un condensat de chrome pour létude des interactions dipolaires. bruno laburthe tolra laboratoire de...
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Un condensat de chrome pour l’étude Un condensat de chrome pour l’étude des interactions dipolaires.des interactions dipolaires.
Bruno Laburthe Tolra
Laboratoire de Physique des LasersUniversité Paris NordVilletaneuse - France
Dipole-dipole interactions : ‘long range’ (1/r3) anisotropic répulsiverépulsive
attractiveattractive chromium:
Study of dipole-dipole interactions in Quantum Degenerate gases
Statistical physics at very low T
Bose-Einstein condensates Degenerate Fermi gases What about interactions ?
In most experiments (alkali) – Van-der-Waals interactions• ‘short-range’ (1/r6)• isotropic
• magnetic moment : 6µB => dipole dipole interactions x 36
• 1 boson et 1 fermion S=3
Ballistic expansion of the BEC modified by dipole dipole interactions
Tune contact interactions using Feshbach resonances: dipolar interaction larger than Van-der-Waals interaction
When dd~1, condensate not stable. Stability depends on trapping geometry.
Collapse of condensate reveals dipolar pattern.
First BEC : team of T. Pfau (Stuttgart 2005) Phys. Rev. Lett. 94, 160401 (2005)
Phys. Rev. Lett. 95, 150406 (2005)
Nature. 448, 672 (2007)
And… collective excitations, Tc, spinor physics, strong rf fields…
16.contact
dipolairedd V
V
répulsiverépulsive
attractiveattractive
All optical production of a Chromium BECAll optical production of a Chromium BEC
A Cr BEC in strong rf fieldA Cr BEC in strong rf field
An rf-assisted d-wave Feshbach resonanceAn rf-assisted d-wave Feshbach resonance
Des outils pour les interactions dipolairesDes outils pour les interactions dipolaires
0.8
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K3/
K3(
0)
76543210
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0
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Dis
plac
emen
t BE
C (m
)
543210
10-4
10-3
10-2
10-1
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10x1038642Time (ms)
Pha
se S
apce
Den
sity
How to make a Chromium BEC in 14s and one slide ?How to make a Chromium BEC in 14s and one slide ?
425 nm
427 nm
650 nm
7S3
5S,D
7P3
7P4
An atom: 52Cr
N = 4.106
T=120 μK
750700650600550500
600
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(1) (2)
Z
An experiment
A small MOT
A dipole trap
A crossed dipole trap An evaporation ramp
A BEC
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K3/
K3(
0)
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All optical production of a Chromium BECAll optical production of a Chromium BEC
A Cr BEC in strong rf fieldA Cr BEC in strong rf field
An rf-assisted d-wave Feshbach resonanceAn rf-assisted d-wave Feshbach resonance
Other things we can doOther things we can do
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Dis
plac
emen
t BE
C (m
)
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Control of the Landé factor Control of the Landé factor On can modify the Landé factor of the atoms gOn can modify the Landé factor of the atoms gJJ with with very strong off resonant rf fields. very strong off resonant rf fields.
