quantum magnetism with a dipolar bec...pasquiou et al., prl (2012) hint for double phase...
TRANSCRIPT
Collaborations: M. Gajda (Varsovie), L. Santos (Hannover)Former members: A. Chotia, B. Pasquiou
A. de Paz (PhD), A. Sharma (post-doc), B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri, O. Gorceix
Quantum magnetism with a dipolar BEC
dipole – dipoleinteractions
AnisotropicLong Range
20
212m dd
ddVdW
m Va V
µ µεπ
= ∝h
comparison of theinteraction strength
0.16ddε =
Dipolar Quantum gases
alcaline 1<<ddε01.0<ddε for 87Rb
chromium
Bm µµ 6=dysprosium 1≈ddε
1>ddεfor the BEC can become unstable
polarmolecules
Bm µµ 10=
1>>ddε
3
220 cos31
4)(
rrV mdd
θµπ
µ −=
r
BJm gJ µµ =
van-der-WaalsInteractions
sam
g24 hπ
=
IsotropicShort range
R
θ
1mµr2mµr
rr
erbium
Tc=few 100 nK
BEC
Quantum magnetism with a dipolar BEC
different spin dynamics induced by dipole-dipole interactions
change of Zeeman states populations in a S=3 BEC
-2-1
01
23
-3
magnetization = Sm
m mPS
S∑
I- demagnetization of the BECat low B field
II- dipolar relaxation in a 3D lattice
III- spin exchange in a 3D lattice
change of the magnetization
constant magnetization
-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 Bµ
Spin changing collisions
dipole-dipole interactionsinduce a spin-orbit coupling
( ) ( ) 02121 ≠+−+=∆ issfssS mmmmm
0=∆+∆ lS mmrotation induced
dipolarrelaxation
V -VV'
-V' magnetici
cf
c EEE ∆+= SBmagnetic mgE ∆=∆ µ
S=3 spinor gas: the non interacting picture
1/ Bk Tβ =
Single component Bose thermodynamics Multi-component Bose thermodynamics
Bmg SiBJi µµµ +=
03/10 )12(1
cBc TS
T+
→→
3/10 94.0 atcB NTk ωh=
TkBg BBJ >>µ
( )[ ]( )∑ −−++=−=zyx nnn
zzyyxxctotth nnnNNN,,
11exp ωωωβh
( ) ( )[ ]( )∑ −−+++=zyx nnn
izzyyxxith nnnN,,
11exp βµωωωβµβ h
TkBg BBJ ≈µ
-2-1
01
23
-3-3-2-10
21
3average trap frequency
Tc is lowered
at low B field excited states are thermally populatedthanks to dipole-dipole interactions
apply even if S>0if no dipole-dipole interactions
Our results: magnetization versus T
B = 0.9 mG > Bc
Solid line: results of theorywithout interactions andfree 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(1
ccc TTTS
<<+
∞→B0→B
(i.e. in the absolute ground state of the system)
B > Bc
Pasquiou et al., PRL 2012
Isoshima et al., J. Phys. Soc. Jpn, 69, 12, 3864 (2000)
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 thelowest energy single particle state
Above Bc
046
2 )(27.0 n
maa
Bg cBJ
−=
hπµ
-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 also 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
S=3 Spinor physics below Bc: spontaneous demagnetization of the BEC
BEC in mS=-3
Rapidly lower magnetic field below Bcmeasure 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 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
mπ
µ−
≈h
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
Fina
l m=-
3 fr
actio
n
2D Optical lattices increase the peak density by about 5
S=3 Spinor physics below Bc: local density effect
Pasquiou et al., PRL 106, 255303 (2011)
S=3 Spinor physics below Bc: thermodynamics change
B > BcB < Bc B < Bc
B >> Bc
Tc1Tc2
for Tc2 < T < Tc1 BEC only in mS = -3
for T < Tc2BEC 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
−=
cTT
TkBg BBJ >>µ
Pasquiou et al., PRL (2012)
hint for doublephase transition
-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 Bµ
Spin changing collisions
dipole-dipole interactionsinduce a spin-orbit coupling
( ) ( ) 02121 ≠+−+=∆ issfssS mmmmm
0=∆+∆ lS mmrotation induced
dipolarrelaxation
V -VV'
-V' magnetici
cf
c EEE ∆+= SBmagnetic mgE ∆=∆ µ
Dipolar Relaxation in a 3D lattice
dipolar relaxation is possible if:
( )zzyyxxi
c nnnE ωωω ++=∆ h)(
(and selection rules)
we observe that spinpopulationschange when :
latticec UE <∆
Ec is quantized
-3-2
-10
12
3
23,22,3
3,3)1( +++++
→++
2,2)2(
++→
kinetic energy gain
BgE Bc µ=∆ )1(
BgE Bc µ2)2( =∆
Dipolar relaxation in a 3D lattice - observation of resonances
width of the resonances: tunnel effect +field, lattice fluctuations
tunnel effect minimal in an excited states along Oy
study of the lowest resonance
nx , ny , nz
kHz
Bg BS µ
