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ZENO EFFECT, RIDGED MIRRORS and ATOMIC NANOSCOPY
Dmitrii Kouznetsov, Inst. for Laser Science, UEC
Collaboration: Hilmar Oberst, Fujio Shimizu, Kazuko Shimizu,
Makoto Morinaga, Junichi Fujita, J-F. Bisson, Kenichi Ueda (Japan);
and
Alexander Neumann, Yulya Kuznetsova, Steve Brueck (UNM, USA)
Quantum reflection is interpreted as Zeno Effect
Ridged atomic mirror is considered as focusing element for
the sub-micron resolution atom optics (atomic nanoscope).
The reflectivity is approximated with elementary functions.
Such fit agrees with experimental data and
allows optimization of ridged mirrors.
Ridged mirrors in the atomic imaging system: ~ 20 nm ?
and
A.Neumann, Yu.Kuznetsova, S.R.J.Brueck (UNM, USA)
Fujio Shimizu
清水
富士夫
collaboration with
Kazuko Shimizu
清水和子, Hilmar Oberst
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Makoto
Morinaga
J. Fujita
藤田
淳一
K. Ueda
JF Bisson
植田憲一
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Center for High Technology Materials,
UNM, USA
A. Neumann Yu.Kuznetsova
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Steve Brueck
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Qu i c k Ti m e ™ a n d a
TIF F (L Z W) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c tu
ATOMIC BOMB
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ATOMIC SKI
ATOMIC
STAFF
ATOMIC PLANT
ATOMIC CLOCK
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ATOMIC FORCE
atomic mirror
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More atomic staff
P.Bertram, H.Merimeche, M.M\"utzel, H.Metcalf, D.Haubrich,
D.Meschede, P.Rosenbusch, E.A.Hinds. Magnetic whisperinggallery mirror for atoms. PRA 63, 053405 (2001)
Ashok Mohapatra. The same for
the normal incidence.
(reported here yesterday, 2007)
atomic Fresnel zone plate
Bruce Doak et al. Towards realization of an atomic de
Broglie microscope: helium atom focusing using Fresnel
zone plates. PRL 83, p.4230-4232 (1999)
atomic lens
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
V. Balykin, V. Klimov, V. Letokhov.
Atom nano-optics.
Opt. and Phot. News 16, 44 (2005)
What is QUANTUM REFLECTION?
Wikipedia:
Quantum reflection is a classically counterintuitive phenomenon
whereby the motion of particles is reverted "against the force“
acting on them.
How about reflection of solitons?
Andy Martin.
Quantum reflection of solitons and bright solitary waves.
Ilya Dodin (Classical analogies of atom manipulation
Techniques using laser radiation)
also doubts if that he does is Quantum reflection.
Perhaps, any counter-intuitive reflection should be called so.
Should we call “quantum reflection”
any scattering of any wave at any structure?
Reflection of oceanic waves from a periodic groin
field, is it also quantum reflection?
The Zeno effect is
Class of phenomena when a transition is suppressed by interaction
which allows the interpretation of the final state in terms
transition has not yet occurred
or
transition already occurred.
In quantum mechanics, such an interaction is called measurement;
its result can be interpreted in terms of classical mechanics.
Frequent measurement prohibits the transition.
We apply the concept of the Zeno effect
to the transition of the atom from the
half-space y>0 to the half-space y<0 .
Ridges appear as a device that measures, whether the atom already
collided with the mirror or not yet. y - position is periodically measured.
rate of measurement
frequent measurement prohibits the transition.
Most of our results are published.
D.Kouznetsov, H.Oberst. Reflection of waves from a ridged surface and the
Zeno effect. Opt.Rev. 12, p.363-366. (2005)
http://www.ils.uec.ac.jp/dima/PAPERS/optrevri.pdf
D.Kouznetsov, H.Oberst. Scattering of atomic matter waves from ridged
surfaces. PRA 72, 013617 (2005)
http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevA_72_013617.pdf
H.Oberst, D.Kouznetsov, K.Shimizu, J.Fujita, F.Shimizu.
Fresnel diffraction mirror for an atomic wave. PRL 94, 013203 (2005).
http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevLett_94_013203.pdf
D.Kouznetsov, H.Oberst, A.Neumann, Y.Kuznetsova, K.Shimizu, J.-F.Bisson,
K.Ueda, S.R.J.Brueck. Ridged atomic mirrors and atomic nanoscope.
