat’s death. The cat has 50% chances to be dead and 50% chances to be alive. There is only one way to know beyond any doubt: opening the chamber. Thus, as long as the chamber is closed, the cat is both dead and alive. Schrödinger saw this as a paradox in the interpretation of quantum mechanics.
The researchers are now proposing a molecular analogy to this famous experiment.
Figure 1: Scheme illustrating the performed experiment. The molecule is ionized and a hole is created on one of the sulfur atom (up). The hole is filled by the intern reorganization of the electrons and the molecular charge increases (middle). Depending on the fragmentation pathway, concerted (A) or sequential (B), the core hole appears localized or delocalized. © Marc Simon
The electronic structure of atoms is well described in quantum mechanics by mathematical items, the so-called orbitals, linked to the probability of presence of electrons around the nucleus. Inside a molecule, whose different constituting atoms are sharing the electrons, one can distinguish between the core orbitals localized around one atom, and the external orbitals, possibly delocalized around several atoms. Nevertheless, the question of the localization of core electrons arises when a molecule is made of identical atoms. What is happening when one removes –with light for example (we then speak of photoionization of the molecule) - a core electron in a molecule made of two identical atoms? Quantum mechanics tells us we cannot know a priori the atomic origin of the electron, and the electronic hole created must be delocalized on both atoms. The ionized molecule is thus in a superposition of quantum states where the hole is delocalized on both atoms. By analogy with Schrödinger’s experiment, the cat is both dead and alive.
Scientists have chosen a simple molecule, carbon disulfide CS2, with only three atoms: one carbon atom at the center and two identical sulfur atoms on the left and on the right hand side. With help of the X-rays produced on the LUCIA beamline at SOLEIL, they removed a core electron from sulfur, without being able to tell a priori which atom it came from. The CELIMENE experiment they conceived and performed allowed them to measure the angular distribution of the electron, i.e. the direction in which it escapes from the molecule. This distribution may show where the electron escaped, whether it is from the left or from the right atom.
When the molecule is ionized, it can fragment in three electrically charged atoms: three distinct ions. By identifying the dissociation pathway, the researchers showed that the answer to the localization of the electron actually depends on how the molecule dissociates. In the first case, when the molecule suddenly fragments into three ions (Figure 2 case A), it remains impossible to determine the origin of the electron, and the angular distribution shows a superposition of both left and right possibilities. By analogy with Schrödinger’s thought-experiment, the chamber is never open, and the cat is both dead and alive. In the other case, when the molecule dissociates in two steps, first into two ions, then into three (Figure 2 case B), it is possible to tell where the electron comes from because its angular distribution localizes it on a single sulfur atom. By analogy, the chamber is open and the state of the cat is determined.
Figure 2: In case A, the hole is delocalized on both sulfur atoms, as shown by the symmetric angular distribution of the emitted electron.
In case B, it is localized on the atom giving the S2+ ion and the electron angular distribution appears asymmetric. © Marc Simon
The question of localization or delocalization of core holes created by photoionization has long been passionate for the community of physico-chemists. This issue is even more fundamental as a large number of applications of photoionization rely on the ability to select precisely the targeted atom inside a molecule, thus localizing the hole (as for example the control of radiation damages). The results, published in Nature Communications bring an answer as a paradox typical of quantum mechanics: the electron can be considered totally delocalized or totally localized depending on the dissociation pathway (fragmentation in one or two steps).
(1) Synchrotron SOLEIL, Université de Trieste (Italie), Université de Las Vegas (Etats-Unis), Université de Oulu (Finlande), Université d'Uppsala (Suède).