The quantum theory may be regarded as a unique scientific success story traced back for nearly hundred years. Nevertheless, many of its statements seem to contradict our "normal" human perception, which is shaped by our everyday experience. Since quantum phenomena are to be observed particularly well with isolated objects, and it is easier to isolate small objects from its environment, it is argued often that quantum physics is valid in the micro-cosmos only. Whether there is, however, a well-defined transition between the quantum and the 'classical' world is still an open question.

Our laboratory has undertaken the task to show that quantum phenomena may be observed also with a relatively large object, and then to examine, under which circumstances "normality" is recovered in its behavior. In these experiments the wave - particle duality of large and complex molecules is investigated.
The basic concept that a wave should be assigned to an individual solid object goes back to Louis de Broglie. He used the example of an electron with a wavelength l=hlm•V where h is Planck's constant, m is the mass of the moving particle and v is its velocity.
If we speak about waves, we mean expanded, oscillating phenomena. A characteristic feature of waves is their ability of interference, i.e. the reinforcement and extinction of overlaying wave crests and troughs. What is completely descriptive for continuous media, e.g. surface waves on water, becomes apparently paradoxical if we ask "has also an individual particle a wave nature"? This question sounds rather like a Koan, a mystery of the Zen Buddhism. While the word wave implies an expanding phenomenon, the term particle is closely linked in our language with the concept of a clearly localized object. And similarly, as with the Eastern meditation puzzle, the answer to our question is not to be reached by logical deduction.
We shall try to answer this classical non-recognition question by a thought experiment, for which we have to meet three conditions. First of all - quantum physics is valid also in our macroscopic world, which is indeed accepted by many physicists. Secondly, we increase the Planck's constant by approximately 35 orders of magnitude, in order to be able to see clearly the quantum effects, and thirdly we assume that we can isolate a quantum object from all external influences. Then we can draw the picture series as in figure 1.

Figure1: A thought experiment of the quantum interference of footballs. The arrow in the left corner points to the direction of the wall gap the ball passes through. If both gaps are open, the wave associated with the ball passes through both gaps. But is it still legitimate to speak in this situation about a "location" of the ball?

Therein we see a scorer that shoots through a gap in a brick wall on a gate standing behind it. The first quantum physical effect exists therein that the kicker never encounters the same spot in the gate in spite of the quite narrow gap in the wall and in spite of perfect aiming accuracy. This is a result of the Heisenberg's uncertainty principle stating that each attempt to determine the place of an object – for example, by the wall gap in fig. 1 – will necessarily be connected with the uncertainty of the impulse (in this case with the angle of the ball’s flight path). A ball series aimed through the left gap in the wall while the right one is closed (fig. 1b) leads qualitatively to the same result.
The quantum physics leads, however, to spectacular results if one opens both gaps in the wall at the same time. Each "normal "player would expect now that he has simply more possibilities to penetrate the wall and thus also more encounters in the gate. The quantum player (in fig. 1c) is now surprised, however, that he cannot any longer reach certain places at the gate.
Does the position of the right opening in the wall affecting the flight of the ball and its place of encounter in the gate while flying through the left opening? How does the ball becoming influenced by the position of the openings in the wall?
We can explain apparently the observation made by the quantum player if we suppose, that material objects propagate as "de Broglie" waves, and their free flight is affected by the superposition of local conditions they are found in. The meaning of the word "found" is to be treated here with caution, since if one tries to observe particles in flight, no waves can be observed, but only real balls at certain defined places.

How does one observe the quantum nature of matter in experiment?

The proof of the wave nature of matter can be reached by analogy to our thought experiment. In the first example we examine the Fulleren C60, a molecule composed of 60 carbon atoms, arranged as a "nano-soccer". Its de Broglie wavelength is associated with the total mass of the molecule, and is only one thousandth of the molecule's diameter small.

