Un condensat de chrome pour létude des interactions dipolaires. Bruno Laburthe Tolra Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse.

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

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K3/

K3(

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76543210

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Dis

plac

emen

t BE

C (m

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543210

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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(

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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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

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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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40

0

V(r)

B (t)rf

2'),(

2

1t

m

Bgm BJS

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Pro

babi

lity

toco

me

back

tom

=-3

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Sweep time ( s)

2 5 02 0 01 5 01 0 05 0

1 8 0

1 7 0

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1 6 0

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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

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2pardt

d

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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

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6789

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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 !!

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K3(

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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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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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4321

Internuclear distance (arb.)

Ene

rgy

(arb

.)

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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

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789

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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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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

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Atom

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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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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

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6

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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

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Single shot image from BEC10 000 atomsSpin population measurementUseful for spinor physics and dipolar physics (spin exchange, relaxation at zero field)

2 mm

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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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ius

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ixel

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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)