1. Dipolar chromium BECs de Paz (PhD), A. Chotia, B. Laburthe-Tolra,
E. Maréchal, L. Vernac,
P. Pedri (Theory),
O. Gorceix (Group leader)
Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov , Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu
Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) 1 1 1 1

2. Chromium (S=3): Van-der-Waals plus dipole-dipole interactions
Long range
Anisotropic R
Relative strength of dipole-dipole and Van-der-Waals interactions
Cr: 2 2

3. Relative strength of dipole-dipole and Van-der-Waals interactions
BEC collapses
Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007)) R
Anisotropic explosion pattern reveals dipolar coupling.
Stuttgart: d-wave collapse, PRL 101, (2008)
See also Er PRL, 108, (2012)
See also Dy, PRL, 107, (2012)
… and Dy Fermi sea PRL, 108, (2012)
BEC stable despite attractive part of dipole-dipole interactions
Cr:

4. Hydrodynamic properties of a BEC with weak dipole-dipole interactions
Striction
Stuttgart, PRL 95, (2005)
Collective excitations
Villetaneuse,
PRL 105, (2010)
Anisotropic speed of sound
Bragg spectroscopy
Villetaneuse
arXiv: (2012)
Interesting but weak effects in a scalar Cr BEC 4

5. Dipolar interactions introduce magnetization-changing collisions
without 1
Dipole-dipole interactions -1 3
with 2 R 1 -1 -2 -3

6. In a finite magnetic field: Fermi golden rule (losses)
B=0: Rabi
In a finite magnetic field: Fermi golden rule (losses) -3 -2 -1 1 2 3
(x1000 compared to alkalis)

7. Dipolar relaxation, rotation, and magnetic field
Angular momentum conservation -3 -2 -1 1 2 3
Rotate the BEC ?
Spontaneous creation of vortices ?
Einstein-de-Haas effect
Important to control magnetic field
Ueda, PRL 96, (2006)
Santos PRL 96, (2006)
Gajda, PRL 99, (2007)
B. Sun and L. You, PRL 99, (2007) 7 7

8. Particle leaves the trap
B=1G
Particle leaves the trap -3 -2 -1 1 2 3
B=10 mG
Energy gain matches band excitation in a lattice
B=.1 mG
Energy gain equals to chemical potential in BEC

9. S=3 Spinor physics with free magnetization
New features with Cr:
S=3 spinor (7 Zeeman states, four scattering lengths, a6, a4, a2, a0)
No hyperfine structure
Free magnetization
Magnetic field matters !
Alkalis :
- S=1 and S=2 only
- Constant magnetization
(exchange interactions)
Linear Zeeman effect irrelevant
Technical challenges :
Good control of magnetic field needed (down to 100 mG)
Active feedback with fluxgate sensors
Low atom number – atoms in 7 Zeeman states

10. S=3 Spinor physics with free magnetization
New features with Cr:
S=3 spinor (7 Zeeman states, four scattering lengths, a6, a4, a2, a0)
No hyperfine structure
Free magnetization
Magnetic field matters !
Alkalis :
- S=1 and S=2 only
- Constant magnetization
(exchange interactions)
Linear Zeeman effect irrelevant
1 Spinor physics of a Bose gas with free magnetization
Thermodynamics: how magnetization depends on temperature
Spontaneous depolarization of the BEC due to spin-dependent interactions
2 Magnetism in opical lattices
Depolarized ground state at low magnetic field
Spin and magnetization dynamics

11. Spin temperature equilibriates with mechanical degrees of freedom
At low magnetic field: spin thermally activated -1 1 -2 -3 2 3
We measure spin-temperature by fitting the mS population
(separated by Stern-Gerlach technique) 11

12. Spontaneous magnetization due to BEC
T>Tc
T<Tc
Thermal population in Zeeman excited states
a bi-modal spin distribution
BEC only in mS=-3
(lowest energy state)
Cloud spontaneously polarizes !
Non-interacting multicomponent Bose thermodynamics:
a BEC is ferromagnetic
Phys. Rev. Lett. 108, (2012) 12