In order to carry out an experiment similarly to the quantum-soccer player, the molecules must be isolated and held far from any disturbing interactions. The Fullerenes are evaporated therefore in high vacuum and sent individually on a diffraction lattice (a "wall" with 50 nm wide gaps). The quantum nature of the molecules should become noticeable in an Interference-like manner far behind the lattice.

Figure 2: Setup to show the diffraction display of Fulleren-molecules (above). The molecules distribution detected behind the diffraction lattice proves the wave nature of the molecules (below).

For the sake of proof, the molecules are first ionized by means of a well- focused laser beam and then counted individually. We found actually the expected molecular density distribution much analogously to the Interference of water waves. Here, however, each single molecule only with itself interfered (figure 2). In the unobserved flight, the particle is to be described obviously best as a wave. At the source and at the detection, the particle is found, however, at definite locations, as appropriate for an orderly particle.
It may be asked now whether this double nature can be demonstrated also for objects larger and more complex than C₆₀. Since such macromolecules have a smaller wavelength, it is desirable to use the Talbot Lau interferometer, as presented in figure 3. We use now three lattices with the same periods and the same distance from each other.

Figure 3: In the Talbot Lau-Interferometer the wave nature of organic dye porphyrin can be shown, here with an Interference contrast of 35%. The three lattices structure is especially advantageous for the near-field interference.

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The Talbot Lau-experiment is accomplished in the "near field", which means that because of the smaller distance between the lattices, the curvature of the molecular wave fronts must be considered also in the mathematical description. The use of the three lattices array has two crucial technical advantages: the good scaling of the particle mass and the increased transmission. While we had to use lattices with a gap distance of only 100 nanometers during the far field diffraction of C₆₀, the grating space in the near field interferometer could be nearly ten times larger (990 nm). Extending this idea further, it can be proven that using 100 nm lattices in a 10 cm short interferometer the wave nature of particles with a mass of up to 800,000 times the mass of a hydrogen atom can be revealed if the molecular beam had a thermal speed (300 K) of approximately 2.5 m/s. This mass corresponds to the one of a small virus, a giant protein or a large nano-crystal. Naturally, with this estimation, neither the phase averaging and decoherence mechanism, nor the enormous technical requirements with regard to sources, lattices, detectors and adjustment devices were considered.
Incidently the Talbot Lau arrangement permits more than a thousandfold higher counting rate, compared with the simple diffraction experiment, which facilitates substantially the anyway difficult proof of the wave nature of large particles. This is due to the fact that each of the nearly 1000 parallel slits of the first lattice may be considered as a small source.
The second lattice ensures, by diffraction and interference, that at a given distance from the lattice image a Talbot picture of the molecular waves is formed. For the proof of the interferograms one could use simply a detector with good spatial resolution. In past experiments a third lattice was moving over the molecular structure, having the same period as the expected interferogram. The molecules are thus blocked or transmitted through depending upon the position of the mask lattice. By measuring the intensity of all remaining molecules as a function of the mask position, one gets an indirect image of the wave sample (see figure 3b).
With such interferometer we could ultimately prove the wave nature of fluoridated Fullerens as well as Tetraphenylporphyrins (TTP). The carbon ball C₆₀F₄₈ provided with a fluorine bowl is more than twice as heavy as C₆₀. Porphyrins are bio-coloring materials, which are found also in chlorophyll and hemoglobin. In particular, TPP is twice more abundant than C₆₀, and appears, in comparison with the spherical Fulleren, rather in the shape of a molecular disk.

Why is our everyday-life world so normal?

Quantum phenomena as well as the interference behavior of matter particles seem to remain basically undetectable, and we have learned to accept it as a fundamental component of nature. Nevertheless, many physicists ask the question why our everyday-life world looks in general so "normal", and which technical or fundamental factors limit the appearance of the quantum nature of macroscopic matter.
It is quite obvious that due to the extreme smallness of the de Broglie wavelength the quantum-mechanical wave nature of a person will always remain unobserved. But on a much smaller scale we find already straightforward fundamental quantum effects.
Since the development of the quantum theory the question whether one can observe the location and the wave nature of an object at the same time and same experiment was debated again and again. It is shown also that even minimal invasive measurement methods, without significant energy or impulse transfer, may impair substantially the interference-capability. Already Bohr has referred to the principle of complementarity, implying that we can never observe perfectly at the same time the particle- and the wave character of an object.
For the sake of clarity the notion of cross-setting is also referred to. It is therefore necessary to describe not only the quantum particle, but also each object, which might be in connection with by a common quantum-mechanical condition. This is symbolized by the arrows in figure 1, which point always to the direction of the gate, to which the ball flies. Thus, the quantum ball remains in superposition of "flight through the left gap" and "flight through the right gap", which forces also the arrow to superposition of "shows to the left" + "shows to the right". In our ordinary world, however, we never see a measuring device functioning in such superposition.
During the last years many studies were carried out examining the conditions under which there is a loss of the quantum characteristics, the "decoherence" mechanism is thus well understood. This is of special interest, in particular in view of its connection with the arising quantum information technologies. For example, the existence of a future quantum computer is strictly bound to the condition of maintaining coherency over many particles and during extended time periods.

Experiments examine the transition between waves and particles

The possibility to demonstrate the wave nature is also closely dependent on the preservation of coherency. In wave physics coherence means that there is a firm phase relationship between different points in the wave. Only if this relationship remains constant, the interference samples remain also stable enough so that they can be noted.
The question rises now, under which circumstances and to which extent the coherency is destroyed, i.e. which decoherence mechanism in the molecular interferometry becomes effective. We have concentrated in our experiments first on those influences of the environment, which are relevant also in our everyday-life world: impacts with gas particles of the environment, and emission of radiant energy by the interfering body (fig. 4).

Figure 4: Decoherence in the molecular interferometer. The emission of radiant heat can destroy the wave characteristics of the interfering Fullerens just like collisions with particles in the environment.

Impacts with particles of the environment gas

In order to examine the influence of molecular impacts on the interference pattern, the pressure, and thus the probability of an impact in the vacuum chamber, was continuously increased. Different gases have thereby quantitatively different effects since the scattering cross-section depends on the specific molecular interaction. Qualitatively, however, a reduction of the interference contrast with increasing gas pressure is assumed (figure 5a).

It can be explained from different points of view: on one hand we can adopt the view that the place of the quantum delocalization in the interferometer (e.g. C₆₀) can be determined precisely according to the impact with a gas particle. Similarly is with the thermal wavelength of nitrogen molecules, which is shorter at ambient temperature than the diameter of the Fullerene. A fictitious nitrogen microscope would have thereby a resolving power of orders of magnitude higher than an optical microscope. Even if no human observer collects available information from the scattered gas particles, then, due to scattering, unambiguous locality information remains in the apparatus. Since according to Bohr's complementarity principle, a quantum cannot have at the same time both a perfect particle- and wave nature, the availability of the locality information of the interference is destroyed.
We can adopt also a point of view, which Heisenberg presented earlier: each attempt to measure the place of a particle is connected with a recoil of this particle. The interference pattern is then smeared also by the fact that the Fullerenes are diverted from their path through the interferometer.
Finally we can introduce a third picture, which unites both aspects: since the interfering molecule is in a coherent superposition of local conditions before the impact, the interaction with a gas particle leads to a cross-setting of the two impact partners. The condition of the scattered gas particle depends on the place of the interaction effect with the delocalized Fulleren. Further impacts of gas particles with other gas molecules, and with the walls of the equipment act effectively like a measurement of the cross-setting conditions of the Fulleren and gas particles. The Fulleren is thus located again by this measurement.

Emission of radiant heat:
"the quantum-mechanical breakdown safety device"

To discover a body, one must scan it from outside, however, not necessarily by test particles. We can use also infrared detectors, which react to the radiant heat of an intruder to the breakdown safety device. In a manner of speaking, we can say that molecules try to fly in our interferometer through many doors at the same time. They can reveal themselves there as intruders by their internal warmth. As the molecules leave the source, they have an internal temperature of approximately 900 K. A small solid body appears already at this temperature red glowing. Molecules, however, even well isolated, are not perfect black emitters, and in case of Fullerene one needs even higher temperatures, in order to be able to observe sufficient light- emitting particles. In the interferometer each molecule is delocalized at the second lattice at least during the lattice period of a micrometer. Photons at wavelength under 1µm, and thus observable with the human eye, are sufficient in principle to determine, through which gap the molecule flies.
In our experiments the Fullerenes (here C₇₀) are heated by intensive laser beams to a high temperature, prior to entering the interferometer. Within the interferometer the molecules deliver then spontaneously thermal photons. In order to halve the interference contrast, on the average 3-4 visible photons are needed (figure 5b). The process of localization and decoherence of the Fullerens by thermal emission is very similar to the one caused by molecular impaction. Depending on the emission place, only several emissions are necessary in order to affect considerably the interference pattern.

Figure 5: The intensification of the interaction with the environment destroys the wave nature. The interference contrast is a measure of the "quality" of the wave. If it disappears, then the molecule is no more different from a classical body.

We have examined two important mechanisms, i.e. gas impaction and radiant heat, which are responsible for the localization of the macromolecules, as well as for objects in our everyday-life world. In both cases quantum mechanics provides quantitatively the explanation for the disappearance of the interference pattern. At the same time it is shown that the decoherence effect can also be suppressed by using sufficiently cold particles and operating in high vacuum. What other effects, which perhaps cannot be shielded easily, we should take into account?
One can think about the radiant heat from the equipment, the influence of cosmic radiation, or about vibrations, practically representing the largest challenge, which are caused particularly by noisy vacuum pumps, building oscillations, impact sounds, etc.. They smear the interference pattern during the recording and thus reduce its contrast. This phase averaging is a purely classical effect, which in the final result hardly differs from decoherence.
In addition, the gravitational pull of the Earth, and Earth's rotation cause a reduction in the interference contrast by a shift of the interferograms. Since this shift depends on the speed of the molecules, their velocity distribution will inevitably lead to the washout of the interference pattern.
Even if one could place the experiment, for the avoidance of such influences, on a satellite, gravitational waves may smear the path difference through the different slits, representing a basic obstacle. Such effects can hardly be shielded, just like the scattering of cosmic neutrinos. Certainly it is not to be expected that in the foreseen future these will become relevant for the matter-wave interferometry.

Molecular quantum waves perspectives

The advance in macroscopic objects interference is not limited at present by fundamental laws of nature, but rather by the technical requirements for efficient molecular beams, new interferometers, high-resolution detectors and the need to avoid the above mentioned phase averaging and decoherence.
All molecules used so far in our interferometer experiments have a wavelength of approximately 2-5 pico-meters, which is about 400 to 1000 time smaller than the diameter of the molecules. There is good progress at present in the laboratory indicating that we will be able to examine soon the wave nature of particles ten times heavier. For even more complex particles further development of new sources and detectors of neutral molecular beams is necessary.
Large molecules enrich the spectrum of the interference experiments with numerous new internal characteristics, e.g. structural anisotropies, chirality, magnetic and electrical dipole moments, all are interesting new parameters with respect to the coupling of the quanta to their environment. It is also of interest to examine, how the interferograms of large molecules develop, having the same atomic content and the same mass, but with different spatial arrangements.
These new molecular features may probably contribute to the decoherence of the matter waves. But it is also evident that one can use Interferometry to measure molecular features. Such 'metrological' applications were already very fruitful in atom-interferometry, suggesting an important new branch of research. Further application of molecular-interferometry opens new perspectives for the production of molecular nano-structures on surfaces. This appears not only technically feasible, but also much promising from the physical, chemical and information-technology aspects.