Prsentation PowerPoint

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Down-scaling of atom optics into the nanometer
range
Martial Ducloy
Collaborations M. Boustimi, V. Bocvarski
Laboratoire de Physique des Lasers Université
Paris Nord and CNRS Villetaneuse, France
Rusnanotech Forum09 Moscow October 6-8, 2009
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Particle-Wave duality
- De Broglie wave associated to massive particles
(1924) frequency w, wavevector k Ehw/2p
phk/2p DB wavelength l h/p h/Mv -
Schrodinger (1926) wave equation, wave
mechanics - Davisson-Germer (1927) experiments
on electron interference - Development of
electron interferometry, and then neutron
interferometry Since the 1970s, development of
the wave optics of composite particles (atoms,
molecules)
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Particle-Wave duality
- De Broglie wave associated to massive particles
(1924) frequency w, wavevector k Ehw/2p
phk/2p DB wavelength l h/p h/Mv -
Schrodinger (1926) wave equation, wave
mechanics - Davisson-Germer (1927) experiments
on electron interference - Development of
electron interferometry, and then neutron
interferometry Since the 1970s, development of
the wave optics of composite particles (atoms,
molecules) Optics and interferometry with
matter waves
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• Many light optics functions already realised in
  the field of atom optics
• atom diffraction,
• atom mirrors
• atom beam splitters
• atom laser
• quantum reflection
• atom holography, quantum statistics, etc.

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• Many light optics functions already realised in
  the field of atom optics
• atom diffraction,
• atom mirrors
• atom beam splitters
• atom laser
• quantum reflection
• atom holography, quantum statistics, etc.
• What are the specific characteristics of atom
  optical processes?
• atom internal structure, polarisability, vacuum
  intrinsic dispersion

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• Many light optics functions already realised in
  the field of atom optics
• atom diffraction,
• atom mirrors
• atom beam splitters
• atom laser
• quantum reflection
• atom holography, quantum statistics, etc.
• What are the specific characteristics of atom
  optical processes?
• atom internal structure, polarisability, vacuum
  intrinsic dispersion
• Can we perform all the photon optics operations
  in atom optics?
• atom nano-optics?

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COHERENT NANO-OPTICS WITH SLOW METASTABLE ATOMS

• Three novel projects

• Atomic Fresnel biprism interferometer
• Non diffracting coherent nano-beams
• Atom meta-optics (NIM for matter wave)

