Laser cooling and trapping of atoms: beyond the limits

Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Doppler Limit temperature
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
1
Laser cooling of atoms: a breakthrough
1 cm/s
−
10 9 K
−
10 6 K
1 m/s
300 m/s
−
10 3 K
1K
Dilution
cryostats
Sub recoil
cooling
1988
Sisyphus
1988
Doppler
molasses
1985
103 K
room
Liquid He
1908
L’échelle logarithmique montre l’ampleur du refroidissement,
caractérisée par une division de la température absolue, pas par une
soustraction.
2
Cooling and trapping: increase of phase
space density
Cooling:
• Increase of density in velocity space
• ≠ filtering
Trapping :
• Confinement in real space
Cooling and Trapping :
• Increase of phase space density
3
Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Doppler Limit temperature
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
4
Semi classical model of atom-light
interaction
Matter (atoms) is quantized
Light described by classical
electromagnetic field
Successful to describe all matter-light interaction phenomenon
known until 1970 (except spontaneous emission)
• Absorption, stimulated emission: lasers
• Photoelectric effect!!!
Modern quantum optics is about radiation that demand
quantization of light
• Single photon wave packets
• Entangled photons
Semi-classical model is very useful, provided one knows its limits
5
Two level atom in motion: quantum
description
Etat interne
ψ ∈ Eint (dimension 2)
⎡γ a (t ) ⎤
ψ ↔⎢
⎥
γ
(
t
)
⎣ b ⎦
Eb
=ω 0
Ea
⎡0 0 ⎤
ˆ
H0 = ⎢
⎥
ω
=
0
0⎦
⎣
Mouvement du centre de masse (observables r , P )
ψ ∈ Er
ψ ↔ ψ (r , t )
Hˆ ext
2
Pˆ 2
=
=
↔ Hˆ ext = −
Δ
2M
2M
↔
spineur
Description globale
ψ ∈ Eint ⊗ Er
⎡ψ a (r, t ) ⎤
ψ ↔⎢
⎥
⎣ψ b (r, t ) ⎦
Hˆ = Hˆ 0 + Hˆ ext
Description quantique de la dynamique interne et du mouvement
6
Interaction avec une onde électromagnétique
classique
G
Interaction dipolaire électrique avec E(r, t ) = ε E0 (r ) cos (ω t − ϕ (r ) )
⎡0
ˆ
ˆ
ˆ
H I = − D ⋅ E = − Dε Eε (r, t ) = − ⎢
⎣d
G
d⎤
ˆ
ˆ
Eε (r, t ) avec Dε = D ⋅ ε
⎥
0⎦
ˆ2
0
0
⎡
⎤
⎡ 0 dε ⎤
P
ˆ
ˆ
ˆ
ˆ
H = H 0 + H ext + H I = ⎢
Eε (r, t )
+
Δ−⎢
⎥
⎥
⎣0 =ω 0 ⎦ 2 M
⎣ dε 0 ⎦
⎡ψ a (r, t ) ⎤
Agit sur [ψ ] = ⎢
⎥
t
γ
r
(
,
)
⎣ b
⎦
L’hamiltonien dipolaire électrique est valable dans le cadre de
l’approximation des grandes longueurs d’onde: distance électronnoyau << λ
Cela ne met aucune contrainte sur ψa(r,t) et ψb(r,t) qui pourraient
être étalés sur une distance >> λ
7
Paquet d’onde localisé: limite classique
Atome localisé
Paquet d’onde étroit, identique pour les deux états
⎡ψ a (r, t ) ⎤ ⎡γ a (t ) ⎤
ψ (r , t )
=⎢
[ψ ] = ⎢
⎥
⎥
⎣ γ b ( r , t ) ⎦ ⎣γ b ( t ) ⎦
ψ (r, t ) « piqué » autour de rat
largeur << λ
Position classique
rˆ (t ) = ψ rˆ ψ = ∫ψ * (r, t ) rψ (r, t ) d 3 r rat (t )
Vitesse classique définie par
Th. d’Ehrenfest:
ˆ
d
1
P
⎡rˆ , Hˆ ⎤ =
Vat =
rˆ =
⎦
dt
i= ⎣
M
d
d
Vat = rat (t ) =
rˆ (t )
dt
dt
⎡ Pˆ 2 ⎤
Pˆ
Pˆ
ˆ
⎡rˆ , P ⎤ =
car ⎢rˆ ,
i=
⎥ =2
⎣ ⎦
2
M
2
M
M
⎣
⎦
8
Dynamique de la position classique
ˆ
drat
P
On applique le th. d’Ehrenfest à la vitesse classique
= Vat =
dt
M
d
1 ˆ ˆ
1 ˆ ˆ
⎡ P, H ⎤ =
⎡ P, H I ⎤
M Vat =
⎣
⎦
⎦
dt
i=
i= ⎣
= ˆ G
ˆ
ˆ
ˆ
ˆ
⎡ P, H I ⎤ = − Dε ⎡ P, E (r, t ) ⎤ = − Dε ∇ {E (r, t )}
⎣
⎦
⎣
⎦
i
G
G
d2
d
ˆ
ˆ
M 2 rat = M Vat = Dε ∇ { E (r, t )} = Dε ⎡⎣∇ { Eε (r, t )}⎤⎦
rat
dt
dt
L’atome suit une trajectoire classique moyenne déterminée par la force
G
ˆ
F = Dε ⎡⎣∇ { Eε (r, t )}⎤⎦
rat
G
E
=
ε
Eε (r, t )
cf. électrodynamique classique, pour un dipôle dε dans
G
G
F = dε ∇Eε (et pas ∇( dε Eε ): important quand dε dépend de Eε )
9
Forces radiatives
Oscillation forcée du dipôle atomique, sous l’effet du champ
G
G
E(r, t ) = ε E0 (r ) cos (ω t − ϕ (r ) ) = ε E (r, t ) + c.c.
