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Talbot Lau interferometry of carbon-70 fullerenes

  1. Sep 7, 2004 #1

    Hans de Vries

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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

    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

    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:

    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

    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.

    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

    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

    [2] Collisional decoherence observed in matter wave interferometry

    [3] Collisional decoherence reexamined

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

    [5] The wave nature of biomolecules and fluorofullerenes

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

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

    [8] Matter wave interferometry with large molecules
    Last edited: Sep 7, 2004
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