Quantum engineering based on atoms and photons Hannover, 26020203

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Quantum engineering based on atoms and photons
Hannover, 26/02-02/03
Laboratoire Aimé Cotton CNRS, bat 505 Orsay
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------------------------------------------ Cesium
exp Rubidium exp theory -----------------------
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------------------ P Pillet L Pruvost F
Masnou D Comparat B Viaris de Lesegno O
Dulieu N Vanhaecke A Crubellier E
Luc M Aymar N Bouloufa -------------
--------------------------------------------------
----------------------------- G Stern, H
Jelassi J Mur Petit M Viteau, M Mestre G
Amosten F Diry
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Quantum engineering based on atoms and photons
Hannover, 26/02-02/03
Photo-associative spectroscopy of weakly bound
Rb2 molecules. Lu-Fano method analysis Shaped
dipole potentials for cold atom manipulation
Laboratoire Aimé Cotton CNRS, bat
505 Orsay Laurence PRUVOST
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3
Group activities

• Atom optics
• Shaped dipole potentials for cold atom
  manipulation
• M. Mestre, PhD
• F. Diry, PhD
• B. Viaris de Lesegno,
• L. Pruvost,
• Photo-associative spectroscopy of rubidium
• Photoassociative spectrocopy of weakly bound
• molecules. Lu-Fano analysis.
• H. Jelassi, PhD
• B. Viaris de Lesegno,
• L. Pruvost,

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Part I

• Photo-associative spectroscopy of weakly bound
  Rb2 molecules.
• Lu-Fano method analysis
• Main interest
• Precise determination of the potentials V(R),
  coupling
• Formation of cold molecules cold chemistry
• Many processes
• direct Feshbach resonances ,
• indirect pump/probe excitation Raman
  excitation, STIRAP
• Use of continuous lasers, or pulse lasers
• time shaped lasers (femto range) to enhance
  one process

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Photoassociation process
Two neighbouring cold atoms (5s5s), submitted to
a resonant laser light, are photo-associated to
a weakly-bound excited molecule M. (1)
Photo-association Rb(5s) Rb(5s) hn ?
Rb2 The lifetime of the molecule M is very
short. The molecule either spontaneously decays
to atoms or to a more stable molecule. (2)
spontaneous emission Rb2 ? hn Rb Rb (3)
molecule formation Rb2 ? hn Rb2
In both processes (2,3), an atom loss of the
trap is observed as soon as the laser wavelength
is resonant with a bound state of the excited
molecular potential curve. To get the molecular
spectrum, trap loss is recorded by scanning the
PA laser.
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Trap loss spectroscopy

• The atom number is recorded while scanning the PA
  laser..

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Experimental data
3 molecular series 0g-, 0u and 1g Close to the
dissociation limit weakly bound states
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Weakly bound molecules
For large internuclear distances, R, the binding
energy is due to the dipole-dipole interaction.
The main term of the asymptotic potential is V(R)
-cn/Rn According the molecular symmetry n3 or
6.
LeRoy-Bernstein model BKW solution for a 1/Rn
potential The binding energy of the molecular
vibrational level v e En (vD-v)2n/(n-2) vD-v
(e /En ) (n-2) /2n En is a parameter defined
from atom constants (mass, dipole element, cn).
vD gives the number (equal to IntvD) of levels
lying under the dissociation limit and the
binding energy of the last one eD En dD2n/(n-2)
, with dD vD - IntvD.
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Data analysis

• Mostly, the experimental data are connected to
  numerical calculations, which are very precise
  and require the molecular potentials (for example
  ab-initio or model potential). The comparison
  with the exp. data allows to improve molecular
  potentials.
• We have applied a semi-empirical approach
  Lu-Fano graph
• adapted for powerlaw potentials,
• No computation,
• Widely applied for Rydberg atoms V(r)-1/r
• Requires only the asymptotic form of the
  potential -cn/Rn

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Lu-Fano method
The binding energy, e, experimentally measured,
gives the effective quantum number v v (e /
En )(n-2)/(2n) the quantum defect d. d v -
Intv The Lu-Fano plot (d versus e) analyses
the discrepancies between data and the
LeRoy-Bernstein energy law. d cte is expected.
The variations of d give information about the
molecular potential and its perturbations.
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Application to 0g- and 0u molecular states

• Limitation to 2 quite simple examples For 1g
  symmetry, hyperfine interaction has to be
  considered.
• 0g- one channel problem,
• short range potential effects
• 0u two channel problem
• coupling due to fine interaction and spin-spin
  interaction

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Improvment of the model  core effect 

• The Lu-Fano graph is an horizontal line if LRB is
  ok
• ? Take into account the short range potential
• For weakly bound levels, it slightly modifies
  the binding energy and the wavefunction
• Some models
• infinite barrier -cn/Rn
• square -cn/Rn
• parabola -cn/Rn
• For weak binding energies, applying
  BKWBohr-Sommerfeld , one gets
• vD-v (e /En ) (n-2) /2n g e
• A linear correction is expected
• The parameter g is connected to the short range
  potential. We deduce the barrier at R? 4.2 au,
  the potential minimum at Re 12.5 au, the
  asymptotic range at Rc17.7 ua.

