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

2. Chromium : an artificially large spin (S=3):
(magnetic) dipole-dipole interactions
Long range
Anisotropic R
Van-der-Waals (contact) interactions
Short range
Isotropic 2 2

3. Anisotropic explosion pattern reveals dipolar coupling.
Hydrodynamic properties of dipolar BECs
Large dipolar interactions: spherical 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 (BEC, Innsbruck), or Dy (BEC, Fermi sea, Stanford)
… and heteronuclear molecules coming up …
For Cr, BEC stable despite attractive part of dipole-dipole interactions
Small (but interesting) effects observed – at the % level :
Striction – Stuttgart, PRL 95, (2005)
- Collective excitations - Villetaneuse, PRL 105, (2010)
- Anisotropic speed of sound, Villetaneuse, PRL 109, (2012)

4. Study magnetism with large spins (S=3)
This talk :
The impact of dipole-dipole interactions on
multicomponent (« spinor ») BEC
Magnetism
Anistropy :
Interactions couple spin and orbital degrees of freedom
Long-range interaction :
Intersite coupling in lattices
Study magnetism with large spins (S=3)
0 Introduction to spinor physics
1 Spinor physics of a Bose gas with free magnetization
2 (Quantum) magnetism in opical lattices 4 4

5. Introduction to spinor physics
Chapman,
Sengstock…
Exchange energy
Coherent spin oscillation
Klempt
Stamper-Kurn
Domains, spin textures, spin waves, topological states
Stamper-Kurn, Chapman, Sengstock, Shin…
Quantum phase transitions
Stamper-Kurn, Lett,
Gerbier

6. High Spin Fermions coming up…
Spin oscillations
(F=9/2 K atoms, Sengstock)
Pomeranchuk-like cooling
(Yb atoms)
New SU(N) symmetry (alkaline-earth atoms)
(see talk F. Schreck)
Rey, Gorshkov, Gurarie…

7. Dipole-dipole interactions
Main ingredients for spinor physics
Main new features with Cr
S=3
S=1,2,…
7 Zeeman states
4 scattering lengths
New structures
Spin-dependent contact interactions
Spin exchange
Strong spin-dependent contact interactions
Purely linear Zeeman effect -1 1
And
Dipole-dipole interactions
Quadratic Zeeman effect

8. Dipolar interactions introduce magnetization-changing collisions
Dipole-dipole interactions R -1 1
without -1 1
with

9. Dipolar relaxation, rotation, and magnetic field
Angular momentum conservation -3 -2 -1 1 2 3 1D
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)
B(mG) 9 9

10. S=3 Spinor physics with free magnetization
1 Spinor physics of a Bose gas with free magnetization (bulk)
2 (Quantum) magnetism in optical lattices
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

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)
Related to Demagnetization Cooling expts,
Pfau, Nature Physics 2, 765 (2006) 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 !
A non-interacting BEC is ferromagnetic
New magnetism, differs from solid-state
PRL 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
PRL 108, (2012) 13

14. Good agreement between field below which we see demagnetization and Bc-1
Cr spinor properties
at low field 3 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
Good agreement between field below which we see demagnetization and Bc
PRL 106, (2011) 14

15. 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)
Polar
Cyclic
!! Depolarized BEC likely in metastable state !!
- 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 ? 15

16. 0 Introduction to spinor physics
1 Spinor physics of a Bose gas with free magnetization
2 (Quantum) magnetism in opical lattices

17. Magnetization changing collisions
Study quantum magnetism with dipolar gases ?
Hubard model at half filling, Heisenberg model of magnetism (effective spin model)
Dipole-dipole interactions between real spins
Magnetization changing collisions

18. Mott state locally coupled to excited band
Magnetization dynamics resonance for a Mott state with two atoms per site (~15 mG)
Rf sweep 1
Rf sweep 2 -3 -2 -1 1 2 3
Load optical lattice
m=+3, wait time
Produce BEC m=-3
detect m=-3
Dipolar resonance when released energy matches band excitation
Mott state locally coupled to excited band
arXiv: (2012)

19. Spin dynamics at constant magnetization (<15mG)
From now on : stay away from dipolar magnetization dynamics resonances,
Spin dynamics at constant magnetization (<15mG)
Magnetization changing collisions
Can be suppressed in optical lattices
Differs from Heisenberg magnetism:
Related research with polar molecules:
A. Micheli et al., Nature Phys. 2, 341 (2006).
A.V. Gorshkov et al., PRL, 107, (2011),
See also D. Peter et al., PRL. 109, (2012)

20. Control the initial state by a tensor light-shift-1 -2
A s- polarized laser
Close to a JJ transition
(100 mW nm) -3
D=a mS2
Quadratic effect allows state preparation

21. Adiabatic state preparation in 3D lattice
quadratic effect t -2 -3
Initiate spin dynamics by removing quadratic effect
vary time
Load optical lattice
quadratic effect

22. Short times : fast oscillations due to spin-dependent contact interactions-3 -2 -1 G=
( 250 µs)
Up to now unknown source of damping
(sudden melting of Mott insulator ?)
(period  220 µs)
PRELIMINARY

23. Long time-scale spin dynamics in lattice : intersite dipolar exchange
Intersite dipolar interaction
(much slower than on-site dynamics)
Magnetization is constant
Intersite dynamics disappears in presence of a gradient

24. Spin dynamics for (at most) one atom per site
Effect of doublons ?
Oscillations arise from interactions between doubled-occupied sites
Slow spin dynamics for one particle per site:
Intersite dipole-dipole coupling

25. Theoretical understanding : dipolar spin exchange
(Very) long time-scale dynamics due to intersite dipolar exchange between singlons
MS=(-3, -2, -1, 0)
1/e timescale = 25 ms 10 20 30 40 50
Spin oscillations due to intersite dipolar exchange between doublons
Time (ms)
Calculation Paolo Pedri
Exact diagonalisation
Plaquette 3x2
336 states
Timescale = 4 ms
Faster coupling because larger effecive spin

26. spinor physics with free magnetization
Conclusions
Bulk Magnetism:
spinor physics with free magnetization
New spinor phases at extremely low magnetic fields
Lattice Magnetism:
Magnetization dynamics is resonant
Intersite dipolar spin-exchange

27. de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut,
B. Laburthe-Tolra, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov, O. Gorceix
Arijit Sharma
Aurélie
De Paz
Amodsen
Chotia 27 27 27 27