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Talbot Lau interferometry of carbon-70 fullerenes

====================================

I’ve looked at most of the documents published on these macroscopic

quantum interference experiments of fundamental importance. These

experiments seems to shift the border between the quantum mechanical

and the classical world further and further. The (clickable) references can

be found at the end of this post.

I did a number of simulations and also did some analysis of the

experiment with the help of the path-integral formalism of QED.

It allows us to say considerably more about the experiment than with

Schroedinger’s equation or let alone Heisenberg’s principle of uncertainty.

I hope we can have something like a technical discussion on the

subject here:

======================

Basic Setup of the Experiment:

======================

Three identical gratings exactly lined up behind each other on equal

distances. line spacing: ~1000 nanometer, line width: ~500 nanometer,

grating distance: 22cm in early, and 38 cm in later experiments.

==========

Test Particle:

==========

Carbon-70 fullerene (840 atomic masses (420 protons + 420 neutrons)

mass: 1.406 10-24 kg is equal to ~1.55 million times the mass of an electron.

De Broglie wavelength in the 1.406 10-24 kg, experiment: 2 to 6 picometer.

================

Interference Pattern:

================

The interference pattern is exactly equal as the grating pattern (line spacing

~ 1 micrometer) and measured at the location of the third grating.

(The third grating is used to measure the pattern by shifting it sideways to

let more or less of the pattern pass through to the detector)

==============

Signal Noise ratio:

==============

Amazingly good: Up to 66% and more of the fullerenes take part in the

Interference Process, That is: Each of these molecules passes through 2 or

more splits simultaneously and diffract away from the straight-line path

in order produce the interference pattern. This even though the split spacing

is ~1000 nm.

===============================

Average distance between Test particles:

===============================

The fullerenes are on average 0.3 meter to 1.5 meter apart in the experiment

so it is typically an experiment were one-particle-a-time builds up the pattern.

===================================

Equivalent experiment with visible light photons:

===================================

Visible light wavelengths are circa 100,000 larger then the de Broglie wave-

length tested in the experiment. The equivalent experiment for visible light

would scale up to gratings with a split width of 5 cm and a split spacing

of 10 cm. What is amazing is that most of the photons would not diffract

here (only at the edges of the splits), most of them would pass straight

through resulting in a very low signal/noise ratio for the interference patterns.

This contrasts with the extremely good signal/noise ratio for the non-scaled

experiment.

====================

Particle “shadow” patterns.

====================

The interference pattern is exactly the same as the grating pattern in front of it.

The experiment must thus make sure that we are not looking to a shadow

pattern of particles which behavior is dominantly particle-like rather than

wavelike.

====================================

Exact cancellation of particle “shadow” patterns.

====================================

The experiment setup arguments for this can be found in [8] on page 26

It is argued that the shadow patterns exactly cancel at the location of the

3rd grating because of the beams unique radial density distribution.

The particle beams overlap with their left and right neighbors and the split

width / spacing ratio (50%) in both the 1st and 2nd grating should provide the

exact radial density distribution of the narrow beam and the right fan-out

angle (circa 3 micro radians)

The simulation I did shows that the pattern will reappear again further away

and disappear and reappear repetitively at equal distances. The image of a

simulation I did can be found here:

http://www.chip-architect.com/physics/talbot_lau_01.jpg

==========================================================

Particle speed dependent aberrations as a result of van der Waals interactions

==========================================================

The first experiments use a 22 cm distance between the gratings and show a

large discrepancy with theory. The maximum found in the experiment almost

correspond with the minimum of the theoretical prediction. See the image in

[1] , page 3. It is argued that this discrepancy is caused by van der Waals

interactions with the walls of the gratings. A nice image can be found in [8]

on page 25 which shows the experimenters theoretical model for interference

and their theoretical model which combines interference with a van der Waals

effect.

=========================

Varying the de Broglie wavelength

=========================

A key assumption in the experiments to differentiate between macroscopic

quantum interference and particle beam shadow effects:

By varying the speed of the fullerene molecules one can vary the de Broglie

wave-length of the center of mass of the molecule.

The repetition distance of the interference pattern changes with the varying

de Broglie wave-length. Such a variation is said to be impossible with particle

beam shadow patterns and thus proves macroscopic quantum interference.

===================================

More particle beam shadow pattern simulations

===================================

I presumed that slower beams would be more deflected by the van der Waals

interaction with the walls of the gratings than faster beams. A result for three

different speeds can be seen in this image.

http://www.chip-architect.com/physics/talbot_lau_02.jpg

It shows a pattern very similar to that of what the experimenters expect from

macroscopic quantum interference. (It should be noted that the fan-out

angles in the experiment are in the order of 3 micro radians. the image above

should be stretched by a factor of 10,000 in the x-direction to scale to the

ratio of the experiment)

========================

QED Path Integral considerations

========================

The path integral formalism allows us to determine the probabilities for the

paths taken by the fullerenes. The probability is given as the square of the

amplitude. The total amplitude is the sum of the amplitudes of all possible

paths. The amplitude of a single path is the product of the amplitudes of

all the sub-paths. This product rule is important: If a part of a path has a

very low amplitude then it follows that the entire path has a very low

amplitude.

The product rule excludes paths for instance that include a turn somewhere

in “mid-vacuum” Only paths that pass very close to a border (within a

wavelength) do diffract. paths further away from borders are straight lines.

========================================================

The split width of the experiment compared with the de Broglie wave-length

========================================================

When we scaled the experiment to visible wave-lengths we saw that the

gratings sized up to a split period of 10 cm with a split width of 5 cm.

Very large compared to the wavelength. Nevertheless. The experimenters

presume that the fullerenes do diffract even if they are passing at a distance

from the wall tens of thousands times larger then the de Broglie wave-length.

The high ratio of the fullerenes (>50%) that passes through two or more splits

simultaneously and diffracts in order to get the very high signal to noise

ratio requires such a diffraction which seems to be at odds with the path-

integral formalism. A schematic drawing of the diffraction can be found

in [8] at page 18.

Regards, Hans

[1] Matter-wave interferometer for large molecules

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0202158 [Broken]

[2] Collisional decoherence observed in matter wave interferometry

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0303093 [Broken]

[3] Collisional decoherence reexamined

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0303094 [Broken]

[4] Decoherence in a Talbot Lau interferometer: the influence of molecular scattering

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0307238 [Broken]

[5] The wave nature of biomolecules and fluorofullerenes

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0309016 [Broken]

[6] Decoherence of matter waves by thermal emission of radiation

http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0402146 [Broken]

[7] Exploring the classical limits of quantum interferometry with clusters and molecules

http://latsis2004.epfl.ch/Jahia/eng...U.pdf?actionreq=actionFileDownload&fid=118993

[8] Matter wave interferometry with large molecules

http://www-lab15.kuee.kyoto-u.ac.jp/~lc/proceedings/2-3.pdf [Broken]

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