H. Jelassi, B.Viaris De Lesegno and L. Pruvost,
Phys. Rev. A 73, 32501, 2006.
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Méthode de Lu-Fano appliquée aux molécules
faiblement liées

• En utilisant la loi de Le Roy-Bernstein, on
  construit le graphe de Lu-Fano
• ei ? vi (ei/ E3)1/6 ? di
  vi-E(vi) ? d f(e)
• la série 0u

• 2 niveaux perturbateurs sont identifiés.
• Ils signent un couplage entre 2 courbes
  moléculaires.
• Les sauts de d ne valent pas 1, donc le défaut
  quantique, même non perturbé dépend un peu de
  lénergie.

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Case of 0u

• Such a LF graph exhibits a coupling between two
  series (well known for Rydberg states)
• Spin-orbit and spin-spin interactions in the
  molecule

R

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A model with 2 series of states

• V constant in the vicinity of E2
• Diagonalisation of

D1
E2
Demkov, Ostrovski, J Phys B, 28, 403,1995
Cohen-Tannoudji, Dupont-Roc, Grynberg, processus
dinteraction entre photons et atomes, p 52.
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Characterisation of the coupling

• Some modifications of the previous model because
• (i) LRB not valid for V2
• (ii) linear variation of the quantum defect
  versus the energy
• Fit with tan(p(d - m1)). tan(p(e - e2)/D2)
  p2K2 et m1 m1? - g e
• Perturbing level e2 4.724 cm-1
• Coupling constant K 0.1221
• Quantum defect at e0 m1? 0.6932
• Linear variation g -0.0448

m1? 0.6932 0.0167 g -0.0448 0.0031 e2
4.724 0.066 D2 6.803 0.084 K 0.1221 0.0086
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consequences

• d at e0 g and ? la position of the barrier
  18 ua.
• The coupling ? wavefonction mixing
• y cosq y1(R) sinq y2(R)
• at 4.72 cm-1 q 31.8 (72, 28)
• y1(R) external, max at the turning point R182
  ua
• y2(R) internal, max at the turning point R2
  24 ua
• extrapolation of the Lu-Fano graph ? position and
  width of the first predissociated level of (5s -
  5p3/2) 0u

By increasing the probability near R0, cold
molecule formation is increased
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first predissociated level of (5s - 5p3/2) 0u

• position 2.1 cm-1
• G 4 cm-1
• Confirmation by the experiment

Jelassi, Viaris, Pruvost, PRA 74, 012510, 2006.
Jelassi, Viaris, Pruvost, PRA 73, 032501, 2006.
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Part II

• Shaped dipole potentials for cold atom
  manipulation
• For a better use of the dipole potentials
• Arbitrary shaped dipole potentials
• ( arbitrary shaped far-detuned laser beam)
• ? Create new shapes
• ? New atom optics components
• New optical traps
• Reconfigurable potentials
• ? feed back loops
• ? improve and correct the shapes
• ? reduce aberrations of atom optics
• components
• Time-dependent shaped potentials
• ? apply successive dipole potentials
• ? rapidly modify the shape of the potential
• (dynamical studies)

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General scheme

• The laser beam is arbitrary shaped using a
  Spatial Light Modulator, whose pattern is
  prepared and addressed via a computer.