zyx nnn ,,0,0,03,3 ⊗→⊗++
1 mG = 2.8 kHz
(Larmor frequency)
23,22,3 +++++
2,2
kHzzyx )2(100,55,170 πωωω ===
yBS Bg ωµ h22 =
Initial Final
0,0,03,3 ⊗ 0,2,02,2 ⊗
pair orbital momentum
spin state
energy substructure relatedto onsite contact interactions
kHz
Bg BS µ
Dipolar relaxation in a 3D lattice – study of the first resonance
B (kHz)
Frac
tion
in m
=+3
our limit: lattice fluctuations
6,63;3 =good agreement between theory fortwo atoms per site and experimentboth for the shape and position of the resonance
Final spin states
Initial spin state
Dipolar relaxation in a 3D lattice – effect of onsite contact interactions
4,41154,6
1162;2 −=
6a
6a4a
B (kHz)
Frac
tion
dans
m=+
3
2
1test of the Mott distribution
atomic distribution expectedfor an adiabatic loading of the3D lattice (25 Er)
good agreement between theory fortwo atoms per site and experimentboth for the shape and position of the resonance
Dipolar relaxation in a 3D lattice – effect of onsite contact interactions
for a diabatic loading,sites with 3 atoms
(or more) are expected
"few-body" physicsproduction of intricated 3 body states
probe of the atomicdistribution in the lattice
Production of intricated states with a fast lattice loading
Theory for 3 atoms per site:4 resonances expected(4 different energies in the final state)
B (kHz)
Frac
tion
dans
m=+
3
good agreement between experimentand theory for three atoms per site
A. de Paz et al., (ArXiv december 2012)
0,0,23,2,20,0,03,3,3 ⊗→⊗ ∑spin orbit
-3-2-1
Spin exchange dynamics in a 3D lattice
vary time
B
dipolar relaxation suppressedevolution at constant magnetization
experimental sequence:
spin exchange from -2
first resonance0
10 mG
Preparation in an atomic excited state
-3 -2
-1
σ-π
-3
Ramantransition
-2 -3
laserpower
mS = -2
A σ- polarized laserClose to a J→J transition
(100 mW 427.8 nm)
creation of a quadratic light shift
-3 -2 -1 0 1 2 3
energy
quadratic effect
-3-2
-1
-1
0
1
-2-3 transfer in -2 ~ 80% transfer adiabatic
expected Mott distribution doublons removed = only singlons
Different Spin exchange dynamics in a 3D lattice
dipolar relaxation with
latticec UE >>∆
( )+−−+ +−= 212121ˆˆˆˆ
41ˆˆˆ SSSSSSH zzdd
Contact interaction (intrasite) Dipole-dipole interaction (intersite)
without spin changing term
4,41154,6
1162;2 −−−=−−
0.3
0.2
0.1
0.0
403020100
1.0
0.8
0.6
0.4
20151050
1.0
0.8
0.6
0.4
20151050Time (ms)
P/P
-3-2
Spin exchange dynamics in a 3D lattice: with only singlons
the spin populations change!
comparison with a plaquette model (Pedri, Santos)3*3 sites containing one atom – work in progressquadratic light shift and tunneling taken into accountProof of intersite dipolar coupling
time ms
relative populations
0.4
0.3
0.2
0.1
0.80.60.40.2time (ms)
popu
latio
ns mS=-3 mS=-2 mS=-1 mS=0
Spin exchange dynamics in a 3D lattice with doublons at short time scale
4,41154,6
1162;2 −−−=−−
Sgn0
SS am
g2
4 hπ=
initial spin state
onsite contact interaction:
( ) sggn
hTcontact µ280460
=−
=
spin oscillations with the expected periodstrong damping (rate > 1O J)
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
2 4 6 8 10 12 14
0.1
0.2
0.3
0.4
Time (ms)
Popu
latio
nsresult of ourtoy model:
Spin exchange dynamics in a 3D lattice with doublons at "long" time scale
two sites with two atoms
coordination factor (10)
our experiment allows the study of molecularCr magnets with larger magnetic moments than Cratoms, without the use of a Feshbach resonance
intersite dipolarcoupling
Spin exchange dynamics in a 3D lattice: strong reduction by a magnetic gradient
1.4
1.2
1.0
0.8
0.62015105
time (ms)
P/P
-2-3
0.6
0.4
0.2
0.05004003002001000
Magnetic gradient (Hz/266 nm)
Am
plitu
de
amplitude
if the spin dynamics results fromintersite coupling it should disappearwhen: >∆Bg BS µ dipolar coupling rate
-3-2-1
expected Mott distribution
doublons removed = only singlons
Different Spin exchange dynamics in a 3D lattice
intrasite contact intersite dipolar
intersite dipolar
( )1 2 1 2 1 214z zS S S S S S+ − − +− +
Heisenberg like hamiltonian
quantum magnetism withS=3 bosons and truedipole-dipole interactions
thank you for your attention!