in matter wave interferometry

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 C

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").

* 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

* 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

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).

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 for various gases.

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 10^{7} amu), provided
we can reduce the background pressure to below 3 10^{-10} mbar.

Appl. Phys. B.