Why is our daily world described by classical physics?
Why is quantum mechanics usually limited to the world of photons and small
particles? One answer to these questions is decoherence - processes that
limit the observability of quantum effects and turn them into classical phenomena.
To be able to predict under which circumstances a system will behave according
to quantum mechanics we have to study possible processes of decoherence.
For macroscopic particles there are two main 'natural' ways of decoherence:
On the one hand collisions with other particles (more
), and on the other hand the thermal emission of radiation due
to the internal heat of an object. The warm macroscopic bodies in our
everyday 'classical' world emit by far too many photons to behave like a
quantum object, whereas atoms or molecules can be sufficiently isolated to
show their quantum nature.
Fullerenes have the interesting feature that they can be turned into a crossborder
commuter between the classical and quantum descriptions. When they are relatively
cold (900 K) they can show perfect quantum behavior, but they possess already
sufficiently many degrees of freedom to store and partially release thermal
energy in form of photons. We can control the stored amount of energy in terms
of their temperature and thus trace the quantum-to-classical transistion in
a controlled and quantitative way.
A beam of fullerenes produced in a sublimation source (an
oven with a temperature of 660 ° C) shows quantum interference in a nearfield
interferometer under high vacuum conditions (more
). In order to gradually increase the internal energy of the molecules
we heat them right in front of the interferometer. The heating stage consists
of a focussed Ar+
laser beam (514 nm, 0-10W) that is
folded up to 16 times in front of the first grating. Fullerenes can store
50-100 green photons and convert them into internal heat before they
decompose. A certain fraction out of the beam will ionize during this process.
We record the number of ions in dependence of the beam velocity and
use a theoretical model to determine the temperature of the fullerenes.
Setup of the experiment: heating stage in front of the molecule
In the heating region the fullerenes are heated to temperatures of up to
5000 K, but due to the rapid radiative cooling even the hottest molecules
reach a temperature of about 3000 K when they enter the interferometer. In
order to detect the molecules behind the interferometer they pass another
laser beam (488 nm, 15 W) where a large fraction of the beam
ionizes and the ions are counted in another channeltron. Since hot molecules
are more likely to ionize in the detection stage the mean countrate also increases
with heating power.
Hot fullerenes are known to radiate a continous spectrum. The form of the
radiation density differs from the usual Planck law for a number of reasons.
First, the average thermal wave length is much larger than the size of the
fullerene molecule turning it into a colored emitter caracterized by the absorption
cross section σabs
. Second, the particle is not in thermal equilibrium
with the surrounding radiation field, but rather emitting into a cold environment,
where stimulated emission does not occur. Third, the virbrational modes do
not constitute an infinite heat bath, but have a finite heat capacity CV
Due to these corrections the spectral photon emission rate is given by
Figure 2 shows the wavelength dependent spectral photon emissio rate as a
function of temperature. One observes that the emission rate is negligible
below 2000 K, whereas at higher temperatures the molecules may emit photons
whose wave length are comparable to the path separation in the interferometer
Spectral photon emission rate of C70
A mean temperature of 3000 K can lead to the emission of 4-5 photons
at a wavelength of 400 - 800 nm, which should be sufficient to resolve the
path taken by the molecule and thus to completely destroy the quantum behavior.
A quantitative description is given by decoherence theory. It considers the
entanglement of the molecule with the emitted photon, and shows how coherences
vanish once a trace over the photon state is performed. Taking into asccount
the temperature evolution T(t)
due to cooling, the expected visibility
is given by
is the visibility at zero temperature. In effect,
the quantum contrast is reduced exponentially whenever photons are emitted
whose wavelength is sufficiently small to resolve the effective path separation.
By heating the molecules in steps of 0.5 Watts from 0 to 10 Watts we record
the molecular density pattern after the interferometer and determine the visibility
of the interference fringes. The visibiltiy is given by the amplitude of
the fringes divided by the mean count rate. Fig. 3 shows the measured
signal depending on the laser heating power. For relatively low heating power
the mean count rate rises due to the increasing detection efficiency with
rising temperature. At the same time the amplitude is increasing on a smaller
rate. For heating powers > 5 W the mean countrate (and also the amplitude)
decreases, since now a part of the beam is no longer entering the interferometer
due to ionisation and fragmentation at the heating stage. For very high heating
powers the amplitude vanishes completely.
We extract the dependence of the interference
contrast on the laser heating power, i.e. the mean temperature of the fullerene
beam and compare this curve with the theoretical prediction. In Fig. 4 and
Fig. 5 we do this for the two velocities classes that lead to (nearly) perfect
interference contrast in the absence of laser heating. These mean velocities
are v = 100 m/s and v = 200 m/s.
We find good agreement with the theoretical