avec E (r, t ) =
E0 (r )
2
exp {iϕ (r )}exp {−iω t}
Dˆ ε = ε 0α E (r, t ) + ε 0α *E *(r, t ) après amortissement du transitoire
Polarisabilité complexe
α = α ′ + iα ′′
(cf. chap II)
Force due à l’interaction entre le champ et le dipôle atomique induit
G
G
* *
ˆ
F = Dε ⎡⎣∇ {E (r, t )}⎤⎦ = ε 0 (α E + α E ) ∇ {E + E * }
rat
En ne gardant que les termes qui n’oscillent pas (moyenne temporelle)
G *
F = ε 0α E ⎡⎣∇E ⎤⎦ + c.c.
rat
10
Radiation pressure vs Dipole force
G *
F = ε 0α E ⎡⎣∇E ⎤⎦
α = α ′ + iα ′′
rat
+ c.c.
F=
avec E (r, t ) =
ε 0α
4
E0 (r )
2
exp {iϕ (r )}exp {−iω t}
G
G
E0 (r ) ∇ [ E0 (r ) ] − i∇ [ϕ (r ) ] E0 (r ) + c.c.
(
)
G
ε 0α ′′
2 G
=
E0 (r )∇ [ E0 (r ) ] +
( E0 (r ) ) ∇ [ϕ (r )]
2
2
l’expression étant évaluée en r = rat
ε 0α ′
G
• Partie réactive (réelle) de la
Fdip =
E0 (r)∇[ E0 (r)] Force dipolaire polarisabilité
2
ε0α′
• Gradient de l’amplitude
ε0α′′
2 G
Fres =
( E0 (r)) ∇[ϕ(r)]
2
Pression de
radiation
résonnante
• Partie dissipative (imaginaire)
de la polarisabilité
• Gradient de la phase
11
Closed two level transition (resonance line)
Raie « de résonance »: niveau du bas fondamental
¾ Durée de vie infinie Γa = 0
=ω 0 =ω Γ
¾ Largeur de raie Γ = Γb
Ea
¾ Transition fermée
G
G
Dipôle forcé sous l’effet de
E = ε E0 cos (ω t − ϕ ) = ε E + E *
Eb
(
)
Utilisation du formalisme de la matrice densité et des équations de
Bloch optiques (dissipation, cf. Maj. 2)
G
Dˆ ε = ε 0α E + ε 0α *E *(r, t )
D = ε D̂ε
=Ω = − d E
1
⎡0 d ⎤
Dˆ ε = − ⎢
⎥
0
d
⎣
⎦
15
d2
1
1
α=
ε 0 = (ω − ω ) − i Γ 1 + s
0
2
Réponse linéaire
0
Ω12 / 2
s=
(ω 0 − ω ) 2 + Γ 2 / 4
saturation
12
Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Doppler Limit temperature
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
13
Pression de radiation résonnante
Onde plane progressive
E0
exp {ik ⋅ r}exp {−iω t}
2
G
ε 0α ′
=
E0 (r )∇ [ E0 (r ) ] = 0
2
E (r , t ) =
amplitude E0 constante ⇒ Fdip
G
d 2 E0 2
Γ/2
1
E
(
)
(
)
Fres =
r
∇
ϕ
r
=
k
( 0 ) [ ]
2
2= (ω 0 − ω ) 2 + Γ 2 / 4 1 + s
ε 0α ′′
2
Ω12
Γ/2
1
Γ s
Fres ==k
= =k
2
2
2 (ω 0 − ω ) + Γ / 4 1 + s
2 1+ s
Ω12 / 2
I
1
s=
=
(ω 0 − ω ) 2 + Γ 2 / 4 I sat 1 + 4(ω 0 − ω ) 2 / Γ 2
paramètre de saturation
14
Resonant radiation pressure: properties
Fres ==k
Γ s
2 1+ s
• Dirigée suivant le
vecteur d’onde du laser
Fres
k
