November 04, 2005
In the macroscopic world of everyday life we often have ‘deterministic chaos’. Phenomena such as weather and flows, the motion of celestial bodies, or the growth of insect populations can all be described by exact formulas; they are ‘deterministic’. But the way they develop is highly sensitive to their initial state. Even the smallest error in measuring the initial conditions can make long-term prediction impossible. Physicists call such processes ‘chaotic’.
Microscopic processes can also be very complex. But quantum mechanics rules out ‘deterministic chaos’ in the world of atoms. One reason for this is that quantum mechanical systems develop non-deterministically from many simultaneous initial states. In quantum chaos research physicists are therefore looking in the quantum world for correspondences to the deterministic chaos of the everyday world. In this way, scientists at Max Planck Institute of Quantum Optics are investigating quantum mechanical systems that would be deterministically chaotic according to the rules of macroscopic physics.
Scientists working with Gernot Stania and Herbert Walther have now succeeded in obtaining the first experimental evidence of quantum chaos in a system in which the components can become separated by arbitrarily large distances during the experiment. They harked back to an historical experiment demonstrating the photoelectric effect, i.e. the releasing of electrons from metal irradiated with light.
In the classical experiment, an electric voltage is applied to two metal plates facing each other, one of them coated with an alkali metal. The alkali metal is irradiated with light of a particular frequency (and thus energy). As soon as the frequency exceeds a certain value, the light frees electrons from the metal, which are detected as electric current. A hundred years ago, Albert Einstein published his explanation of this effect, which was decisive for the development of quantum theory and recognised with the Nobel Prize in 1921.
The scientists from Max Planck Institute of Quantum Optics adapted this experiment to their requirements. In the modern version, the alkali metal is not deposited on a metal plate, but traverses the experimental setup as a beam of rubidium atoms (see Fig.). The atoms are there subjected to an electric field and a strong magnetic field. As in the historic experiment, the atoms are now irradiated with light of a particular frequency which can release electrons from them. This electron current is measured as a function of the light frequency. The magnetic field, the electric field, and the electrostatic forces in the atom (attraction of protons and electrons) constitute three different forces acting on the electrons in the rubidium atoms which each provoke very different electron motions. As long as one of these forces outweighs the others, the motion of the electrons is simple and not chaotic. That is the case, for example, when the electron has not yet absorbed laser light and finds itself near the atomic nucleus. However, whenever the electron absorbs a light particle, it changes to a higher energy state and thus falls more under the influence of the external electromagnetic field. Its motion then becomes chaotic. In the course of this motion, the electron moves farther and farther from the nucleus until it is free.
The chaos in the motion is manifested by the fact that the electron current fluctuates in a particular way which matches the energy of the light particles. These fluctuations are called ‘Ericson fluctuations’. The researchers were able not only to identify the Ericson fluctuations, but also to regulate with the electric and magnetic field strengths how chaotically the system behaves according to the rules of macroscopic physics. In this way, they were able to show the connection between deterministic chaos and the fluctuations of the photocurrent: The more chaotically the system behaved according to the rules of macroscopic physics, the stronger the measured fluctuations.