Heavy%20Atom%20Quantum%20Diffraction%20by%20Scattering%20from%20Surfaces

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Heavy Atom Quantum Diffraction by Scattering from
Surfaces

• Eli Pollak
• Chemical Physics Department
• Weizmann Institute of Science
• Coworkers
• Dr. Jeremy M. Moix
• Grants
• Israel Science Foundation Weizmann-UK Joint
  Research Program

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http//www.ams.org/featurecolumn/archive/rainbows.
html

Bill CasselmanUniversity of British Columbia,
Vancouver, Canadacass at math.ubc.ca
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qf
 
b
4r
R
nsin(qr) sin(qi)b/Rx, n4/3 qf(x)
4qr-2qi 4sin-1(x/n)-2sin-1(x) dqf/dx0 gt
xv(20/27), qf42o
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The rainbow angular distribution
Water n4/3
Perspex n3/2
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Rainbow scattering from a hard wall
h(x)
qf (x)qi2fqi-2h(x)
qi
p/2-f-qi
qf
f
p/2-f
p/2-f-qi
l
f-tan-1h(x)-h(x)
x
The rainbow angles are found when
they arise from the deflection points of the
corrugation function.
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The angular distribution for scattering from a
hard wall
If the corrugation is sinusoidal
then the angular distribution is readily seen to
be
l30 mm h0.42 mm qRqi10o
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Experimental observations
I. In plane scattering of Ar atoms on a LiF(001)
surface
Note At 100 meV the de Broglie wavelength of Ar
is 0.25 a.u.. The lattice length is 8 a.u.. It
is then not surprising that the measured
distribution is classical.
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II. In plane scattering of Ar and Kr on a Ag(100)
surface
Ar
Kr
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III. In plane scattering of Ar on a 2H-W(100)
surface
At 100 meV the de Broglie wavelength is 0.25
a.u.. Why then does one see diffraction at Ei27
meV? (The lattice length is 10 a.u..) Beam
energy uncertainty of 1/30 implies a parallel
coherence wavelength of 7.5 a.u., enough to see
the diffraction peak.
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Krypton mass - 84, at 35 meV, dBwl0.3
a.u.. Beam energy uncertainty of 1/35 implies a
parallel coherence wavelength of 10 a.u.,
enough to see the diffraction peak.
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Heavy molecule interference experiments
Two slit diffraction experiment - Waves at the
two slits must be coherent
Fullerene speed of 100 m/s ? 5.6 pico m de
Broglie wavelength
Note the r2 dependent loss of signal due to the
long path between the collimating slits.
Collimating the beam with 7 mm slits separated by
1 m implies that transverse speed is less than
1.410-3 m/sec ? 400 nm de Broglie wavelength or
an angular width of 8 10-4 degrees.
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High energy grazing collisions
Diffraction of Fast Atomic Projectiles during
Grazing Scattering from a LiF(001) Surface
PRL 98, 016103 (2007)
A. Schueller, S. Wethekam, and H.
Winter Institut fuer Physik, Humboldt
Universitat zu Berlin, Brook-Taylor-Strasse 6,
D-12489 Berlin-Adlershof, Germany
Light atoms and molecules with energies from 300
eV to 25 keV are scattered under a grazing angle
of incidence from a LiF(001) surface.
Experimental results for scattering of H, D,
3He, and 4He atoms as well as H2 and D2 molecules
can be unequivocally referred to atom diffraction
with de Broglie wavelengths as low as about 0.001
A
Analysis At 10 keV the de Broglie wavelength of
4He is 0.0027 a.u. a 1o grazing angle implies
p-p/60 so a perpendicular wavelength of 0.16
a.u.. The angular resolution is 0.01o so that
the coherence wavelength is 16 a.u., enough to
observe diffraction.
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Theory A typical diffraction pattern
A square surface
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A hexagonal surface
At low energy quantum mechanics prevails
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Consider again the Ar-LiF scattering experiment
Classical and quantum scattering on frozen
(model) surface.
Ar energy of 705 meV ? 5.5 pm de Broglie
wavelength while LiF lattice length 400 pm.
The angular width of the beam is 2 degrees so
the perpendicular coherence wavelength is 180
pm.
Classical Wigner
Exact quantum
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Reducing the uncertainty in the transverse
momentum so that the angular width of the
incident beam is 0.2o leads to the quantum
mechanical diffraction pattern
The typical lattice length is 1 nm, a factor of
100 smaller than the size of the grating used in
the two slit experiment, implying a reduction of
the collimation length by 102 and thus a gain of
104 in the signal to noise ratio.
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The final momentum distribution with an angular
incident width of 0.2o
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Decoherence via increase of surface temperature
Phonons modeled as single oscillator coupled to
the vertical motion
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Preliminary experimental results scattering of
Ar on Ru(0001) M. Minniti and D. Farias, Madrid.
Energy 64 meV, de Broglie wavelength 18
pm. Lattice length 300 pm Coherence length
180 pm (2 mm aperture) 400 pm
(.75 mm aperture) 720 pm (0.4 mm
aperture)
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• Summary
• Quantum diffraction of heavy atoms is
  observable in surface
• scattering at low temperatures.
• Collimation of the incident beam leads to partial
  diffraction
• patterns.
• At sufficiently low surface temperature, surface
  phonons do
• not wipe out the coherence
• Decoherence may be studied quantitatively by
  varying the
• surface temperature

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Future directions

• Use better theory (MCTDH) to include a realistic
• representation for the continuum of phonon
  modes.
• Study diffraction of molecular systems do
  internal
• modes destroy the quantum diffraction through
• energy exchange?
• Can heavy atom diffraction be used to study
  surface
• interactions phonons or electronic?
• Is it possible to use the quantum coherence to
• manipulate energy transfer with the surface?
• Can one conehrently control reactive processes on
  the
• surface?

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Energy loss rainbows J. Moix, E. Pollak and S.
Miret-Artès, Phys. Rev. Lett. 104, 116103 (2010).
From the perturbation theory we found the
Gaussian energy transfer kernel and the energy
distribution of the scattered particle
Consider then the energy loss as a function of
impact parameter for Ar-LiF scattering
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Joint energy and angular distribution for a 15O
angle of incidence, 3eV incidence energy and
surface temperature T30K.
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Have they been seen experimentally?
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Rotational Rainbows
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C20.01, C10
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For simplicity consider a diatomic molecule with
angular momentum parallel to the surface. Let qi
denote the initial angle of the diatomic axis
relative to the vertical to the surface
q
For a smooth surface, the interaction potential
will be a function of the angle q. The final
angular momentum will then depend on the initial
rotational angle.
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Perturbation theory
The Hamiltonian
The unperturbed motion
1st order perturbation theory
Energy conservation
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The angular distribution
When the molecule is not too slowly rotating one
readily finds
? The rotational rainbows cause maxima in the
angular distribution!
Examples
? Morse potential
(C10 for a homonuclear diatomic)