Collisional decoherence
in matter wave interferometry

Klaus Hornberger, Stefan Uttenthaler, Björn Brezger, Lucia Hackermüller,
Markus Arndt & Anton Zeilinger

Introduction. One of the corner stones of quantum mechanics is the wave-particle duality of massive objects. According to quantum theory even complex particles, such as the C70 fullerene buckyball shown on the right side, may exhibit the interference properties of a wave. In our group we are performing experiments to demonstrate the wave nature of particles with an ever increasing complexity. Nowadays, we are routinely observing the interference of C70 fullerenes, and have the current record in mass and complexity being held by the fluoro-fullerene C60F48, (   more details coming soon).
      An obvious motivation for doing experiments with matter waves is the everyday experience that particles do not at all spread out like waves; rather they have a well-defined position whenever they are observed. How to understand this quantum-to-classical transition linking two incompatible descriptions of reality is still a matter of debate among the various interpretations of quantum theory. In any case, one can probe the borderline between the classical and the quantum realm by performing interference experiments with particles of increasing complexity.

Decoherence Theory. As is well understood, a reason for the perceived loss of a particle's ability to interfere is the coupling with other, unobserved degrees of freedom. An important decoherence mechanism for the interfering fullerene is the interaction with particles from the background gas. After a collision the state of the two particles is entangled, in general, and one could in principle obtain which-way information about the fullerene by a measurement on the gas atom. The coherence in the fullerene wave, which is required for interference, now resides in the joint two-particle state. Hence, if one disregards the gas particle (formally by "tracing out" the unobserved degree of freedom) the fullerene gets effectively localized by a reduction of the spatial coherence in the fullerene wave. This way decoherence theory gives a quantitative explanation for the perceived loss of coherence in a quantum state (although it does not necessarily solve the "measurement problem").

Sketch of Talbot-Lau inerferometer




Fig.1 Schematic setup of the near-field interferometer for C70 fullerenes. The third grating uncovers the interference pattern by yielding an oscillatory transmission with lateral shift xs. Collisions with gas molecules localize the fullerene center-of-mass wave function leading to a reduced visibility of the interference pattern.

The Decoherence Experiment. In the present experiment we studied the controlled loss of coherence in extended fullerene matter waves due to the interaction with various gases. The matter wave is produced and monitored by a Talbot-Lau interferometer, which is based on a near-field interference effect. In brief, an uncollimated beam of fullerene molecules passes three identical, equally spaced gratings, see Fig.1 above. Each slit of the first grating acts as an independent (point) source of fullerene waves. Diffraction at the second grating leads to a density pattern at the position of the third grating. This interference pattern has the same period as the gratings such that the incoherent sum over all point sources yields a high contrast density pattern, which in turn can be observed by modulation with the lateral position of the third grating. The large visibility of the resulting transmission signal is quantitative evidence for the observation of quantum interference, since a classical shadow effect would yield a significantly smaller visibility (   more details on the Talbot-Lau interferometer).
      By flooding the interferometer with various gases at low pressure (p< 2.5 10-6 mbar) we can control the likelihood for collisions in the interferometer. According to decoherence theory a typical collision with a gas particle localizes the fullerene to the scale of about 1 nm, while the spatial coherence required for interference is on the scale of a grating period, about 1 µm. It follows that a single collision suffices to destroy completely the ability to interfere, and therefore one expects an exponential decrease of the observed fringe visibility. This collisional decoherence could not be observed so far, since in usual matter wave interferometry the particles are so light that they would be kicked out of the interferometer after colliding with a gas particle - unlike in the present experiment, where the fullerenes are heavy enough to remain in the interferometer after a typical collision.

Observation of Collisional Decoherence. Figure 2 shows the experimentally observed loss of visibility as a function of the (methane) gas pressure. As expected one observes an exponential decrease of visibility with increasing gas pressure giving clear evidence for collisional decoherence. Note that, in contrast, simple loss or absorption would give rise to an exponentially decreasing flux at a constant visibility.
      Moreover, we obtain a good quantitative agreement with the theoretical prediction (solid line). The latter assumes a van der Waals interaction between the molecules and is based on a semiclassical evaluation of the scattering cross section. (Corrections due to the particular velocity selection scheme and geometry of the experiment are also included).

Argon visibility



Fig.2 Fullerene fringe visibility vs. methane gas pressure on a semi-logarithmic scale. The exponential decay indicates that each collision leads to a complete loss of coherence. The solid line gives the prediction of decoherence theory. The inset shows the observed interference pattern at (a) p=0.05 10-6 mbar and (b) p=0.6 10-6 mbar.


Decoherence pressures for various gases.
Figure 3 shows the observed characteristic decoherence pressures for a number of monatomic and molecular gases, and compares them to the theoretical prediction. We find a rather good agreement. Most remarkable is the observed weak dependence of the decoherence pressure on the specific type of collision partners. This can be explained by a near cancellation of the mass dependencies of the polarizability and the gas velocity. Xenon, for example, in spite of being the heaviest gas used, lies right in the middle of the observed range of decoherence pressures. We also note that the effect of molecular background gases does not deviate systematically from atomic ones.

Decoherence pressures



Fig.3 Experimental decoherence pressure for various gases (red) compared to the predictions of decoherence theory (blue).

Based on the good overall agreement between experiment and theory we can estimate the vacuum conditions that are required for the successful observation of quantum interference of much larger objects. We find that collisions would not limit quantum interference in a TL-interferometer even for an object as large as a virus (5 107 amu), provided we can reduce the background pressure to below 3 10-10 mbar.

Reference

Phys. Rev. Lett. 90, 160401 (2003)
Eprint arXiv:quant-ph/0303093

Klaus Hornberger, 03/2003