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Atomic Fresnel biprism

• Basic principle van der Waals-Zeeman transitions

Two quantisation axes (Scalar) quadrupolar
interaction (n) magnetic interaction (B)
m lt m0
m0
Transitions among Zeeman sublevels m0 ? m
For m lt m0, repulsive deflection by an angle g ?
(DE / E0) 1/2 , where DE gµB B Dm, E0
incident energy
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Experiment
Ne 3P2 supersonic beam
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OBSERVATION
Metastable Ne(3P2) atoms traverse a micrometric
copper grating submitted to a static magnetic
field B. Exo-energetic transitions (Dm -1, -2,
-3, -4) are identified by the deflection angles g
This is a multiple tunable beam splitter
B 289 Gauss In blue incident beam profile (dq
0.35 mrad) Peaks are widened by diffraction
(dotted line)
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Fraunhofer diffraction from one inelastic
(vdW-Z) complex transition amplitude A(r)
Re(A)
Fourier Transform
g
B(q)
r (nm)
Range a ? 2.2 nm
Angular aperture dq ? l / a
slit surface
Angular shift by g W / k W l / (2p)
Mean spatial frequency W
W (2 M g µB B Dm)1/2 / , independent of
velocity
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Fraunhofer diffraction from one inelastic
(vdW-Z) complex transition amplitude A(r)
Re(A)
Fourier Transform
g
B(q)
r (nm)
Range a ? 2.2 nm
Angular aperture dq ? l / a
slit surface
Angular shift by g W / k W l / (2p)
Mean spatial frequency W
W (2 M g µB B Dm)1/2 / , independent of
velocity
vW-Z experiments yield transition amplitude
averaged over impact parameter. How to get
spatially resolved amplitude? Atom
Interferometry
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Two opposite surfaces two coherent amplitudes
A(r) becomes A(-x w/2) A(x w/2) B(q)
becomes eikw/2 B(q) e-ikw/2 B(-q)
Resulting intensity (where f Arg B)
I(q) B(q)2 B(-q)2 2 B(q)B(-q)cos
kwq f(q) f(-q)
w gtgt a fast oscillation
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Two opposite surfaces two coherent amplitudes
A(r) becomes A(-x w/2) A(x w/2) B(q)
becomes eikw/2 B(q) e-ikw/2 B(-q)
Resulting intensity (where f Arg B)
I(q) B(q)2 B(-q)2 2 B(q)B(-q)cos
kwq f(q) f(-q)
w gtgt a fast oscillation
Principle of Fresnel atomic bi-prism in progress
on laser-cooled Ar atom beam Grucker et al,
Eur. Phys. J. D 47, 427 (2008)
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2. Non-diffracting coherent nano-beams
The basic idea is to use a Stern-Gerlach
interferometer as a spatial filter for the
metastable atom beam
But what is a Stern-Gerlach interferometer ?
S-G
S-G
Phase object
a0
b
b
B-profile
He m0 0
Final amplitude a0 cc ss cos f where c
cos b, c cos b s sin b, s sin
b
Majorana zones B is small and rotates quickly,
the spin remains at rest ? linear combination
of m-s
Adiabatic evolution m accumulates the phase mf
with f
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A magnetic quadrupole is an atomic axicon
Constant radial gradient G, equivalent to a
matter wave index linear in the distance r to z
axis In an interferometer, the phase shift is
proportional to r ? annular fringes Example
with Ar atoms (v 1650 m/s), G 1.66 mGauss/cm
(experiment / calculation)
B. Viaris et al, EPJD 23, 25 (2003)
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A phase object aimed at producing an ultra narrow
profile
Two opposite quadrupoles Q1, Q2 a longitudinal
field b
d
x
sudden (diabatic) passage
Total phase shift
W 2g µBG d/( v)
b is
fixed to get f(0) p The stronger the gradient
G, the narrower the peak width 3b/(2G)
Perales et al, Europhys. Lett.78, 60003 (2007)
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Results for the transmitted wave amplitude
(using Huygens Kirchhof integral to calculate
wave propagation and transmitted profile)
(q 0.4157) ? 2gµBG d /( v)
a(r) ? G(r) 1 (q W r)2)-1/2
G(r) incident Gaussian amplitude

• The interferometer does not alter the amplitude
  at center
• This  quasi square root of a Lorentzian  form
  (much narrower than G) is indeed very simple.
  Moreover it will provide us with a very
  interesting property of the atom wave propagation.

Perales et al, Europhys. Lett.78, 60003 (2007)
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Beam width propagation for various diaphragms
(log-scale)
R intensity ratio
Perales et al, Europhys. Lett.78, 60003 (2007)
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Beam width propagation for various diaphragms
(log-scale)
R intensity ratio
This makes this beam the atom-nano-optics
counterpart of  Bessel beams , well known in
light optics (Durnin et al JOSA A 1987, PRL 1987)
Perales et al, Europhys. Lett.78, 60003 (2007)
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Experimental details
Source
He
Campargue nozzle beam
Exchanged He beam
DC discharge He
dv/v ? , dq 0.4 mrad J.-C. Karam et al, J.
Phys. B. (2005)
Phase object
triple µ-metal shielding
- i
Position sensitive detector
Observation of the profile
Electron microscope x 100
e
He
Secondary emission plate
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• - Atomic Fresnel bi-prism interferometer
• - Ultra narrow non-diffracting atom beam
• Negative-index meta-medium for atom optics