If the RF frequency If the RF frequency ωω is larger than the Larmor frequency is larger than the Larmor frequency ωω00, , ggJJ is modified : is modified :
• Serge Haroche thesis• S.Haroche, et al., PRL 24 16 (1970)
0.2 0.4 0.6 0.8 1 1.2 1.4
-3
-2
-1
1
2
3
Rf power
Eig
ene
nerg
ies
Can we use this Can we use this degeneracy for spinor degeneracy for spinor physics ?physics ?See L. Santos et al., PRA See L. Santos et al., PRA 7575, , 053606 (2007)053606 (2007)
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280260240220200180160140
-3-2-1 0
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Dis
plac
emen
t BE
C (m
)
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40
0
V(r)
B (t)rf
2'),(
2
1t
m
Bgm BJS
1.0
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Pro
babi
lity
toco
me
back
tom
=-3
2 3 4 5 6 7 8100
2 3 4 5 6 7 81000
Sweep time ( s)
2 5 02 0 01 5 01 0 05 0
1 8 0
1 7 0
1 6 0
1 5 0
1 4 0
2 5 02 0 01 5 01 0 0
1 8 0
1 7 0
1 6 0
1 5 0
1 4 0
2 5 02 0 01 5 01 0 05 0
1 7 0
1 6 0
1 5 0
1 4 0
2 0 01 5 01 0 0
1 8 0
1 7 0
1 6 0
1 5 0
1 4 0
2 0 01 5 01 0 05 0
1 7 0
1 6 0
1 5 0
1 4 0
2 0 01 5 01 0 05 0
1 8 0
1 7 0
1 6 0
1 5 0
1 4 0
2.8
3.6
m=-3 30
t =500 s
t =20 s
t =25 s
t =32 s
t =50 s
t =80 s
Modified motion of dressed atoms in a magnetic potential
Timescales for adiabaticity of dressing
1.0
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0.0
-0.5
-1.0
2000150010005000
2pardt
d
-3
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-1
0
1
2
3
543210
répulsiverépulsive
attractiveattractive
Elastic s-wave collisions: Rf does not couple different molecular potentials -> s-wave elastic collisions should be unchanged.
Collision properties of off-resonantly rf dressed states :
)(tBgdt
drfJ
)(tBrf
)(t
cste
Dipolar interactions:« geometrical averaging ? » (non calculated)
1/e
life
tim
e (m
s)
3
4
5
6789
100
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3
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5
6789
6 7 80.1
2 3 4 5 6 7 81
2 3 4
•No emission of rf photons during a collision•An inelastic collision in a fixed (rf) field -> Dipolar relaxation•Roughly ok for thermalization ? Other atoms ?
Inelastic collision properties of off-resonantly rf dressed states :
Two timescales : collision time << dressing time.
Beware of the lowest energy state argument !!
-3
-2
-1
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543210
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K3/
K3(
0)
76543210
All optical production of a Chromium BECAll optical production of a Chromium BEC
A Cr BEC in strong rf fieldA Cr BEC in strong rf field
An rf-assisted d-wave Feshbach resonanceAn rf-assisted d-wave Feshbach resonance
Other things we can doOther things we can do
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0
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Dis
plac
emen
t BE
C (m
)
543210
At ultra-low temperature scattering is inhibited in l>0, because atoms need to tunnel through a centrifugal barrier to collide: collisions are « s-wave ». In a « d-wave » Feshbach resonance, tunneling is resonantly increased by the presence of a bound molecular state.
Su
pere
last
ic c
olli
sion
To probe a feshbach resonance: 3 body losses
Tunneling to short internuclear distance is increased by a Feshbach resonance.
A third atom triggers superelastic collisions, leading to three-body losses, as the kinetic gained greatly exceeds the
trap depth
A d-wave Feshbach resonance in chromium
| 6; 5; 0SS m l
Bg B
| 6; 6; 2; 1S lS m l m
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-0.1
-0.2
4321
Internuclear distance (arb.)
Ene
rgy
(arb
.)
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0.0
25.525.024.524.023.523.022.5
14 .
Thr
ee-b
ody
loss
par
amet
er (
m s
)
M ag n e tic fie ld (M h z)
6-1
3
4
5
6
789
104
2
3
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5
Ato
mN
umb
er
252015105Time (s)
Three-body losses measured
Original temperature dependence
Conclusions: - « 2-body » three-body losses.-Loss parameter proportionnal to T-Feshbach coupling measured; very narrowUseful to tailor anisotropic interactions ?
psdFeshbach coupling
nnn dBm 3
Rf spectrocopy of the Feshbach resonance
Resonant (three-body) losses when =Eb-Ei
Bg B
Rf photon
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-0.1
-0.2
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We modulate the magnetic field close to the Feshbach resonance. The colliding pair of atoms emits a photon while it is colliding, and the pair of atoms is transfered into a bound molecule
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rf r
eson
ance
(kH
z)
25.0x103
24.524.023.523.022.522.0 Magnetic field (kHz)
25x103
20
15
10
5
0
Atom
Num
ber after 7s (no rf)
Rf spectroscopy: not so high precision…
Amplitude of losses analysis: A radio-frequency assisted d-wave A radio-frequency assisted d-wave Feshbach resonance in the strong field regimeFeshbach resonance in the strong field regime
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K3(
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kHz kHz kHz kHz kHz kHz kHz
13(exp)3 0, JKK
We describe a four body process (three atoms and one photon) by a simple analytical Bessel function !
