Chirality in quantum systems

J.Berakdar

Since the early days of chemistry it has been observed (Malus 1808, Biot 1812) that some compounds exist in two different states that have similar physical and chemical properties. Their optical properties are, however, completely different, milk and wine acids are examples of such "optically active" molecules.

The investigation of the molecular structure of such complexes revealed that these compounds have two different geometrical shapes that are mirror image of each other (cf. Fig.1), just like the left and right hand. Thus, the optical activity of such systems can be assigned to a special case of spatial symmetry "the stereoisomery". Stereoisomery occurs only when the molecules are spatially asymmetric (or chiral as termed by Lord Keliv), i.e. if they do not possess a symmetry plane.
As a matter of definition, a chiral linear molecule does not exist. However, chirality, can be induced in photoemission experiment of linear molecules either adsorbed on surfaces (Westphal et al 1989) or fixed in space (Heiser et al 1996). In this case, the molecular axis, the direction of the incident radiation and the momentum vector of the photoelectron form a right-handed frame with its left-handed reflection being well defined. In recent years, it became clear that chirality can also be observed in the double excitations of completely isotropic targets by circular photons (cf. Fig.1). In this case the coordinate frame is spanned by the two photoelectrons and the wave vector of the photon. Since the photon is absorbed by the two photoelectrons one can say that the chirality of the photon is transferred to the two electron pair. That is the pair has a chirality as an internal degree of freedom that can probed by varying the helicity of the photon.
The aim of our research in this area is to investigate the mechanisms for the chirality transfer and to explore possible applications. The theoretical methods used range from simple model calculations to heavy numerical simulations of the double excitations process.



Chirality can also be observed in the excitations of laser pumped targets. A simple example is shown in Fig.2 where an atom is pumped into a specific circular state and subsequently ionized by a monoenergetic electron beam. Here the helicity of the photon is first transferred to the atom and subsequently to the electron pair in the continuum.

Previous studies on non-oriented targets have shown (Weigold and McCarthy 1992) that, under certain conditions, the electron spectra can be related to the electronic density of the target. Now by exploring the chirality of the pair as an additional observable we gain an insight into the phase of the circular state of the atom, i.e. in which way the electron is circulating around the nucleus.

Collaborations:


E. Weigold and J. Lower (Australian National University, Canberra)
S. Mazevet (Los Alamos National Laboratory)
H. Schmidt-Boecking (Frankfurt am Main)
U. Becker (Fritz-Haber Institute, Berlin)