Cold atoms BEC
addressing

• Requirements for cold atoms
• Atom optics with MOT 0.5 mm, 10 mK Sa-Ti
  _at_779 nm or 796nm, 1W, 1mm2
• fiber laser_at_1070 nm, 20 W, 1mm2
• Manipulation of BEC 0.1 mm, 1mK Sa-Ti , 0.1W
  
• fiber laser, 1 W
• Atom trapping for BEC fiber laser, 10-50 W
• Reconfigurable
• time-dependent potentials 1ms-1ms time scale

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Spatial Light Modulators

• Deformable mirrors (low resolution)
• Digital Micro mirror Devices (DMD)
• Liquid Crystal Devices (LCD)
• ? Phase modulation
• phase object for wave front correction or
  diffraction
• ? Polarisation modulation (amplitude)
• ? Other uses
• both amplitude and phase modulation,
• phase contrast imagery

?
LC birefringence
!! Light losses
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SLM

• LC Devices
• ferroelectric LC ? binary modulation (0/p)
• nematic LC ? continuous mod. (0 to 2p)
• electrically addressed ? pixellated
• optically addressed ?non-pixelated
• Optically addressed nematic liquid crystal device
  
• ? one diffraction pattern the light losses are
  weak
• ? a better definition of the phase hologram
• ? change the LC orientation needs 10-100 ms !

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Optically addressed liquid crystal valve

• The LC layer (2cm x 2cm) is sandwiched between 2
  large electrodes. The electric field, created
  between the 2 electrodes, is modulated through a
  photoconductor layer which is illuminated by a
  blue picture delivered by a video-projector. The
  phase pattern (copy of the blue picture) is then
  printed to the laser beam (red or IR) passing
  through the LC layer.

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holography

• A priori, a good determination of the hologram
  guarantees the correct intensity shape
• 1- Analytical holograms
• ? Spot generation
• Holographic Optical tweezers,
• many optical trap for cold atoms
• see P. Grangiers group , Orsay
• C. Foots group, Oxford
• ? Helicoidal phase to create laser beams in
  Laguerre-Gaussian modes
• Transfer of angular momentum of light to small
  objects
• Cold atom guiding, see also K Dholakias group,
  St Andrews
• ? Conical phase to create Bessel modes
• 2- Computed holograms

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Holography

• 2- Computed holograms

0
MM BV
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Response time of nematic LC spatial light
modulator

• Example 30 rotation of a blazed grating
  elementary step of a 12-frame full-rotation
  sequence
• The nematic LC are very slow 10-100ms to change
  the orientation depending on the LC layer
  thickness

• ? arbitrary shaped laser beams
• ? Reconfigurable
• ? time-dependent potentials

Transient regime
order 1 0 -1
Tréponse?300 ms !
 bleed effect  30 drop in trap depth
flashing of 0th order
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AOM/SLM

• Collaboration avec Thales RT, Palaiseau
• To speed up the device and clean up the
  transition, the laser beam is driven by an AOM
  (acousto-optic modulator) in order to read
  successive holograms already addressed on the
  SLM.

AOM
SLM
Laser
Mestre, Viaris, Farcy, Pruvost, Bourderionnet,
Delboulbé, Loiseaux, Dolfi,  Improvements on the
refresh rate and transient regime of a SLM by
sequential readout using an acousto-optic
modulator, SPIE procedings.
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AOM/SLM setup

• Videoprojector Infocus LP530 DMD 800x600 pixels,
  modified to use a 300 mW 455nm LED instead of the
  original 200W sodium lamp
• AOM Thales RT (custom) 2D, 30MHz central
  frequency
• Laser 5mW HeNe 633nm
• CCD WinCamD USB Beam profiler, 1 MPix, 13bits,
  25µs min exp

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AOM/SLM

• Collaboration avec Thales RT, Palaiseau
• To speed up the device and clean up the
  transition, the laser beam is driven by an AOM
  (acousto-optic modulator) in order to read
  successive holograms already addressed on the
  SLM.

• The response time depends on the AOM and its
  driver, here 5 ms
• The bleed effect is suppressed, because the LC
  orientation is not changed
• Compromise between speed and hologram size
  (p/n)2 pixels/hologram
• Possible partial refreshing of the hologram
  during the readout

Mestre, Viaris, Farcy, Pruvost, Bourderionnet,
Delboulbé, Loiseaux, Dolfi,  Improvements on the
refresh rate and transient regime of a SLM by
sequential readout using an acousto-optic
modulator, SPIE procedings.
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AOM/SLM

• Scenario to partially refresh the holograms
  tload/(n2-1)

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Laguerre-Gaussian beams for cold atoms

• Easily generated with helicoidal phase

Harmonic potential

• Dark at the centre ? no spontaneous emission
• k1, harmonic potential
• Achromatic lens applying the potential to cold
  atoms during a period (or half a period) gives a
  reconstruction of the cloud the effect is
  achromatic and the magnification is 1 (or -1)
• Achromatic focus lens obtained by applying
  successive harmonic potentials with different
  frequencies and time durations.
• The AOM/SLM device will provide laser pulses,
  LG01 mode, with different sizes and different
  pulse durations.