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 Meta-materials  in light optics
J.B. Pendry, PRL 85, 3966 (2000) H. Lamb, Proc.
London Math. Soc. 1, 473-479 (1904)V.G.
Veselago, Sov. Phys. Usp., 10, 509 (1968), etc
Principle if e real negative and m real
negative, the optical index is (NIM-
or left-handed material)
In permanent regime, the energy flux is directed
outward the source In a LH medium, phase
velocity vj is reversed
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Snell-Descartes Law
( Poynting vectors )
Negative refraction
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A  meta-medium  for matter waves is necessarily
different from a meta-material for light waves
R
k
Light source
Pulsed atom source
The group velocity vg is transiently
reversed The wave vector k remains outwards
The Poynting vector R is outwards The wave vector
k is reversed
() vg ?Y?-2 J , where J is the standard
current density of probability flux
J. Baudon et al PRL, 102, 140403 (2009)
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Meta-medium for Atom Optics How to realize such a
transient reversal of the group velocity ?
One of the simplest answer is a COMOVING
potential V(t, x), e.g., for atoms with spin, a
comoving magnetic field B(t, x)
y
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Meta-medium for Atom Optics How to realize such a
transient reversal of the group velocity ?
One of the simplest answer is a COMOVING
potential V(t, x), e.g., for atoms with spin, a
comoving magnetic field B(t, x)
y
B
Transverse magnetic field B moving along x, at an
(adjustable) velocity u n L cos (2pn (t-t0))
cos (2p x/L) cos (2p (n(t-t0) x/L) cos (2p
(n(t-t0) x/L) /2 A continuous frequency
spectrum H(n) can be used as well V(t, x)
s(t) cos (2p x / L) ? comoving magnetic
pulse
Mathevet et al, PRA 56, 2954 (1997) 61, 033604
(2000)
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Meta-medium for Atom Optics How to realize such a
transient reversal of the group velocity ?
One of the simplest answer is a COMOVING
potential V(t, x), e.g., for atoms with spin, a
comoving magnetic field B(t, x)
y
B
atoms
Transverse magnetic field B moving along x, at an
(adjustable) velocity u n L cos (2pn (t-t0))
cos (2p x/L) cos (2p (n(t-t0) x/L) cos (2p
(n(t-t0) x/L) /2 A continuous frequency
spectrum H(n) can be used as well V(t, x)
s(t) cos (2p x / L) ? comoving magnetic
pulse
Mathevet et al, PRA 56, 2954 (1997) 61, 033604
(2000)
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Total phase of a k-component of the atomic wave
packetj(t, k) is the phase shift induced by
co-moving potential V(t, x)
The motion of the wave packet centre is derived
from the stationary phase condition ?k F 0 ?
The group velocity is then By a proper
choice of s(t), it can be made (transiently)
negative
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s(t)
Negative group velocity obtained by using a
co-moving magnetic field of spatial frequency L
5mm s(t) cst e/(t e)2 exp(- t / t) if 0
t t1 0 elsewhere e 1 ms, t 0.37 ms, t1
1.2 ms Atomic velocity v0 20m/s, M 2,
Bmax 400 Gauss
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SIMULATION with a co-moving potential of spatial
period L 5 mm s(t) cst e/(t e)2 exp(- t /
t) pour 0 t t1, 0 elsewhere e
7.4 ms, t 0.37 ms, t1 1.2 ms Atomic
velocity v0 20 m/s, B max 600 Gauss, M 2
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Meta-lenses
(a) Potential s(t) cos(2px/L) (b)
Potential s(t) cos(2px/L) cos(2py/L)
x
J. Baudon et al PRL, 102, 140403 (2009)
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Prospects for Matter Wave NIMs
Beam splitters, atom interferometers
Atom meta-lenses
Astigmatism, Chromatism, Ultimate limits?
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Conclusion - Prospects

• New ultra-narrow metastable atom source for atom
  optics and atom surface interaction studies
• Coherent optics with fast metastable atoms
• Study of atom-surface interaction effects on
  magnetic sublevels (e.g. scattering with
  )
• Novel type of tunable beam splitter for atom
  interferometry
• Experiments toward atomic nanoscope under way
• Zeeman/laser cooling on Ar (3P2) is in
  operation
• Surface-induced quantum jumps observable with
  a nm resolution
• Coherent nano-beam of metastable Helium
  experiments in progress
• Potential applications in atom
  nano-lithography and atom-surface
• studies at the nm level
• Negative-index media for atom waves are under
  study

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Conclusion - Prospects

• New ultra-narrow metastable atom source for atom
  optics and atom surface interaction studies
• Coherent optics with fast metastable atoms
• Study of atom-surface interaction effects on
  magnetic sublevels (e.g. scattering with
  )
• Novel type of tunable beam splitter for atom
  interferometry
• Experiments toward atomic nanoscope under way
• Zeeman/laser cooling on Ar (3P2) is in
  operation
• Surface-induced quantum jumps observable with
  a nm resolution
• Coherent nano-beam of metastable Helium
  experiments in progress
• Potential applications in atom
  nano-lithography and atom-surface
• studies at the nm level
• Negative-index media for atom waves are under
  study

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 IOA  Team - Laser Physics Laboratory Universit
y Paris Nord
Francisco PERALES
Jules GRUCKER

Mehdi HAMAMDA
Gabriel DUTIER
Jaques BAUDON
Constantin MAINOS
Georges VASSILEV
Martial DUCLOY

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