E. Maréchal, O. Gorceix , P. Pedri, Q. Beaufils, B. Laburthe, L. Vernac,
B. Pasquiou (PhD), G. Bismut (PhD)
Excitation of a dipolar BEC and Quantum MagnetismExcitation of a dipolar BEC and Quantum Magnetism
We study the effects of Dipole-Dipole Interactions (DDIs) in a 52 Cr BEC
M. EfremovIFRAF post doc
A. de Paz1st year PhD student
Radu Chicireanuformer PhD student
J.C. KellerR. Barbéformer members
A. Crubeliercollaboration (theory)
6 electrons in the outer shells
Specificities of chromium
S=3 in the ground state
permanent magnetic moment 6 µBparamagnetic gas with ratherstrong dipole-dipole interactions(DDIs)
DDIs change the physics of a polarized BEC(all atoms in the same Zeeman substate)
DDIs allow the cold gas magnetization to change
High temperature oven (T=1350°C in our case)
Obtaining a chromium BEC
Preliminary works of J. Mc Clelland (NIST) - Tilman Pfau, J. Mlynek
Trapping Transition at 425 nm
High inelastic loss rates due to light assisted collisions
choice of the materials
needs to double a Ti:Sa laser
low atom number MOT
Experiment at Stuttgart (Tilman Pfau)
High dipolar relaxation rate BEC only possible in an optical trap
Accumulation in metastable states is efficient Red light repumpers required
Our way to BEC: direct loading of an optical trap in metastable states
optimization of the loading with depumping to a new metastable state + use of RF sweep
Physics of a dipolar BEC at Villetaneuse
polarized BECin the ground statemS=-3
polarized BECin the excited statemS=+3
unpolarized ultra cold gas
Study of dipolar relaxationin 3D, 2D, 1D, and 0D
Spin Flip
lowerB field
BEC excitations("quadrupole" mode)
S=3 spinor gas withfree magnetization
BEC excitations (phonons, free particle,…)
multi-component BEC
D wave Fescbach resonance
RF association of molecules
Ground State RF induced degeneracy
Braggspectroscopy
trapmodulation
I- Dipole – dipole interactions in a polarized chromium BEC
how DDIs have been evidenced in ground state BECs
why larger effects are expected with the excitations (phonons, free particles, …)
how do we observe them
II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field
study of S=3 spinor gas with free magnetization
how thermodynamics is modified when the spin degree of freedom is released
observation of a phase transition due to contact interactions:below a critical B field we observe a multi-component BEC
Summary of the talkSummary of the talk
Dipole-dipole interactions (DDIs)
Anisotropic Long Range
20
212m dd
ddVdW
m V
a V
Relative strength of dipole-dipole and Van-der-Waals interactions
0.16dd
Different interactions in a polarized Cr BEC
alkaline 1dd01.0dd for 87Rb
chromium
Bm 6dysprosium 1dd
1ddfor the BEC is unstable
polarmolecules
Bm 10
1dd
ddcext gVm
22
2
GPE :
')'()'()( 3rdrnrrVr dddd
3
220 cos31
4)(
rrV mdd
BJm gJ
R
Van-der-Waals interactions
sc am
g24
Isotropic Short Range
1m 2m
r
B
J. Stuhler, PRL 95, 150406 (2005)
Some effects of DDIs on Cr BECs
Eberlein, PRL 92, 250401 (2004)
Striction of the BEC(non local effect)
dd adds a non localanisotropic mean-field
B
Modification of theBEC expansion
0.16dd
The effects of DDIsare experimentallyevidenced bydifferential measurements,for two orthogonalorientations of the B field
DDIs
TF profile
B
1.2
1.0
0.8
0.6
2015105
Collective excitationsof a dipolar BEC
Bismut et al., PRL 105, 040404 (2010) t (ms)
Aspe
ct ra
tio
DDIs change in the few % range the ground state physics of a polarized BEC
DDIs induce changes smaller than dd !
Some effects of DDIs on Cr BECs
Trap anisotropy
Shift of the quadrupole
mode frequency (%)
Shift of the aspect ratio
(%)
)cos()(
)cos()(
)cos()(
0
0
0
tcRtR
tbRtR
taRtR
zz
yy
xx
A new and larger effect of DDIs: modification of the excitation spectrum of a Cr BEC
Experiment: probe dispersion law
c is the sound velocity
c depends on
In the BEC ground state the effects of DDIs are averaged due to their anisotropic nature
New idea: probe the effects of DDIs on other kind of excitations of the BEC
the dipolar mean field depends on trap geometry
the excitation spectrum is given by the Fourier Transform of the interactions
1cos33
)(~ 220
kmdd kV
Quasi-particles, phonons
measure the modification of c due to DDIs: 15% ?
kB all dipoles contribute
in the same way
kck
k
attractive and repulsive contributions of DDIs almost compensate
k
0.16dd
Excitation spectrum of a BEC with pure contact interactions
Rev. Mod. Phys. 77, 187 (2005)
c is the sound velocity
c is also the critical velocity
is the healing length
0( 2 )k k k cE E n g
Bogoliubov spectrum:
1k
m
kEk 2
22
/12 0 kgnE ck
Quasi-particles, phonons
1k Free particles kk E
kck
A 20% shift due to DDIs expected on the speed of sound !much larger than the (~3%) effects measured on the ground state and the "quadrupole" mode
An effect of the momentum-sensitivity of DDIs:
Excitation spectrum of a BEC in presence of DDIs
kB
1cos312 20 kddckkk gnEE
if , and if ,0k //cc 2/ k cc
0( 2 )k k k cE E n g becomes:
2.11
21///
dd
ddcc
0.16dd
k
1cos33
)(~ 220
kmdd kV
Excitation spectrum of a BEC: the local density approximation (LDA)
* the BEC is trapped, the density is not uniform
* the BEC has a non zero width momentum distribution
validity of LDA:
= the theory giving predictions that you can compare with
2222220 ///1)( TFzTFyTFx RzRyRxnrn
TFzRk /2 zuk
//with
k
LDA not valid at small k
TFzz Rk /1
two sources of broadening: the excitation spectrum of the BEC has a non zero width
and the effect of DDIs is going to be less than naively expected…
LDA = consider the gas locally uniform
Two laser beams detuned:Momentum and energy transfer
Excitation of a BEC: principle of Bragg Spectroscopy
1k
2k
21 kkk
)2/sin(2 Lkk
Lkkk 21
E
k
Bragg beams very far detunedfrom atomic resonances
For a given , tune to find a good excitation,and register the excitation spectrum
)2/sin(2 Lk
532L nm
= 100 Hz to 100 kHz
Bragg Spectroscopy: experimental realization
Two lasers "in phase" are required
We use two AOMs driven by a digital double RFsource providing two RF signals in phase
ttt )()( 21
For given (accessible) values of , we register excitation spectra
1k
2k
6° to 14°, 28°, 83°optical access we measure the excited fractionfor a given
excited and non-excited partsspatially separated by momentum transfer
Bragg Spectroscopy: experimental difficulties
* choice of t = the excitation duration (of the Bragg pulse)
* poor spatial separation of the excited fraction at low k
if t is too small, we add a Fourier broadening
if t is too large, the mechanical effect of the trap comes into play
kRk TFzz /1 to have a good spatial separation after expansion
zk
k/1k becomes hard to reach in our case
(we don't work with an elongated BEC)
nonexcited excited
excitedfraction
t << Ttrap / 4
not quite possible at low k…
t >> 1 / f
non excitedfraction
a) b)
d)c)
Bragg Spectroscopy: experimental difficulties
poor separation ofthe excited fractionat low k !
data analysiscomplicated,noisy data
no excitation = 6°
= 14° = 83°
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Width of resonance curve: finite size effects (inhomogeneous broadening)The excitation spectra depends on the relative angle between spins and excitation
Bragg Spectroscopy of a dipolar BEC: experimental results
Excitation spectra at =14°
iBk ,//
iBk ,
f //f
From the different spectra,registered for a given ,we deduce the value of:
2///
//
ff
ff
= shift of the excitationspectrum due to DDIs
Bragg Spectroscopy of a dipolar BEC: experimental results
q
0.20
0.15
0.10
0.05
0.00
-0.05
43210
14
8
2
x10-3
4.2
2///
//
ff
ff
11 2 3 4
1
0
0.1
0.2
k
1.2
1.0
0.8
0.6
2015105
Asp
ect
rati
o
Villetaneuse
Collective excitations
Striction
0.16dd
Anisotropicspeed of sound
0.15
0.10
0.05
0.00
3000200010000
Frequency difference (Hz)
Fra
ctio
n of
exc
ited
atom
s
Conclusion: a 52Cr BEC is a "non-standard superfluid"
StuttgartExpansion
I- Dipole – dipole interactions in a polarized chromium BEC
how DDIs have been evidenced in ground state BECs
why larger effects are expected with the excitations
how do we observe them
II- Demagnetization of ultracold chromium gases at "ultra" low magnetic field
Study of S=3 spinor gas with free magnetization
how thermodynamics is modified when the spin degree of freedom is released
observation of a quantum phase transition due to contact interactions: below a critical B field we observe a multi-component BEC
Summary of the talkSummary of the talk
DDIs can change the magnetization of the atomic sample
iyxr /
Elastic collision
Spin exchange
Inelastic collisions
Dipole-dipole interaction potential with spin operators:
Induces several types of collision:-101
222
111
212121
2
24
32
1
SrSrzS
SrSrzS
SSSSSS
z
z
zz
-1
-2
-3
Cr+3
+2
+1Cr BEC in -3
magnetizationbecomes free
0 totSm
iSSfSStotS mmmmm 2121
2,1 totSm
change in magnetization:
Optical trap
DDIs can change the magnetization of the atomic sample
iyxr /
0 lStot mm
Inelastic collisions
Dipole-dipole interaction potential with spin operators:
Induces several types of collision:
222
111
212121
2
24
32
1
SrSrzS
SrSrzS
SSSSSS
z
z
zz
-1
-2
-3
Cr+3
+2
+1Cr BEC in -3
magnetizationbecomes free
2,1 Stotm
rotation induced
=> Einstein-de-Haas effect
S=3 Spinor physics with free magnetization
- Up to now, spinor physics with S=1 and S=2 only
- Up to now, all spinor physics at constant magnetization exchange interactions (VdW), no DDIs
- The ground state for a given magnetization was investigated-> Linear Zeeman effect irrelevant
-101
New features with Cr
- First S=3 spinor (7 Zeeman states, four scattering lengths, a6 , a4 , a2 , a0)
- Dipole-dipole interactions free total magnetization
- We can investigate the true ground state of the system (need very small magnetic fields)
-10
1
-2-3
2
3
Ultra cold gas of spin 3 52Cr atoms at "ultra" low magnetic fields
ZeemanddVdWext VVVm2
2
The spin degree of freedom is unfrozen when:
7 components spinor
TkBg BBJ
Optical trap, (almost) sametrapping potential for the 7Zeeman states
3B mG at 400 nK
allows the magnetizationto change
Two different B regims for the ground state are predicted:when B > Bc , the Zeeman interactions dominate: one component (ferromagnetic) BECwhen B < Bc , the contact interactions dominate: multi-component (non-ferromagnetic) BEC
-1
-2
-3Bg BJ
Above Bc: is 52Cr close to a non-interacting S=3 gas with free magnetization ?
Why Bc ? What do we observe below Bc ?
S=3 spinor gas: the non interacting picture (I)
1/ Bk T
Single component Bose thermodynamics Multi-component Bose thermodynamics
Simkin and Cohen, PRA, 59, 1528 (1999) Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
Bmg SiBJi 03/10 )12(
1c
Bc T
ST
3/10 94.0 atcB NTk
TkBg BBJ
zyx nnn
zzyyxxctotth nnnNNN,,
11exp
zyx nnn
izzyyxxith nnnN,,
11exp
TkBg BBJ
-2
-1
01
2
3
-3-3-2-1 0
2 1
3
Similar to:M. Fattori et al., Nature Phys. 2, 765 (2006)at large B fields and in the thermal regime
average trap frequency
Tc is lowered
Magnetization
B phaseBEC in mS=-3
A phase(normal)
C phaseBEC in each component
0cT
T
0 -1 -2 -3
0.2
0.4
0.6
0.8
1.0
For Na:a double phasetransition expected
Evolution at fixedmagnetization
Evolution for a freemagnetization
Tc1(M)
Tc2(M)
3/1)12(
1
S
S=3 spinor gas: the non interacting picture (II)
For Cr:One BEC component,in mS= -3the absolute groundstate of the system
Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
Our results: magnetization versus T
B = 0.9 mG > Bc
Solid line: results of theorywithout interactions and free magnetization
the kink in magnetizationreveals BEC
Tc1
The BEC is ferromagnetic:only atoms in mS=-3 condense
The good agreement shows thatthe system behaves as ifthere were no interactions(expected for S=1)
thermal gasBEC inm=-3
Tc1 is the critical temperaturefor condensation of the spinor gas(in the mS=-3 component)
0103/1)12(
1ccc TTT
S
B0B
(i.e. in the absolute ground state of the system)
B > Bc
Pasquiou et al., ArXiv:1110.0786 (2011)
Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
measurement of Tc1(M),by varying B
0cT
T
Pasquiou et al., ArXiv:1110.0786 (2011)
Our results (II): measurements of Tc1B > Bc
The good agreement shows thatthe system behaves as if therewere no interactions(expected for S=1)
Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
histograms: spin populations
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-3.0-2.5-2.0-1.5-1.0-0.50.0
Magnetization
A
B
C
T (M)c1
T (M)c2
BEC in mS= -3
depolarized thermal gas
468
1000
2
468
-3 -2 -1 0 1 2 3
« bi-modal » spin distribution
A new thermometry
Only thermal gas depolarizes Cooling scheme if selective
losses for mS > -3e.g. field gradient
1.5
1.0
0.5
0.0
1.20.80.40.0
Time of flight Temperature ( K)
Spi
n T
empe
ratu
re (
K)
8000
6000
4000
2000
-3 -2 -1 0 1 2 3mS
popu
latio
n Boltzmanian fit
Tspin moreaccurate atlow T !
bimodal distribution
Our results (III): spin populations and thermometry B > Bc
Pasquiou et al., ArXiv:1110.0786 (2011)
S=3 Spinor physics below Bc: emergence of new quantum phases
-2-1
01
23
-3
As a6 > a4 , it costs no energy at Bc to go from mS=-3 to mS=-2 : the stabilizationin interaction energy compensates for the Zeeman energy excitation
the BEC isferromagnetici.e. polarized in lowest energy single particle state
Above Bc
046
2 )(27.0 n
m
aaBg cBJ
-2-1
01
23
-3
Below Bc
All the atoms in mS= -3interactions only in themolecular potential Stot= 6because ms tot = -6
The repulsive contactinteractions set by a6
If atoms are transferred in mS= -2then they can interact in the molecularpotential Stot= 4 because ms tot = -4
The repulsive contact interactions are set by a6 and a4
the BEC is nonferromagnetici.e. it is a multicomponent BEC
(1,0,0,0,0,0,0)
( )a,0,0,0,0,0, ( , , )a 0,0,0,0 ,0
( , )a 0,,0,g,0,
Bc
a0 (Bohr radius)0-10 -10
Mag
netic
fiel
d
All populated0
Allpopulated
S=3 Spinor physics below Bc: new quantum phases
Santos et Pfau PRL 96, 190404 (2006)Diener et Ho PRL 96, 190405 (2006)
For an S=3 BEC, contact interactions are set by four scattering lengths, a6 , a4 , a2 , a0
Quantum phases are results of an interplay between Zeeman and contact interactions
Quantum phases are set by contact interactions and differ by total magnetization
ferromagnetici.e. polarized in lowest energy single particle state
Critical magnetic field Bc
DDIs ensure the coupling between states with different magnetization
polarphase
046
2 )(27.0 n
m
aaBg cBJ
unknown
nematicphase
S=3 Spinor physics below Bc: spontaneous demagnetization of the BEC
BEC in mS=-3
Rapidly lower magnetic field below Bc
measure spin populations with Stern Gerlach experiment
1 mG
0.5 mG
0.25 mG
« 0 mG »
Experimental procedure:
-3 -2 -1 0 1 2 3
(a)
(b)
(c)
(d)
B=Bc
Bi>>Bc
Bf < Bc
Performances: 0.1 mG stabilitywithout magnetic shield, up to 1 Hour stability
Magnetic field control below .5 mG (!!) dynamic lock, fluxgate sensorsreduction of 50 Hz noise fluctuationsfeedback on earth magnetic field, "elevators"
BEC inall Zeemancomponents !
Pasquiou et al., PRL 106, 255303 (2011)
+ Nthermal << Ntot
20 6 42
J B c
n a ag B
m
3D BEC 1D Quantum gas
Bc expected 0.26 mG 1.25 mG
1/e fitted 0.3 mG 1.45 mG
Bc depends on density
1.0
0.8
0.6
0.4
0.2
0.0543210
Magnetic field (mG)
BEC BEC in lattice
Fin
al m
=-3
fra
ctio
n
2D Optical lattices increase the peak density by about 5
S=3 Spinor physics below Bc: local density effect
NoteSpinor Physics in 1 D canbe qualitatively differentsee Shlyapnikov and TsvelikNew Journal of Physics 13 065012 (2011)
Pasquiou et al., PRL 106, 255303 (2011)
Bulk BEC
2D optical lattices
In lattices (in our experimental configuration), the volume of the cloud is multiplied by 3
Mean field due to dipole-dipole interaction is reduced
Slower dynamics, even with higher peak densities
Non local character of DDIs
S=3 Spinor physics below Bc: dynamic of the demagnetization
Pasquiou et al., PRL 106, 255303 (2011)
Corresponding timescale for demagnetization:
good agreement with experiment both for bulk BEC ( =3 ms)and 1 D quantum gases ( = 10 ms)
At short times, transferbetween mS = -3 and mS = -2
~ a two level system coupled by Vdd
Simple model
But dynamics still unaccounted for:
BgVBBB BJddddc /
ddVt /
Bc
S=3 Spinor physics below Bc: thermodynamics change
B > Bc
B < BcB < Bc
B >> Bc
Tc1Tc2
for Tc2 < T < Tc1
BEC only in mS = -3
for T < Tc2 BEC in all mS !
for B < Bc, magnetization remains constantafter the demagnetization processindependent of T
This reveals the non-ferromagneticnature of the BEC below Bc
B=Bc(Tc2)
3
0
1
cT
T
TkBg BBJ
Pasquiou et al., ArXiv:1110.0786 (2011)
hint for doublephase transition
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-3.0-2.5-2.0-1.5-1.0-0.50.0
Magnetization
A
B
C
T (M)c1
T (M)c2
Thermodynamics of a spinor 3 gas: outline of our results
A phase: normal (thermal)
B phase: BEC in one component
C phase: multi-component BEC
evolutionfor B > Bc
evolutionfor B < Bc
In purple: our data
measurement of Tc1(M),by varying B
0cT
T
histograms: spin populations
Pasquiou et al., ArXiv:1110.0786 (2011)
Bc
reached
Conclusion: what does free magnetization bring ?
A quench through a (zero temperaturequantum) phase transition
- We do not (cannot ?) reach the new ground state phase
- Thermal excitations probably dominate but…
- … effects of DDIs on the quantum phases have to be evaluated
The non ferromagnetic phase is setby contact interactions,
but magnetization dynamics is set by dipole-dipole interactions
first steps towards exotic spinor ground state
- Spinor thermodynamics with free magnetization of a ferromagnetic gas - Application to thermometry / cooling
Above Bc
Below Bc
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