13. Below a critical magnetic field: the BEC ceases to be ferromagnetic !
B=100 µG
B=900 µG
Magnetization remains small even when the condensate fraction approaches 1
!! Observation of a depolarized condensate !!
Necessarily an interaction effect
Phys. Rev. Lett. 108, (2012) 13

14. Cr spinor properties at low field -13 3 2 2 1 1 -2 -1 -1 -2 -2 -3 -3 -3
Large magnetic field : ferromagnetic
Low magnetic field : polar/cyclic
Santos PRL 96,
(2006)
Ho PRL. 96,
(2006) -2 -3
Phys. Rev. Lett. 106, (2011) 14

15. Density dependent threshold
BEC
Lattice
Critical field
0.26 mG
1.25 mG
1/e fitted
0.3 mG
1.45 mG
Phys. Rev. Lett. 106, (2011)
Load into deep 2D optical lattices to boost density.
Field for depolarization depends on density
Note: Possible new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, (2011) 15

16. Dynamics analysis Meanfield picture : Spin(or) precession
Produce BEC m=-3
Rapidly lower magnetic field
PRL 106, (2011)
Meanfield picture :
Spin(or) precession
Ueda, PRL 96,
(2006)
Natural timescale for depolarization: 16

17. Phases set by contact interactions, dipole-dipole interactions
Open questions about equilibrium state
Phases set by contact interactions,
magnetization dynamics set by
dipole-dipole interactions
Santos and Pfau
PRL 96, (2006)
Diener and Ho
PRL. 96, (2006)
Magnetic field
Demler et al.,
PRL 97, (2006)
- Operate near B=0. Investigate absolute many-body ground-state
We do not (cannot ?) reach those new ground state phases
Quench should induce vortices…
Role of thermal excitations ?
Polar
Cyclic
!! Depolarized BEC likely in metastable state !! 17

18. 1 Spinor physics of a Bose gas with free magnetization
Thermodynamics: Spontaneous magnetization of the gas due to ferromagnetic nature of BEC
Spontaneous depolarization of the BEC due to spin-dependent interactions
2 Magnetism in 3D opical lattices
Depolarized ground state at low magnetic field
Spin and magnetization dynamics

19. -2 -3 Spontaneous demagnetization of atoms in a 3D lattice 3D lattice
Critical field
4kHz
Threshold seen
5kHz -3 -2

20. Control the ground state by a light-induced effective Quadratic Zeeman effect-1 1 -2 -3
Energy
A s- polarized laser
Close to a JJ transition
(100 mW nm)
D=a mS2
In practice, a p component couples mS states
Typical groundstate
at 60 kHz
Quadratic effect allows state preparation

21. 3D lattice (1 atom per site)
Adiabatic (reversible) change in magnetic state (unrelated to dipolar interactions)
quadratic effect t -2 -3
3D lattice (1 atom per site)
Note: the spin state reached without a 3D lattice is completely different !
Large spin-dependent (contact) interactions in the BEC have a very large effect on the final state -1 -2 1 -1 -2 -3 -3
BEC (no lattice)

22. Sign for intersite dipolar relaxation ?
Magnetization dynamics in lattice
(with 1 atom per site)
Load optical lattice
quadratic effect
vary time
Repolarization remains even with very few atoms
Sign for intersite dipolar relaxation ?

23. Magnetization dynamics resonance for two atoms per site-3 -2 -1 1 2 3
Dipolar resonance when released energy matches band excitation
Towards coherent excitation of pairs into higher lattice orbitals ?
(Rabi oscillations)
Mott state locally coupled to excited band
Resonance sensitive to atom number

24. Strong anisotropy of dipolar resonances
Anisotropic
lattice sites
At resonance
May produce vortices in each lattice site (EdH effect)
(problem of tunneling)
See also PRL 106, (2011)

25. Conclusions
Magnetization changing dipolar collisions introduce the spinor physics with free magnetization
New spinor phases at extremely low magnetic fields
Tensor light-shift allow to reach new quantum phases 0D
Control of dipolar relaxation in optical lattices
magnetization dynamics in optical lattices
can be made resonant
could be made coherent ?
towards Einstein-de-Haas (rotation in lattice sites)

26. de Paz, A. Chotia, B. Pasquiou (PhD), G. Bismut (PhD),
B. Laburthe, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov, O. Gorceix 26 26 26 26