Fres
Ω12 / 2
Γ
Fres ==k
2 (ω 0 − ω ) 2 + Ω12 / 2 + Γ 2 / 4
Fmax
• Lorentzian resonance (power broadening)
Ω12 / 2
I
• Saturation
s0 = 2
=
Γ / 4 I sat
Γ s0
Fmax = =k
2 1 + s0
=k
Γ
2
ω0
1
1
s
ω
Order of magnitude
⎧ Γ / 2π = 6 MHz
Rb ⎨
2
I
=
1.6
mW
/
cm
⎩ sat
Fmax
Γ 1 + s0
=k
= 5.9 ×10−3 m / s
M
max
Fmax
=k Γ
=
≈ 105 m / s −2 ≈ 104 g
M
M 2
Easily achievable with lasers
15
Decelerating atoms with radiation pressure
Jet thermique de sodium
V≈
2 k BT
≈ 600 m / s
M
V 2 36 × 104
≈
= 1.8 m
distance d'arret =
5
2γ
2 × 10
Challenges (Phillips, 2002): keep atoms on resonance during
deceleration (Doppler effect changes); avoid optical pumping into
other levels
Ralentissement « Zeeman »
(Phillips et coll., 1982)
Distribution des vitesses
Densité dans
l’espace des
vitesses
augmente: vrai
refroidissement
Full stop achieved in 1985
16
Stopping metastable
Helium atoms
17
Radiation pressure and fluorescence rate
Pression de radiation résonnante
Γ s
Fres ==k
2 1+ s
Rfluo =
Γ s
2 1+ s
E0
E (r , t ) =
exp {ik ⋅ r}exp {−iω t}
2
Ω12 / 2
s=
(ω 0 − ω ) 2 + Γ 2 / 4
=Ω1 = − d ⋅ E0
Eb
Fres ==kRfluo
=ω 0 = ω Γ
Taux de fluorescence (nombre de
cycles par seconde, calcul par EBO)
Cycle de fluorescence: Un photon du
faisceau incident est diffusé dans une
direction différente, avec une énergie
égale (diffusion élastique) ou un peu
différente (diffusion inélastique)
Ea
k,ω
k sp , ωsp
ksp : direction aléatoire
Réinterprétation de la pression de radiation résonnante ?
18
Radiation pressure and photon
momentum
Bilan d’impulsion dans un cycle de fluorescence (diffusion d’un photon)
Photon dans une onde plane
Eb
=k sp
de vecteur d’onde k : p = =k
=k
=k
=k =k sp
Absorption-Réémission
− =k sp
ΔPat = =k − =k sp
ΔPat
Ea
Moyenné sur un grand nombre de cycles
k sp = 0 ⇒ ΔPat 1 cycle = =k
Force moyenne
Fres =Rfluo ΔPat
1 cycle
Γ s
= Rfluo =k = =k
2 1+ s
Modèle tout quantique (photons): calcul plus simple, image plus
simple, même résultat ! De plus, suggère l’existence de fluctuations de
la force liées aux fluctuations de la direction d’émission.
19
The problem of many ground state
levels: avoiding optical depumping
Alkali atoms have an hyperfine structure
Ground state is split in many components
Optical pumping into non interacting levels leads to deceleration
stopping.
