diffraction of a C_60 beam

[glueck772000@yahoo.de]

Hello

In Nature Vol 401 from 14 OCTOBER 1999
Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller,
Gerbrand van der Zouw and Anton Zeilinger
describe the diffraction of a C_60 beam with
de Broglie wavelength of 2.5 pm=0.0025nm.
See :
http://www.atomwave.org/rmparticle/
ao%20refs/aifm%20refs%20sorted%20by%20topic/
early%20diffraction%20refs/ANV99%20C60%20duality.pdf

The diffraction is done with a free-standing nanofabricated Si-Nx-
grating
consisting of nominally 50-nm-wide slits with a 100-nm period.
My question now is :
how can it be to see an interference with
wavelength = 0.0025nm << slit- width = 50nm ?

The size of C_60 is about 0.7nm >> wavelength.
The coherence length of about 5 pm=0.005nm.
If the molecular-beam is almost tangent to the grating,
then I can imagine to see the interference . But
in figure 1 of the paper the grating seems to be perpendicular
to the beam.
According to the paper the theory for the grating is
standard Kirchhoff diffraction theory.
Are there some internet-links to this theory ?

[Jonathan Thornburg [remove -animal to reply]]

glueck772000@yahoo.de wrote:
> In Nature Vol 401 from 14 OCTOBER 1999
> Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller,
> Gerbrand van der Zouw and Anton Zeilinger
> describe the diffraction of a C_60 beam with
> de Broglie wavelength of 2.5 pm=0.0025nm.
> See :
> http://www.atomwave.org/rmparticle/
> ao%20refs/aifm%20refs%20sorted%20by%20topic/
> early%20diffraction%20refs/ANV99%20C60%20duality.pdf

Professon Zeilinger's web site is also interesting,
http://www.quantum.at/research.html
particularly the links "Molecule Interferometry Foundations" and
"Molecule Interferometry Applications". There's also
http://www.univie.ac.at/qfp/research/matterwave/c60/index.html
which discusses both the C_60 experiments and some of this group's
more recent work with even larger molecules.

> The diffraction is done with a free-standing nanofabricated Si-Nx-
> grating
> consisting of nominally 50-nm-wide slits with a 100-nm period.
> My question now is :
> how can it be to see an interference with
> wavelength = 0.0025nm << slit- width = 50nm ?

There's nothing in the theory of diffraction which has a problem with
the wavelength being much less than the slit width. This does mean that
the diffraction angles are very small,
[To a very rough approximation, the typical diffraction
angle (in radians) is on the order of the ratio of the
wavelength to the slit width. That's about 5e-5 in this
case, i.e. about 50 microradians = about 10 arcseconds.]
but that "just" means that diffraction is (experimentally) hard to
measure, not that it doesn't happen. In this case the experimenters
were (are) very talented, and were able to make measurements which
clearly show the diffraction pattern.

> The size of C_60 is about 0.7nm >> wavelength.
> The coherence length of about 5 pm=0.005nm.
> If the molecular-beam is almost tangent to the grating,
> then I can imagine to see the interference . But
> in figure 1 of the paper the grating seems to be perpendicular
> to the beam.

The grating is indeed perpendicular to the beam.

> According to the paper the theory for the grating is
> standard Kirchhoff diffraction theory.
> Are there some internet-links to this theory ?

It's usually called Fraunhofer diffraction; this corresponds to the
far-field limit where the diffraction pattern is observed at a distance
much larger than the slit width or the width of the diffraction pattern.
Wikipedia is a good place to start,
http://en.wikipedia.org/wiki/Diffraction
http://en.wikipedia.org/wiki/Diffraction_formalism

--
-- From: "Jonathan Thornburg [remove -animal to reply]" <jthorn@astro.indiana-zebra.edu>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

[Jonathan Thornburg [remove -animal to reply]]

glueck772000@yahoo.de wrote:
> In Nature Vol 401 from 14 OCTOBER 1999
> Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller,
> Gerbrand van der Zouw and Anton Zeilinger
> describe the diffraction of a C_60 beam with
> de Broglie wavelength of 2.5 pm=0.0025nm.
> See :
> http://www.atomwave.org/rmparticle/
> ao%20refs/aifm%20refs%20sorted%20by%20topic/
> early%20diffraction%20refs/ANV99%20C60%20duality.pdf

Professon Zeilinger's web site is also interesting,
http://www.quantum.at/research.html
particularly the links "Molecule Interferometry Foundations" and
"Molecule Interferometry Applications". There's also
http://www.univie.ac.at/qfp/research/matterwave/c60/index.html
which discusses both the C_60 experiments and some of this group's
more recent work with even larger molecules.

> The diffraction is done with a free-standing nanofabricated Si-Nx-
> grating
> consisting of nominally 50-nm-wide slits with a 100-nm period.
> My question now is :
> how can it be to see an interference with
> wavelength = 0.0025nm << slit- width = 50nm ?

There's nothing in the theory of diffraction which has a problem with
the wavelength being much less than the slit width. This does mean that
the diffraction angles are very small,
[To a very rough approximation, the typical diffraction
angle (in radians) is on the order of the ratio of the
wavelength to the slit width. That's about 5e-5 in this
case, i.e. about 50 microradians = about 10 arcseconds.]
but that "just" means that diffraction is (experimentally) hard to
measure, not that it doesn't happen. In this case the experimenters
were (are) very talented, and were able to make measurements which
clearly show the diffraction pattern.

> The size of C_60 is about 0.7nm >> wavelength.
> The coherence length of about 5 pm=0.005nm.
> If the molecular-beam is almost tangent to the grating,
> then I can imagine to see the interference . But
> in figure 1 of the paper the grating seems to be perpendicular
> to the beam.

The grating is indeed perpendicular to the beam.

> According to the paper the theory for the grating is
> standard Kirchhoff diffraction theory.
> Are there some internet-links to this theory ?

It's usually called Fraunhofer diffraction; this corresponds to the
far-field limit where the diffraction pattern is observed at a distance
much larger than the slit width or the width of the diffraction pattern.
Wikipedia is a good place to start,
http://en.wikipedia.org/wiki/Diffraction
http://en.wikipedia.org/wiki/Diffraction_formalism

--
-- From: "Jonathan Thornburg [remove -animal to reply]" <jthorn@astro.indiana-zebra.edu>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam