Post on 17-Jan-2016
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Collaboration: L. Santos (Hannover)
Former post doctorates : A. Sharma, A. Chotia
Former Students: Antoine Reigue
A. de Paz (PhD), B. Naylor (PhD), J. Huckans (visitor), O. Gorceix , E. Maréchal, L. Vernac , P. Pedri, B. Laburthe-Tolra
Spin Exchange with ultra cold chromium atomsSpin Exchange with ultra cold chromium atoms
Outline
Magnetism due to dipolar spin exchange with ultracold bosons
Production of a chromium Fermi sea
Dipolar physics with chromium atoms
Dipolar physics with chromium atoms
dipole-dipole interactions permanent magnetic dipole moment= 6 µB
S=3
anisotrope
52Cr
long range
New Physics compared to "usual" BECs
Stuttgart group
Villetaneuse groupCr
Stuttgart group
Stanford group
DyInnsbruck group
Er
Van der Walls interactions
Dipolar physics with chromium atoms
dipole-dipole interactions permanent magnetic dipole moment= 6 µB
S=3
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
iBk ,//
iBk , anisotropic
excitation spectra
52Cr
1 mG
0.5 mG
0.25 mG
« 0 mG »
-3 -2 -1 0 1 2 3
(a)
(b)
(c)
(d)
allow spin changing collisions
magnetizationbecomes free
spontaneous depolarization ofa Cr BEC at low B field
B. Pasquiou et al., PRL 106, 255303 (2011)
G. Bismut et al, Phys. Rev. Lett. 109, 155302 (2012 )
Dipolar physics with chromium atoms
dipole-dipole interactions permanent magnetic dipole moment= 6 µB
S=3 52Cr
allow spin exchange processesat a distance
-1
0
+1
Phys. Rev. Lett. 92, 140403 (2004)
spin 1spin 1/2
observed with contact (van der Walls) interactions
Dipolar Spin Exchange: a tool for Quantum Magnetism
termschangingspinSSSSSSr
H zzdd
2121213
2ˆˆˆˆ
4
1ˆˆcos1ˆ
Ising term Exchange term
DDIs provide a Heisenberg-like Hamiltonian with direct spin-spin interactions:
Spin Exchange can be obtained through Van der Walls interactions…
… for atoms closeby (contact interactions)
Specific study of dipolar Spin Exchangein separated geometries
3D lattices with one atom per site
double well trap
Quantum Magnetism with cold atoms
tunneling assisted super exchange
t t
2t
U
U
Heisenberg Hamiltonian
Magnetism ie quantum phases not set by ddi but by exchange interactions
What is (are) the (quantum) phase(s) of a given crystal at "low" T ?
anti ferromagnetic ferromagnetic
Quantum Magnetism: what is it about?
Quantum Magnetism with a dipolar species in a 3D lattice
long range = beyond the next neighbor
direct spin-spin interaction
real spin
magnetic dipole moment
S=3
quantum regime, high filling factor
Vdd = 10-20 Hz T < 1 nK
Spin dynamics in an out of equilibrium system
Vdd
to reach ground state
2121213
2
ˆˆˆˆ4
1ˆˆcos1ˆ SSSSSSr
H zzdd
similar work in Jun Ye groupbut there are many differences
Heisenberg like Hamiltonian
Cr BEC loaded in a 3D lattice:a Mott state
spin preparation in the excited Zeeman state ms=-2
-2
01
23
-3
-1
Quantum Magnetism with a chromium BEC in a 3D lattice
-2
01
23
-3
-1 constant magnetization
magnetization = Sm
m mPS
S
spin exchange?
S=3
measurement of the evolutionof the Zeeman states populations
expected Mott distribution
Different Spin exchange dynamics in a 3D lattice
Contact interaction (intrasite)
4,411
54,6
11
62;2
-2
-1
-3
expected Mott distribution doublons removed = only singlons
Different Spin exchange dynamics in a 3D lattice
dipolar relaxation with
latticec UE
2121213
2ˆˆˆˆ
4
1ˆˆcos1ˆ SSSSSSr
H zzdd
Contact interaction (intrasite) Dipole-dipole interaction (intersite)
no spin changing term
4,411
54,6
11
62;2
-2
-1
-3
-2 -2-1
-3
Spin exchange dynamics in a 3D lattice: with only singlons
the spin populations change!
1.0
0.8
0.6
0.4
0.2
0.0
302520151050
time (ms)
P-3/P-2
Spin exchange dynamics in a 3D lattice: with only singlons
3*3 sites , 8 sites containing one atom + 1 holequadratic light shift and tunneling taken into account
Proof of intersite dipolar couplingMany Body system
E(ms) = q mS2
measured withinterferometry
comparison with a plaquette model (Pedri, Santos)
A. de paz et alPhys. Rev. Lett. 111, 185305 ( 2013)
Spin exchange dynamics in a 3D lattice: perspective
A giant Entanglement?3,1
2
11,3
2
12;2
How to prove it? Entanglement witness
entangled
separable
EW = condition fulfilled by all full separable satesIf EW violated, then state is entangled
example: jNJJJ zyx 222N
jJ
Vitagliano, Hyllus, Egusquiza, and Toth PRL 107, 240502 (2011)Collaboration withPerola Milman andThomas Coudreaugroup from Paris 7
separable
two atoms: yes !
NoYes
Problem: find one relevant for your system
2121ˆˆˆˆ SSSS
Dipolar Spin exchange dynamics with a new playground: a double well trap
-3 +3
NR
j3
0
4
N atoms N atoms
R
idea: direct observation of spin exchange with giant spins, "two body physics"
compensating the increase in R by the number of atoms realization: load a Cr BEC in a double well trap + selective spin flip
frequency of the exchange:precession of one spin in the B fieldcreated by N spins at R
R = 4 µm j = 3
B field created by one atom
N = 5000
102 Hz
Dipolar Spin exchange dynamics in a double well trap: realization
realizing a double well spin preparation
N atoms in -3
RF spin flip in a non homogeneous B field
non polarizing lateraldisplacement beam splitter N atoms in +3
Spin exchange dynamics in a double well trap: results
No spin exchange dynamics!Hz1024 3
0
N
R
j
-3 +3
Spin analysis by Stern Gerlach:as long as no ms=0 are detected, negative ms belong to one well, positive ms to the other
Inhibition of Spin exchange dynamics in a double well trap: interpretation
What happens for quantum magnets in presenceof an external B field when S increases?
2121213
2ˆˆˆˆ
4
1ˆˆcos1ˆ SSSSSSr
H zzdd
Ising term Exchange term
2S+1 intermediate states
1 2 3 4 5
1 0
1 0 0
1 0 0 0
1 0 4
"half period" of the exchangegrows exponentially
Ising contributiongives differentdiagonal terms
S
half period (au) fast
slow
-2 -2 -3 -1
-3 -3+3 +3
Inhibition of Spin exchange dynamics in a double well trap: interpretation
extB
Evolution of two coupled magnetic moments
dipolarext BBB 2,1if
no more exchange possible
It is as if we had two giant spins interactingTransition from quantum to classical magnetism1B
jR30
2
4
2
in presence of an external B field
A. de paz et al, arXiv:1407.8130 (2014) accepted at Phys Rev A
Dipolar Spin exchange
observed in 3D latticefrozen for double well
Production of a degenerate quantum gas of fermionic chromium
the Fermi sea family: 6Li 3He* 173Yb 161Dy87Sr 167Er 53Cr
dipolar
cooling strategies:- sympathetic cooling- cooling of a spin mixture- "dipolar" evaporative cooling
40K
non applicable for us
Production of a degenerate quantum gas of fermionic chromium
Loading a one beam Optical Trap with ultra cold chromium atoms
direct accumulation of atoms from the MOTin metastable states RF sweep to cancel the magnetic force of the MOT coils
for 53Cr : finding repumping lines
crossed dipole trap
Production of a degenerate quantum gas of fermionic chromium
Strategy to start sympathetic cooling
make a fermionic MOT, load the IR trap with 53Cr
make a bosonic MOT, load the IR trap with 52Cr
more than 105 53Cr
about 106 52Cr
inelastic interspecies collisions limits to 3.104 53Cr + 6.105 52Cr
not great, we tried anyway…
sympathetic cooling
Production of a degenerate quantum gas of fermionic chromium
Evaporation
Production of a degenerate quantum gas of fermionic chromium
Why such a good surprise?
BBBBBB NNfVn
dt
dN )(
FFBFBF NNfVn
dt
dN )(
)()()(
ln
)()()(
ln
212
1
212
1
tttNtN
tttNtN
B
B
F
F
BB
BF
evaporation one body losses
Production of a degenerate quantum gas of fermionic chromium
Results
Nat
In situ images
parametric excitation of the trap
trapfrequencies
Expansion analysis
1000370)6( 3/1 atatB
mF NifnKN
kT
500300 atNifnK
nKT 20220
slightly degenerated
Production of a degenerate quantum gas of fermionic chromium
What can we study with our gas?
Fermionic magnetism very different from bosonic magnetism !
0 1 2 3 4 5
0 .20 .40 .60 .81 .0
T=200 nK
T=50 nK
T=10 nK
Larmorfrequency(kHz)
Populationin mF=-9/2
Fermi T=0
Boltzmann
minimize Etot
-2-1
01
2
3
-3
Picture at T= 0 and no interactions
-7/2
-5/2
-3/2-1/2
1/2
3/2
-9/2
5/27/2
9/2
3/4
FF mmmFermi NE
FmLmFZ mNEF
FL EL
thank you for your attention!
dipole – dipoleinteractions
Anisotropic Long Range
20
212m dd
ddVdW
m V
a V
comparison of theinteraction strength
0.16dd
Dipolar Quantum gases
alcaline 1dd01.0dd for 87Rb
chromium
Bm 6dysprosium 1dd
1ddfor the BEC can become unstable
polarmolecules
Bm 10
1dd
3
220 cos31
4)(
rrV mdd
BJm gJ
van-der-WaalsInteractions
sam
g24
IsotropicShort range
R
1m 2m
r
erbium
Tc= few 100 nK
BEC
-1
-2
-3
+3
+2
+1
the Cr BEC candepolarize at low B fields
from the ground state from the highest energy Zeeman state
spin changing collisions become possible at low B field after an RF transfer to ms=+3 study of the transfer to the others mS
At low B field the Cr BEC is a S=3 spinor BEC Cr BEC in a 3D optical lattice: coupling between magnetic and band excitations
Bg B
Spin changing collisions
dipole-dipole interactions induce a spin-orbit coupling
02121 issfssS mmmmm
0 lS mmrotation induced
dipolarrelaxation
V -VV'
-V' magnetici
cf
c EEE SBmagnetic mgE
-1
-2
-3
from the ground state
spin changing collisions can depolarize the BEC at low B field
At low B field the Cr BEC is a S=3 spinor BEC
Bg B
Spin changing collisions
02121 issfssS mmmmmV -VV'
-V' magnetici
cf
c EEE SBmagnetic mgE
1 mG
0.5 mG
0.25 mG
« 0 mG »
-3 -2 -1 0 1 2 3
(a)
(b)
(c)
(d)
As a6 > a4 , it costs no energy at Bc to go from mS=-3 to mS=-2 :stabilization in interaction energy compensates for the Zeeman excitation
046
2 )(27.0 n
m
aaBg cBJ
Dipolar relaxation in a 3D lattice - observation of resonances
width of the resonances: tunnel effect +B field, lattice fluctuations
nx , ny , nz
kHz
Bg BS
zyx nnn ,,0,0,03,3
1 mG = 2.8 kHz
(Larmor frequency)
2
3,22,3
2,2
kHzzyx )2(100,55,170
zzyyxxB nnnBg 21
-3-2-1
Spin exchange dynamics in a 3D lattice
vary timeLoad
optical
lattic
e
state preparation in -2
B
dipolar relaxation suppressedevolution at constant magnetization
experimental sequence:
spin exchange from -2
first resonanceof the 3D lattice
0
10 mG
Stern Gerlach analysis
Preparation in an atomic excited state
-3 -2
-1
-
-3
Ramantransition
-2 -3
laserpower
mS = -2
A - polarized laserClose to a JJ transition
(100 mW 427.8 nm)
creation of a quadratic light shift
-3 -2 -1 0 1 2 3
energy
quadratic effect(laser power)
-3-2
-1
-1
0
1
-2-3
transfer in -2 ~ 80% transfer adiabatic
Dipolar Relaxation in a 3D lattice
dipolar relaxation is possible if:
zzyyxxi
c nnnE )(
+ selection rules
latticec UE
Ec is quantized
-3-2
-10
12
3
2
3,22,3 3,3
)1(
2,2)2(
kinetic energy gain
BgE Bc )1(
BgE Bc 2)2(
latticec UE If the atoms in doubly occupied sites are expelled
0.4
0.3
0.2
0.1
0.80.60.40.2
time (ms)
popu
lati
ons
mS=-3 mS=-2 mS=-1 mS=0
Spin exchange dynamics in a 3D lattice with doublons at short time scale
4,411
54,6
11
62;2
Sgn0
SS am
g2
4
initial spin state
onsite contact interaction:
sggn
hTcontact 300
460
spin oscillations with the expected periodstrong damping
contact spin exchange in 3D lattice:Bloch PRL 2005, Sengstock Nature Physics 2012
0.4
0.3
0.2
0.1
0.014121086420
Time (ms)
mS=-3 mS=-2 mS=-1 mS=0
Popu
latio
ns
result of atwo site model:
Spin exchange dynamics in a 3D lattice with doublons at long time scale
two sites with two atomsdipolar rate raised(quadratic sum of all couplings)
our experiment allows the study of molecularCr2 magnets with larger magnetic moments than Cratoms, without the use of a Feshbach resonance
intersite dipolarcoupling
not fast enough:the system is many body
-3-2-1
expected Mott distribution
doublons removed = only singlons
Different Spin exchange dynamics with a dipolar quantum gas in a 3D lattice
intrasite contact intersite dipolar
intersite dipolar
1 2 1 2 1 2
1
4z zS S S S S S
Heisenberg like hamiltonian
quantum magnetism withS=3 bosons and truedipole-dipole interactions
de Paz et al, Arxiv (2013)
Inhibition of Spin exchange dynamics in a double well trap: interpretation (1)
What happens for classical magnets?
evolution in a constant external B field
B
M
BMdt
Md
cteM z cteMBE z
evolution of two coupled magnetic moments
cteM zyx ,, cteBMBME 2112 ..
1B
jR30
2
4
BjM
2
Contact Spin exchange dynamics from a double well trap after merging
after merging
without merging
Spin exchange dynamics due to contact interactions
Fit of the data with theory gives an estimate of a0 the unknown scattering length of chromium
Production of a degenerate quantum gas of fermionic chromium
53Cr MOT :Trapping beams sketch
Lock of Ti:Sa 2 isdone with an ultrastable cavity
-245 -150 0
7 7S P3 4Lock
-12,5
R1 MOTMOT
53
52
F=5/2 F’=7/2
Zs53R2 MOT53
F=7/2 F’=9/2
-450 +305
F=9/2 F’=11/2
MOT53
ZSR1 ZS
52
53
Laser 1
225
Laser 2
+75
2*112,5
320
2*112
-413
F=3/2 F’=5/2
F=9/2
F=7/2
F=5/2
F=9/2
F=7/2
F=5/2
Coo
ling
bea
ms
R1
R2
376 MHz
293 MHz
209 MHz
66 MHz
53 MHz
40 MHz
F=11/2
F=3/2
53Cr MOT :laser frequencies production
So many lasers…
7S3
7P4
Production of a degenerate quantum gas of fermionic chromium
Spectroscopy and isotopic shifts
5D J=3 →7P° J=3 for the 52 // 5D J=3 F=9/2 →7P° J=3 F=9/2 for the 53
Shift between the 53 and the 52 line: 1244 +/-10 MHz
Deduced value for the isotopic shift: Center value = 1244 -156.7 + 8 = 1095.3 MHz
Uncertainty: +/-(10+10) MHz (our experiment) +/-8 MHz (HFS of 7P3)
isotopic shift:-mass term-orbital term
isotopicshiftsunknown
Production of a degenerate quantum gas of fermionic chromium
Results
Nat
In situ images
parametric excitation of the trap
trapfrequencies
Expansion analysis
220
2 2)( t
m
Tkwtw B
2
2
exp)(w
xxP
2
22 w
x
Temperature
1000370)6( 3/1 atatB
m NifnKNk
500300 atNifnK
nKT 20220
slightly degenerated
0 1 2 3 4
1
2
3
4
5
Production of a degenerate quantum gas of fermionic chromium
Degeneracy criteria
3/1)6( atB
m
B
FF N
kk
ET
3/1)(94.0 atB
mBEC N
kT
A quantum gas ?
2)( g
3D harmonic trap
FE
0)( 1
)(
e
dgNat
1
1)( e
FET )0(
FF ETT 25.0)5.0(
Chemical Potential
FF ETT 8.1)(
3
3
6ln)(F
BFT
TTkTT
FTT 1.0e
0 1 2 3 4
0.5
1.0
1.5
2.0
FTT 5.0
0 1 2 3 4
0 .0 5
0 .1 0
0 .1 5
0 .2 0
FTT
TkB
1