J.of Physics B 39, p.1605-1623 (2006)
http://stacks.iop.org/0953-4075/39/1605
http://www.ils.uec.ac.jp/~dima/PAPERS/nanoscope.pdf
quotes:
R.Poelsema. G. Comsa. Scattering of thermal energy atoms from disordered surfaces. (Springer-Verlag, 1989)
The method based on the thermal energy atom scattering (TEAS), that we are
reviewing here, appears to complement in an ideal way scanning tunnel
microscopy in the investigation of disordered surfaces.
B.Holst, W.Allison. An atom-focusing mirror. Nature, v.390, p.244 (1997).
(He atoms, wavelength 0.52 A, spot diameter 210 micron):
It follows that a helium microscope with nanometer resolution is possible.
A helium atom microscope will be unique non-destructive tool for
reflection of transmission microscopy.
What is optimal design for the focusing element?
F.Shimizu, J.Fujita. Giant Quantum Reflection of Neon Atoms from a Ridged Silicon Surface. J.Phys.Soc. of
Japan 71, p.5-8 (2002):
The specular reflectivity of slow, metastable neon atoms from a silicon surface was
found to increase markedly when the surface was replaced by a grating structure with
parallel narrow ridges. The reflectivity was found to increase more than two orders of
magnitude at the incident (grazing) angle 10 mrad.
Further improvement of the reflectivity at a larger angle will be possible if the width of
the ridge and the periodicity are reduced.
What is optimal periodicity at given width?
How far can be extended the working range of the grazing angle?
What resolution of the atom optics imaging system does it correspond?
flat mirror
potential
4
U( y ) = C / y
4
Depth:
From the dimensional reasons, the reflectivity of a flat atomic mirror
should be determined by
Fit:
k=Ks
H.Oberst, Y.Tashiro,
K.Shimizu, F.Shimizu.
Quantum reflection of He*
on silicon.
PRA, 71, 052901 (2005)
F.Shimizu. Specular
reflection of very slow
metastable neon atoms
from a solid surface,
PRL 86, 987-990 (2001).
Interaction is described with
Hermitian potential
R
H
F.Shimizu, J.Fujita. Giant quantum reflection
of Ne atoms from a ridged silicon surface
J.Phys.Soc. of Japan, 71, p.5-8 (2002)
H.Oberst, D.Kouznetsov, K.Shimizu, J.Fujita,
F.Shimizu. Fresnel diffraction mirror for an
atomic wave. PRL 94, 013203 (2005)
estimate the reflectivity
of a ridged mirror?
Estimate of reflectivity of ridged mirrors with scaling of the van der Waals constant:
lg(R)
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Ne* atoms, V=3m/s
F.Shimizu, J.Fujita. Giant Quantum
Reflection of Neon Atoms from a
Ridged Silicon Surface J.Phys.Soc.
of Japan 71, p.5-8 (2002):
B. Mielnik. The
screen problem. Foundatons of Phys., 24, p.1113-1129 (1994):
“…interpretation of the quantum mechanical wave packet contains a gap.”
Can we reflect an object by the intensive observation in a half-space?
detectors
normal component of velocity
frequency of measurement
k=K
normal component of wavevector
ridged mirror
C
Continuous absorption with rate f = V／L also causes reflection
P
R
photons
0.1
0.01
Reflectivity can be estimated as
This estimate ignores
width of the ridges and
the van der Waals interaction, but
agrees with experimental data.
Hilmar: Incredible coincidence!
Some colleagues were not satisfied with the deduction.
The numerical analysis for the idealized ridges
can be summarized with fit
Such fit overestimates the reflectivity.
