Björn Brezger, Lucia Hackermüller, Stefan Uttenthaler, Julia Petschinka, Markus Arndt, and Anton Zeilinger

**Introduction**

In the early days of quantum mechanics, Louis de Broglie introduced the idea that any particle should also have wave properties - one speaks of theparticle-wave dualityof quantum mechanics. The success of this idea was overwhelming - today already pupils learn that electrons inside atoms and molecules behave as waves. A "wavy" nature has to be attributed not only to elementary particles but also to atoms and even large molecules, more exactly to the motion of such a composed particle as a whole.

One natural application of waves - most commonly, light waves - isinterferometry. By splitting and recombining a wavefront, various interactions can be measured in a very precise way. Optical interferometers have played an important role in the history of physics - just think of the Michelson-Morley experiment - and today are important technical tools in any area where ultimate precision is crucial. Recently atom interferometers (e. g. at MIT, Stanford, Yale) became competitive in highest-precision measurements of gravitation and rotation.

The work presented here extends interferometry into a new regime where

- the wavelength - few picometers - is well below the radius of a hydrogen atom and leads to a very high sensitivity to accelerations and various interactions
- the interfering molecules consist of many atoms and in many aspects resemble more small solid lumps than atoms: for example, each molecule rotates and vibrates randomly so that a finite temperature can be attributed to it.

We have built and operated the first interferometer for a large molecule, namely the fullerene C_{70}.

The interferometer - of the Talbot-Lau type - consists of three gold gratings and relies on coherent self-imaging (the Talbot effect) of periodic gratings. In comparison to our previous diffraction experiment, we have realized a five times shorter diffraction setup with ten times wider gratings and nevertheless observe high contrast fringes with a fifty times higher count rate. As a first demonstration of the sensitivity of our interferometer we have clearly detected the effect of the weak van der Waals force between the molecules and the gratings although the particles typically pass several hundred nanometers from any surface.

Our interferometer is a powerful instrument for measurements. This includes measurements of accelerations, gravity and molecular properties. However, our main focus are measurements shining light on the fundamental limit "quantum - classical": does quantum wave behaviour survive, or how does it change into classical particle behaviour if we gradually increase the mass and complexity of the molecules? How does the signal change due to the interaction with the environment, via blackbody radiation or collisions with residual gas? The Talbot-Lau interferometer scales to even smaller de Broglie wavelengths (higher masses) in an advantageous way: with unaltered overall length, the grating period has to go down only as the square root of the wavelength, whereas for far-field diffraction there would be a linear dependence. So the Talbot-Lau interferometer opens a way towards the quantum interference of even larger molecules.

The setup is shown in figure 1 together with a result from a scan which was completed in just five minutes.

In principle, fringes could result also from classical particles passing through the gratings. To clarify the origin of our fringes, we have investigated the dependence of the fringe visibility on the velocity of the molecules and compared the results to numerical models based on quantum or on classical physics, as shown in figure 2.

*Fig. 2: Velocity dependence of the fringe visibility:
The experimental data are compared to four different numerical models,
namely quantum wave dynamics versus classical point particle dynamics,
with or without consideration of the van der Waals interaction between
molecules and gratings. The quantum result including the van der Waals
effect is clearly the only adequate one.*

**Outlook**

We will make use of our interferometer to study the decoherence effect of collisions of the molecules in the interferometer. We are working on the application of such an interferometer to molecules of higher mass - experimental issues are suitable schemes for beam generation and detection, as well as the introduction of optical gratings in the interferometer.For a more detailed description of the experiment and the underlying theory you can download our paper here.

**Reference**

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M.
Arndt, and A. Zeilinger, *Matter-wave interferometer for large molecules*,
Phys.
Rev. Lett.
**88**, 100404 (2002).

© *Björn
Brezger, 03/2002*