Transcript Diapositive 1 - Paris 13 University

CLEO/Europe-EQEC Conference
Munich – 23 May 2011
Spin-3 dynamics study in a chromium BEC
Olivier GORCEIX
Laboratoire de Physique des Lasers
Université Paris Nord
Villetaneuse - France
Interactions in BECs
Van der Waals / contact interactions :
short range and isotropic at low T
Effective potential aS d(R), with aS = scattering length in channel S,
aS is magnetically tunable through Feshbach resonances
Dipole-dipole interactions : long range and anisotropic
magnetic atoms Cr, Er, Dy; dipolar molecules; Rydberg atoms
Chromium atoms carry a magnetic moment of 6µB
MDDI are 36 times bigger than in alkali BECs
We produce and study 52Cr Bose-Einstein Condensates
Chromium (S=3): contact AND dipole-dipole interactions
Dipole-dipole interaction potential
Vdd 
0 2
1
2
S  g J  B  1  3cos 2 ( )  3
4
R
Anisotropic
Non local anisotropic
mean-field

R
Coupling between spin
and rotation
PART ONE OF THE TALK
DIPOLAR RELAXATION INHIBITION
SPIN DYNAMICS IN AN OPTICAL LATTICE
How a 2D lattice can stabilize an unstable BEC ?
Inelastic collisions - dipolar relaxation DR
E  mS gB B
3
Zeeman energy
ladder
in B
2
0
-1
-2
-3
1
DR causes heating then losses
and the magnetic field strength
controls DR
Inelastic collisions - dipolar relaxation DR
B
Two allowed channels
for ground state atoms
3,3 
1
 3,2  2,3
2
3,3  2,2
3
2
0