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Achromatic lens for atoms

• One LG01 laser pulse
• Position
• velocity
• at t p/w, the magnification is 1
• Many pulses an achromatic zoom lens
• Example of 2 successive pulses (w,t) and (w,t)
• Example
• if ww/2 et tt
• cos(wt) 1/61/2 x/x0 -0.5
• 1W, LG01 of 1mm radius,
• w100 rad/s
• t11.5 ms
• falling distance 2.6 mm

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Laguerre-Gaussian beams for cold atoms

• High order LG0k

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Laguerre-Gaussian beams for cold atoms

• High order LG0k
• Dark at the centre ? no spontaneous emission
• Near the centre, the light intensity of the LG0k
  mode varying as r2kexp(-r2), is very flat. For
  large values of k, the potential is squared.
• ? guide for atoms
• BEC in non-harmonic optical trap (NHOT) the
  energy levels are not equidistant. BEC condition
  and the BEC wavefunction are strongly modified.
  (Collaboration with E. Charron, LPPM, Orsay)
• 1- Load a BEC into a NHOT
• 2- fill a NHOT with a MOT, then study
  collisions and the evaporation to reach BEC ?
  shape a high power laser

k2 k4 k6 k8

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BEC wavefunctions in r2k potentials
Y(r)2

• LAC Pruvost, Viaris,
• LPPM Gaaloul, Charron

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Preliminary experiment atom guiding inside LG0k
modes
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Preliminary experiment - Cold Rb guided inside a
LG0,12 mode, detuning effects
Spontaneous emission and Heating
The depth of potential decreases
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Preliminary experiment - Cold Rb guided inside a
LG0,k mode, detuning effects
deep potential, spontaneous emission
Flat potential V(r) r2kexp(-r2)
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Conclusion / future

• Future ?
• 1- Lu-Fano method applied to others molecules
• homonuclear, heteronuclear.
• 2. Experiments with LG0k and cold atoms
• 2D traps, 3D traps,
• 3- SLM for high power lasers
• in collaboration with B. Loiseaux, J.
  Bourderionnet, Thales, Palaiseau
• ? shape a 10-25 W laser _at_1070 nm or a 10 W laser
  _at_532 nm
• ? to create new all optical traps
• 4- Other applications MOCA Modern Optics for
  Cold Atoms, ifraf
• atom optics, quantum computing, atom lithography
  
• coll. with O. Gorceixs, V. Lorents groups ,
  LPL, Villetaneuse
• P. Grangiers group, IOTA, Palaiseau
• 5- Improve the hologram calculation and reduce
  the speckle
• in collaboration with M. Padgetts group ,
  Glasgow university
• ? atoms in random potentials

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Une photo
Photographe Benoit Lantin LAC
Haikel Jelassi, Fabienne Diry, LP Michael Mestre,
Bruno Viaris de Lesegno
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Atom in a harmonic potential with speckle

• Lens simulation 0.3mm Rb cloud _at_10µK, falling
  under gravity in a 16Hz potential well. The cloud
  is observed after a half-period (31ms), 2-D
  simulation. Even with speckle the cloud
  reconstruction is correct.

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Future

• Atom holography a shaped light sheet is applied
  during t .
• Order of magnitude Df 2p with U1mK, t50 ms

Df U(x,y).t/h
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Response time of nematic LC spatial light
modulator

• ? arbitrary shaped laser beams
• ? Reconfigurable
• ? time-dependent potentials gt1kHz

• The nematic LC are very slow to change the
  orientation 10-100ms depending on the LCF layer
  thickness

order 1 0 -1
Tréponse?300 ms !
 bleed effect  the intensity repartition is
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A beam splitter for cold atoms realised with two
dipole guides

• The cold atom cloud is guided inside a Nd-YAG
  laser which creates a 2D dipole potential.
• During the transfer a second Nd-YAG laser beam is
  switched on and modifies the dipole potential
  into a double-well one.

Cold atom beamsplitter realized with two crossing
dipole guides , O. Houde, D. Kadio, L. Pruvost,
Phys. Rev. Lett. 85, 5543, 2000
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A beam splitter for cold atoms

• During the transfer a second Nd-YAG laser beam is
  switched on and modifies the dipole potential
  into a double-well one.
• 2 exit ways are possible for the atoms. A
  splitting of the cloud is observed.

a 0,12 rad 7
a
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A beam splitter for cold atoms

• During the transfer a second Nd-YAG laser beam is
  switched on and modifies the dipole potential
  into a double-well one.
• 2 exit ways are possible for the atoms. A
  splitting of the cloud is observed.

a 0,12 rad 7
a