Take advantage of selection rules (choice of polarization)
Use repumping lasers
20
Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Doppler Limit temperature
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
21
Force dipolaire
Fdip =
ε 0α ′
2
G
E0 (r )∇ [ E0 (r ) ]
2
d
=
=
Fdip
2
exp {iϕ (r )} exp {−iω t}
G
≠ 0 pour une onde inhomogène : ∇E0 ≠ 0
Fdip
Fdip
avec E (r, t ) =
E0 ( r )
G
2
∇ [ E0 (r )]
ω0 − ω
(ω 0 − ω ) 2 +
Γ
2
G
=(ω 0 − ω ) ∇ [ s (r )]
=
1 + s (r )
2
1 + s (r )
4
G
=(ω − ω 0 )
= − ∇ [U (r ) ] avec U (r ) =
log [1 + s (r ) ]
2
1
Dérive d’un potentiel (partie réactive de la s (r ) = I (r )
2
2
+
ω
−
ω
Γ
1
4(
)
/
I
sat
0
polarisabilité) variant comme l’intensité
Applications
⎧ attiré vers haute intensité si ω < ω 0
atome ⎨
⎩repoussé par haute intensité si ω > ω 0
22
An optical trap: optical tweezer
I (r )
1
=(ω − ω 0 )
r
=
avec
s
(
)
U dip (r ) =
log [1 + s (r )]
2
2
+
ω
−
ω
Γ
I
1
4(
)
/
sat
0
2
Trapping by a focused laser beam with ω < ω0 : optical tweezer
laser
Shallow trap: demands very cold
atoms ( T < 1 mK )
Classical interpretation: coupling of the field with the induced dipole
Interpretation by light shifts of the atomic levels
(Cohen-Tannoudji, Dalibard):
Atom spends more time in ground state.
Case of large detuning: atom in g: no
fluctuation, but very shallow, ultra cold atoms
e
ω L < ω0
g
23
Manipulation d’atomes individuels (P. Grangier)
2 atomes
côte à côte
Piégeage intermittent d’un seul atome
24
Piège dipolaire: réseau optique
Piégeage aux ventres (ω < ω0) ou
aux nœuds (ω > ω0) d’une onde
stationnaire 3 dimensions:
potentiel
dipolaire
cf. G. Grynberg et coll.
Atomes dans les micro puits
25
Miroir atomique à ondes évanescentes
ccd
sonde
Onde évanescente
5 cm
Atomes froids
(100 μK) lâchés
depuis un piège
Atomes repoussés (ω > ω0 :
barrière de potentiel) quand
ils entrent dans l’onde
évanescente : rebond
26
Dipole force and photon momentum
Onde inhomogène = plusieurs ondes planes
• Absorption de =k1
• Emission stimulée de =k2
=k1
ΔPat = =k1 − =k 2
=k 2
Eb
− =k 2
=k1
ΔPat
Mais on doit aussi considérer:
• Absorption de =k2
• Emission stimulée de =k1
=k1 =k 2
Ea
Force de signe opposé !!??
La phase relative des ondes 1 et 2 détermine quel processus domine.
• Délicat dans le modèle tout quantique (photons)
• Automatiquement pris en compte dans le modèle classique du champ
(la phase relative détermine le gradient d’intensité)
27
Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Limit temperature of Doppler c.
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
28
Refroidissement Doppler
Pression de radiation par deux ondes opposées
k,ω
−k , ω
Vat
ω < ω0
Lasers non saturants, désaccordés sous la résonance
Eb
=ω 0 = ω Γ
Ea
Vitesse atomique: effet Doppler différent pour les deux ondes
⎧
⎫
Γ2 / 4
Γ2 / 4
Fres =F0 ⎨
−
⎬
2
2
2
2
⎩ (ω − k ⋅ Vat − ω 0 ) + Γ / 4 (ω + k ⋅ Vat − ω 0 ) + Γ / 4 ⎭
F
ω0 − ω
k
ω = ω0 −
Γ
2
Vat
Force opposée à la vitesse:
freinage ⇒ refroidissement
Généralisable à 3 dimensions
29
Mélasse Doppler
Autour de V = 0 : frottement visqueux
dV
F = −α M V ou
= −αV
dt
k,ω
F
ω0 − ω
=k 2
Γ
α=
s0 pour ω = ω 0 −
2
M
Ordre de grandeur (rubidium, s0 = 0.5)
α 2.5 ×10−4 s −1
−k , ω
Vat
k
ω = ω0 −
Vat
Γ
2
Temps d’amortissement : 40 μs !
Milieu très visqueux: « mélasse optique »
Refroidissement exponentiel !
atomes « englués »
d 2
V = −2α V 2
dt
La température décroît : jusqu’où ? Sous le mK !
30
Magneto Optical Trap: molasses with a
restoring force
Zeeman differential detuning and polarized lasers
ω < ω0
Je = 1
−k , ω
k,ω
m = −1 m = 0
B
σ−
σ+
B
σ−
z
m =1
σ+
g
z
Quadrupole magnetic field: sign
changes at z = 0
Jg = 0
Bz < 0 : σ− polarized beam
more efficient than σ+
Atom pushed towards z = 0: trapping. Doppler molasses also at work.
⇒ Overdamped trap. Works in 3D . “The work horse of cold atoms”
31
What is the limit temperature in doppler
molasses of Magneto Optical trap?