with mS  1
with ms  2
  1 or 2
1
-1
-2
-3
mS  ml  0
K. Gawryluk et al. PRL 106, 140403 (2011)
M. Gajda, PRL 99, 130401 (2007)
B. Sun and L. You, PRL 99, 150402 (2007)
Plus many other…
Angular momentum conservation
Induces rotation in the BEC ?
Spontaneous creation of vortices ?
Einstein-de-Haas effect
Dipolar relaxation in optical lattices – Experimental procedure
Adiabatic loading of the ground state M = - 3 BEC in a 1D or a 2D lattice
Rf induced transition to the metastable state M = +3
Hold time while DR takes place
RF sweep back to M = -3
Detection
Produce BEC m=-3
detect m=-3
get the DR rate
BEC m=+3, hold time
Band mapping
adiabatic
01
-1
-2
-3
2
3
01
-1
-2
-3
2
3
Dipolar relaxation in optical lattices
Optical lattices:
periodic potential = ac-Stark shift in
a far-detuned standing wave
B
Lattices provide tightly confined geometries (tubes or pancakes)
They introduce a new energy scale and they change the initial and
final states space.
Above Bc , DR releases energy and creates a « mini-vortex » in a lattice site
gB B  L
m=3
m=2
Spin relaxation and band excitation in optical lattices
B ≈ 40 mG
Spin-flipped atoms get promoted
from the lowest band to the excited bands
when B is over the threshold set by
L
B
3
2
1
g B B  L
What do we measure in 1D ? (band mapping for B above threshold)
3
2
0
(b) Velocity
distribution
along the tubes
1
-1
-2
-3
z
z
(a)
m=3
y
nd
st
2
1
BZ BZ
nd
2
BZ
y
x
m=2
Population in different bands
due to dipolar relaxation
Heating due to collisional deexcitation from excited band
Dipolar relaxation inhibition in 1D (below Bc)
(a)
(b)
0.10
Temperature (K)
Fraction of atoms in v=1
0.12
0.08
0.06
0.04
3
2
1
0.02
0.00
0
40
80
120
160
Magnetic field (kHz)
20
60
100
140
Magnetic field (kHz)
Conversely (almost) complete suppression of dipolar relaxation in 1D
at low field in 2D lattices
B. Pasquiou et al., Phys. Rev. Lett. 106, 015301 (2011)
3D
-19
3 -1
Rate parameter (10 m s )
Log scale !!
10
3D trap
PRA 81,
042716 (2010)
1
2D
0.1
pancakes
1D
0.01
Phys. Rev. Lett.
106, 015301 (2011)
tubes
789
0.01
2
3
4 5 6 789
0.1
Magnetic field (G)
Above threshold: Vortices are expected to pop up
(EdH effect) but
they fade away by tunneling
Below threshold:
a (spin-excited) metastable 1D
quantum gas (>100ms) ;
Interest for spinor physics, spin
excitations in 1D…
PART TWO OF THE TALK
SPONTANEOUS DEMAGNETIZATION OF A SPINOR BEC
What happens at extremely low magnetic fields ?
ie when
gB B  µB
This happens for B <few 0.1 mG
S=3 Spinor physics with free magnetization
- To date, spinor studies have been restricted to S=1 and S=2
1
- Up to now, all spinor dynamics studies were restricted to
0
constant magnetization
-1
As required by contact interactions
- eg in Rb a pair of colliding atoms stays in the M = mS1+mS2 = 0 multiplicity
New features with Cr
-First S=3 spinor
- Dipole-dipole interactions free the magnetization
- Possible investigation
of the true many-body ground state of the system
(which requires stable and very small magnetic fields)
3
2
1
0
-1
-2
-3
Ferromagnetic phase of the spinor condensate
when
-1
B ≈ 4 mG the chemical potential
is much smaller than the Zeeman splittings
Starting point :
BEC in the m= -3 single particle ground state
Procedure:
lower B for example to 1mG
Detection TOF + Stern-Gerlach
-2
Ferromagnetic / polarized phase
-3
3
2
1
0
-1
-2 
-3
Above threshold
Spontaneous demagnetization of the spinor condensate
when
the final B ≈ 0.4 mG
then the chemical potential becomes on the order of Zeeman splittings
Starting point : BEC in the m= -3 single particle ground state
Procedure: lower the magnetic field
Detection TOF + Stern-Gerlach
3
0
-3
Above threshold
-2
1
2
-1
3
2
1
0
-1
-2 
-3
…spin-flipped atoms gain energy
Below threshold
S=3 multi-component BEC with free magnetization
7 Zeeman states; all trapped
four scattering lengths: a6, a4, a2, a0
3
2
1
0
-1
-2 
-3
Phase transitions can occur between:
Ferromagnetic / Polar/ Cyclic phases
3
-2
-1
-3
g J B Bc 
2 n0  a6  a4 
2
ferromagnetic
i.e. polarized in
the lowest energy
single particle
state
Magnetic field
0
1
2
Santos PRL 96,
190404 (2006)
Ho PRL. 96,
190405 (2006)
m
a0/a6
Spontaneous demagnetization : the
reason why it happens !
Contact interactions decide which spin
configuration has the lowest energy
at Bc, it costs no energy to go from m= -3 to m= -2
: loss in interaction energy compensates for the
gain in Zeeman energy)
Phases set by contact interactions
differ by their magnetization
Mean-field effect: when does the transition take place ?
g J B Bc 
Final m=-3 fraction
1.0
2 2 n0  a6  a4 
m
0.8
BEC
Lattice
Critical field
0.26 mG
1.25 mG
Demag time
3ms
10ms
0.6
0.4
BEC
BEC in lattice
0.2
0.0
0
1
2
3
4
Magnetic field (mG)
5
Critical field for depolarization depends on
the density (exp check for linearity)
Magnetic field control below
0.5 mG (actively stabilized)
(0.1mG stability)
(no magnetic shield…)
Remaining atoms in m=-3
Dynamics of the depolarization
1.0
Spontaneous demagnetization :
how it happens ? What triggers
the transistion ?
0.8
0.6
0.4
0.2
0.0
2
3
4
5
6
7 8 9
2
100
Time (ms)
B. Pasquiou et al., Phys. Rev. Lett.
(in the press) and arXiv:1103.4819
3
4
5
Phases are set by contact interactions,
while (de)magnetization dynamics is
due to and set by
dipole-dipole interactions
« quantum magnetism »
Timescale for depolarization:
(a few in 3D to 10 ms in the 2D lattice)
Conclusion
Dipolar relaxation in bulk BECs and in reduced dimensions
Spontaneous demagnetization in a quantum gas
-phase transition
-first steps towards evidence for spinor S=3 ground state structure
-spinor thermodynamics with free magnetization
Outlook
Towards a demonstration of Einstein-de-Haas effect - rotation in 3D lattice sites
Excitation spectrum (poster tomorrow and PRL 105, 040404 (2010))
Project : quantum gas of dipolar fermionic 53Cr
Acknowledgements
Financial support:
•Conseil Régional d’Ile de France
(Contrat Sésame)
•Ministère de l’Enseignement Supérieur
et de la Recherche (CPER, FNS and
ANR)
•European Union (FEDER)
•IFRAF
•CNRS
•Université Paris Nord
Group members : The Cold Atom Group in Paris Nord
Ph.D students:
Gabriel Bismut
Benjamin Pasquiou
www-lpl.univ-paris13.fr:8082
Permanent staff:
Bruno Laburthe-Tolra, Etienne Maréchal, Paolo Pedri, Laurent Vernac and O. G.
Former members
Arnaud Pouderous, Radu Chicireanu, Quentin Beaufils, Thomas Zanon,
Jean-ClaudeKeller, René Barbé
Post-doc position available (Q4 2011) apply now!!
www-lpl.univ-paris13.fr:8082
E.Maréchal, OG, P. Pedri, Q. Beaufils (PhD), B. Laburthe, L. Vernac, B. Pasquiou (PhD), G.
Bismut (PhD), D. Ciampini (invited), M. Champion, JP Alvarez (trainees)