(PRA,2005)
perturbative correction
suggests to reduce L
to improve the reflection…
UNM sample
properties of
R
at large L , small s ,
Fits
Scaling of VWI:
Zeno
-
optical fit (large L )
Perturbative
Combined
holds in wide range of parameters
a=1/4 , b=3 , c=4
Projection of reflectivity
to the p, q plane
4
0
1
2
3
4
5
6
7
3
2
0 < ーLn R < 1
1 < ーLn R < 2
2 < ーLn R < 3
3 < ーLn R < 4
4 < ーLn R < 5
5 < ーLn R < 6
6 < ーLn R < 7
7 < ーLn R < 8
1
all experimental data collected
1
2
q
q
ーLn
R,
experiment
ーLn
R , fit
3
2
1
1
2
p
1
2
p
o
n
Contour of
in the
K = 6.3/nm , s = 0.005 , w = 317 nm
L
,
plane
(He atoms at V=100m/s
dashed:
o
u
0.01
0.1
0.2
0.3
0.4
in vicinity of optimal
R
L,
There is optimal period at given width of ridges
w = 317 nm ,
V = 100 m/s , s = 0.005 , K=6.3/nm
(He, T=1K)
R5
=
L, micron
V=100 m/s
nanoscope
gives 4.8 Kelvin
concentration
Pinhole a=100nm, b=1000nm
flux
small portion reached the focusing element:
atoms/second
geom.optics, spotsize:
wave optics:
resulting spotsize:
Focusing
element
COMPETITORS
of Atomic Nanoscope
optical microscopy (also scanning confocal, and near-field )
electron microscopy (including SEM)
probe microscopy:
atomic force microscopy
electrostatic force microscope
magnetic force microscopy
scanning capacitance microscopy (Kelvin probe)
scanning gate microscopy (also tunneling microscopy)
scanning thermal microscopy
scanning voltage microscopy (maping of the electric potential)
also provide the submicron resolution
CONCLUSIUONS
R
p
1
.1
Rz
.01
q
Estimate for reflectivity:
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-ln R
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1
optimal L at given
:
1nm
R=0.1
0
0.3
1/2
R ~ exp( - 2 w K
3/4
1/4
)
1nm
L
Nanoscope:
For He at V=100m/s (T = 1 K), s = 0.005,
= 10 nm, R 0.1
limit of resolution of the atom optical imaging system at 20 nm
0
1
p
optics.
p Atom
B. Poelsema, G. Comsa. Scattering of thermal energy atoms from disordered surfaces.
1989)
o J. J. Berkhout et al. Quantum reflection: Focusing of hydrogen atoms with(Springer-Verlag,
a concave mirror.
PRL 63, 1689-1692 (1989)
M. Kasevich, D. Weiss, S. Chu. Normal-incidence reflection of slow atoms from an optical
evanescent wave. Opt.Lett. 15, 607-9 (1990)
E. Hulpke. Helium atom scattering from surfaces. (Springer-Verlag, 1992)
D. C. Lau et al. Magnetic mirrors with micron-scale periodicities for slowly moving neutral
atoms. J. of Optics B, 371-377 (1999)
R. B. Doak et al. Towards Realization of an Atomic deBroglie Microscope: Helium Atom
Focusing using Fresnel Zone Plates. PRL 83 , 4229-4232 (1999)
D.A.MacLaren, W.Allison. Single crystal optic elements for helium atom microscopy.
Rev. of Sci. Instr. 71, p.2625-2634 (2000)
M. Drndic et al. Properties of microelectromagnet mirrors as reflectors of cold Rb atoms.
PRA 60, 4012 (1999)
C. Eltschka, M. J. Moritz, H. Friedrich, Near-threshold quantization and scattering for
deep potentials with attractive wells, J. of Physics B 33, 4033-4051 (2000)
R. P. Bertram et al.. Magnetic whispering-gallery mirror for atoms. PRA 63, 053405 (2001)
A. Pasquini, Y. Shin, C. Sanner, M. Saba, A. Schirotzek, D. E. Pritchard, W. Ketterle.
Quantum Reflection from a Solid Surface at Normal Incidence. PRL 93, 223201 (2004)
V, Balykin, V. Klimov,V. Letokhov. Atom nano-optics. Opt. and Phot. News 16, 44 (2005)
N.P.Robins, A.K.Morrison, J.J.Hope, J.D.Close. Limits to the flux of a continuous atom laser.
PRA 72 031606 (2005)
several papers are written by my co-authors:
H F.Shimizu. Specular reflection of very slow metastable neon atoms from a solid surface,
PRL 86, 987-990 (2001).
F.Shimizu, J.Fujita. Reflection-type hologram for atoms. PRL 88, 123201 (2002)
F. Shimizu, J.Fujita Giant quantum reflection of neon atoms from a ridged silicon
surface. J. Phys. Soc. Jpn. 71, 5-8 (2003)
H.Oberst, S.Kasashima, V.I.Balykin, F.Shimizu. Atomic-matter-wave scanner.
PRA 68, 013606 (2003)
H.Oberst, Y.Tashiro, K.Shimizu, F.Shimizu. Quantum reflection of He* on silicon.
PRA, 71, 052901 (2005)
S.C.Lee, S.R.J.Brueck. Nanoscale two-positional patterning on Si(001) by large-area
interferometric lithography and anisotropic wet etching. J.Vac.Technol.B 22, 1949-52
(2004)
H.Oberst, M.Moringa, F.Shimizu, K.Shimizu. One-dimansional focusing of an atomic
beam by a flat reflector. Applied Physic B, 86, 801-803 (2003)

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