We have a cooling process that never stops.
Is there a heating process?
32
Heating: fluctuations of radiative forces
Semi-classical approach
G
ˆ
F = Dε ⎡⎣∇ { E (r, t )}⎤⎦
rat
D : quantum average, over an ensemble of atoms, submitted to the
same radiation. Many atoms: a genuine ensemble!
Each atom is submitted to a different force F , whose average is F.
G
G2
F (t ) = F (t )
F (t ) − F 2 (t ) = ΔF 2
V
V
ΔV 2 /
⇒ Velocity dispersion
⇒ heating
increases with time
t
Heating due to the quantum character of atomic dipole.
There is another point of view, based on momentum exchanges with
photons
33
Fluctuations of radiation pressure: a
photon point of view
At each fluorescence cycle, there
is a spontaneous emission random
recoil which is not taken into
account in the average force
=k sp
=k L
=k L
ΔPat
2DP = ( =k ) Rfluo
2
Random walk in the atom momentum
space: step =k , rate Rfluo
d 2
P = 2D
dt
Diffusion coefficient (Einstein)
Heating
34
Limit of Doppler cooling
d 2
P = −2α P 2
dt
Cooling
d 2
P = 2D
dt
Heating
Steady state
Pat
2
Can be described with a
Langevin equation
=
D
α
Relation d’Einstein
G
d
Pat = −α Pat + Fchauff
dt
Température finale
Pat
3
3
= =Γ
kBT =
2
2M
4
2
Ordre de grandeur : 100 μK
Demonstrated in 1985 (S. Chu)
35
Below the Doppler limit: Sisyphus cooling
Doppler limit: 100 μK range (observed in 1985, S. Chu)
1988: limit temperature found in the 10 μK range, well below the
“theroretical” limit of Doppler cooling (WD Phillips)
Interprétation (C. Cohen-Tannoudji, J. Dalibard): “Sisyphus effect”.
Must take into account ground state degeneracy, and light polarization
gradients that one cannot avoid in a 3D standing wave.
Because of delay to reach
internal steady state (motion) the
atom tends to spends more time
climbing hills than descending:
looses kinetic energy.
Residual velocity: a few recoil velocity
VR =
=k
M
Ultimate limit?
36
Laser cooling and trapping of atoms:
beyond the limits
1. A breakthrough in the quest of 4. Dipolar force
1. Properties; interpretations
low temperatures
2. Applications: optical tweezer
2. Radiative forces
optical lattice, atomic mirror
1. Semi classical approach
3. Photon momentum
2. Atomic motion
interpretation?
3. Radiative forces
5. Laser cooling: optical molasses
4. Resonance transition
1. Doppler cooling
3. Resonant radiation pressure
2. Magneto Optical Trapp (MOT)
1. Properties
3. Doppler Limit temperature
2. Stopping a laser beam
4. Below Doppler limit: Sisyphus
with radiation pressure
6. Below the one photon recoil limit:
3. Photon momentum
dark resonance cooling and Lévy
interpretation
flights
37
The one photon recoil: an ultimate limit?
1 cm/s
−
10 9 K
1 m/s
−
10 6 K
300 m/s
−
10 3 K
1K
103 K
subrecoil
liquid He
Sisyphus
room
Doppler
molasses
Experiments show that ultimate limit of Sisyphus
corresponds to a few single photon recoil
=k )
3
(
kBT ≈ 10
2
2M
2
In agreement with the concept that spontaneous emission is
necessary (dissipation, non hamiltonian), and cannot be controlled.
38
Below the recoil limit: velocity selective
coherent population trapping
(“dark resonance cooling”)
1988 (ENS Paris; CCT, AA): demonstration of a method
allowing one to obtain a gas with velocity distribution
narrower than the recoil velocity associated with the
emission or absorption of a single photon V R = = k
M
Necessary to use a quantum description of the atomic motion
New theoretical approaches:
• Quantum Monte-Carlo; delay function
• Lévy flights statistics
See “special” (vintage) seminar
39
Laser cooling and trapping of atoms:
a fantastic new tool
In less than one decade (1980’s), it has been possible to reach goals
that were thought to be very far ahead:
• Cooling atoms in the μK range
• Trapping atoms and keeping them for seconds
Experimental surprises as well as ingenuity has allowed physicits to
break several so called “limits”, and prompted them to revisit atomlight interaction.
This new tool for atomic physics has paved the way to gaseous Bose
Einstein Condensates and the many recent developments at the
frontier between Condensed Matter Physics and Atomic Molecular
and Optical Physics
40