Decoherence by the emission of thermal radiation

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 details), 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 details). 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.

 

Fig.1 Setup of the experiment: heating stage in front of the molecule interferometer. 

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 Ar⁺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.

Theoretical description

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 σ_abs. 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 C_V. 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 (1 µm).



Fig.2 Spectral photon emission rate of C₇₀ molecules.

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



where V₀ 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.

Experimental Results

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.