Magnetic field
Energy
All optical production of a Chromium BECAll optical production of a Chromium BEC
A Cr BEC in strong rf fieldA Cr BEC in strong rf field
An rf-assisted d-wave Feshbach resonanceAn rf-assisted d-wave Feshbach resonance
Other things we can doOther things we can do
12x103
10
8
6
4
2
0
Det
ecte
d at
oms
450400350300Final rf frequency (kHz)
Rf spectro, quadratic ligth shifts Rf spectro, quadratic ligth shifts (QLS) (QLS) and state preparationand state preparation
- Rf spectroscopy – magnetic field characterization- A BEC near B=0- Prepare a condensate in arbitrary m states
Magnetic field
Stern-Gerlach experiments / Rabi oscillationsStern-Gerlach experiments / Rabi oscillations
35
0
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0
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40
-3 -2 -1 0 21 3
Single shot image from BEC10 000 atomsSpin population measurementUseful for spinor physics and dipolar physics (spin exchange, relaxation at zero field)
2 mm
5000
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0
100806040200Temps pulse micros
Collective excitationsCollective excitations« Historically » collective excitations are an excellent tool to probe interactions in condensates . Dipolar effects can be revealed, by measuring collective excitation frequencies to better than 5 percent.
Requirements and open questions:
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6
TF
rad
ius
x (p
ixel
)
108642 Time (ms)
10
5
0
TF
radius z (pixel)
Pressure-driven dynamicsToo wide oscillations to reveal dipole interaction
•Velocity smaller than sound velocity: RTF<<RTF
•Beware of anharmonicity !!•How far in the Thomas Fermi regime is needed ?
Today: shot to shot noise in the TF radius too important.
Work on laser pointing stabilization (PZT on mirror).
1D Optical lattices1D Optical lattices
Soon in the lab...
2D dipolar gases.repulsive interactions:
reduction of three-body recombination
events ? (discussions P. Pedri)
Other lattice geometry will need other experimental
apparatus
Fermion: (a long way) towards a dipolar Fermion: (a long way) towards a dipolar Fermi seaFermi sea
53Cr: MOT N = 5.105 fermions
T=120 μK
density = 2.5 1010 atoms /cm3
Loading rate = 107 atoms/s
R. Chicireanu et al.Phys. Rev. A 73, 053406 (2006)
A MOT for a mixture (52Cr- 53Cr): N52,53 ~ 105 atoms
Route to degeneracy unknown:Sympathetic cooling ?Scattering cross-section ?Trapping geometry ?Feshbach resonances ?New science chamber design needed
Fermions : non vanishing interactions when T→0
Thermalization in a polarized Fermi gas ?
Money:
Conseil Régional d’Ile de France (Contrat Sésame)
Ministère de l’Education, de l’Enseignement Supérieur et de la Recherche
European Union (FEDER – Objectif 2)
IFRAF (Institut Francilien de Recherche sur les Atomes Froids)
• Fermions:
Phys. Rev. A 73, 053406 (2006)
• Cr Metastable:
Phys. Rev. A 76, 023406 (2007)
• Optical trapping metastable:
Eur. Phys. J. D 45 189 (2007)
• Rf sweeps:
Phys. Rev. A , 77 , 053413 (2008)
•BEC:
Phys.Rev. A 77, 061601(R) (2008)
Thanks!Thanks!
Former PhDs:A. Pouderous
R. Chicireanu
PhD:Q. Beaufils (2nd year)
ATER:T. Zanon (leaving)
Permanent people:B. Laburthe-Tolra, E. Maréchal,
L. Vernac, (R. Barbé), J.C. Keller
O. Gorceix
Newt yearPaolo Pedri (post-doc, theory)
P. Bismut, B. Pasquiou (thèse)
Collabration
Anne Crubellier (Laboratoire Aimé Cotton)