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

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

3. Collective excitations
Striction
Stuttgart, PRL 95, (2005)
Collective excitations
Villetaneuse, PRL 105, (2010)
Anisotropic d-wave collapse when scattering length is reduced (Feshbach resonance)
Stuttgart, PRL 101, (2008)

4. Spin degree of freedom coupled to orbital degree of freedom
- Spinor physics and magnetization dynamics
without 1
Dipole-dipole interactions -1
with 3 2 R 1 -1 -2 -3

5. In a finite magnetic field: Fermi golden rule
B=0: Rabi
In a finite magnetic field: Fermi golden rule -3 -2 -1 1 2 3

6. 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) 6 6

7. From the molecular physics point of view
Energy
Interpartice distance
Rc = Condon radius
PRA 81, (2010)

8. Energy scale, length scale, and magnetic field
Molecular binding enery : 10 MHz
Magnetic field = 3 G
Inhibition of dipolar relaxation due to inter-atomic (VdW) repulsion
( is the scattering length)
Band excitation in lattice : 100 kHz
30 mG
Suppression of dipolar relaxation in optical lattices
( is the harmonic oscillator size)
Chemical potential : 1 kHz
.3 mG
Inelastic dipolar mean-field

9. 3 Gauss
Suppression of dipolar relaxation due to inter-atomic repulsion -3 -2 -1 1 2 3
…spin-flipped atoms gain so much energy they leave the trap

10. Feshbach resonance in d-wave PRA 79, 032706 (2009)
Dipolar relaxation in a Cr BEC
Rf sweep 1
Rf sweep 2
Produce BEC m=-3
BEC m=+3, vary time
detect BEC m=-3
Fermi golden rule
Born approximation Pfau, Appl. Phys. B, 77, 765 (2003)
PRA 81, (2010)
a6 = 103 ± 4 a0.
Feshbach resonance in d-wave PRA 79, (2009)
See also Shlyapnikov PRL 73, 3247 (1994)
a6 = ± 0.4 a0 10 10

11. Dipolar relaxation: measuring non-local correlations
L. H. Y. Phys. Rev. 106, 1135 (1957)
A probe of long-range correlations :
here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model 11

12. 30 mGauss Spin relaxation and band excitation in optical lattices2 3 1
Spin relaxation and band excitation in optical lattices
…spin-flipped atoms go from one band to another

13. Reduction of dipolar relaxation in optical lattices
Load the BEC in a 1D or 2D Lattice
Produce BEC m=-3
detect m=-3
Rf sweep 1
Rf sweep 2
BEC m=+3, vary time
Load optical lattice
One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice 13

14. PRA 81,
(2010)
Phys. Rev. Lett.
106, (2011)

15. (almost) complete suppression of dipolar relaxation in 1D at low field-3 -2 -1 1 2 3
Energy released
Band excitation
Kinetic energy along tubes
B. Pasquiou et al., Phys. Rev. Lett. 106, (2011)

16. a consequence of angular momentum conservation
(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices:
a consequence of angular momentum conservation
Above threshold :
should produce vortices in each lattice site (EdH effect)
(problem of tunneling)
Towards coherent excitation of pairs into higher lattice orbitals ?
Below threshold:
a (spin-excited) metastable 1D quantum gas ;
Interest for spinor physics, spin excitations in 1D…

17. .3 mGauss
Magnetization dynamics of spinor condensates -3 -2 -1 2 1 3 3 2 1 -1 -2 -3
…spin-flipped atoms loses energy
Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large fields and in the thermal regime

18. 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, no dipole-dipole interactions)
They investigate the ground state for a given magnetization
-> Linear Zeeman effect irrelavant 1 -1 3
New features with Cr
- First S=3 spinor (7 Zeeman states, four scattering lengths, a6, a4, a2, a0)
Dipole-dipole interactions free total magnetization
Can investigate the true ground state of the system
(need very small magnetic fields) 2 1 -1 -2 -3 18

19. S=3 Spinor physics with free magnetization -12 1 -2 2 1 -1 -1 -2 -2 -3 -3 -3
Large magnetic field : ferromagnetic
Low magnetic field : polar/cyclic -2 -3
Phases set by contact interactions (a6, a4, a2, a0)
– differ by total magnetization
Santos PRL 96,
(2006)
Ho PRL. 96,
(2006) 19

20. Magnetic field control below .5 mG (dynamic lock, fluxgate sensors)
At VERY low magnetic fields,
spontaneous depolarization of 3D and 1D quantum gases
1 mG
0.5 mG
Produce BEC m=-3
0.25 mG
« 0 mG »
Stern Gerlach experiments
Rapidly lower magnetic field
Magnetic field control below .5 mG (dynamic lock, fluxgate sensors)
(.1mG stability)
(no magnetic shield…) 20

21. Mean-field effect BEC Lattice Critical field 0.26 mG 1.25 mG
1/e fitted
0.4 mG
1.45 mG
Field for depolarization depends on density

22. Dynamics analysis
Meanfield picture : Spin(or) precession (Majorana flips)
When mean field beats magnetic field
Ueda, PRL 96, (2006)
Kudo Phys. Rev. A 82, (2010)
(a few ms)
Natural timescale for depolarization:

23. A quench through a zero temperature (quantum) phase transition-2 -1 1 2 3 -3
Santos and Pfau
PRL 96, (2006)
Diener and Ho
PRL. 96, (2006) -3 -2 -1 2 1 3 3 2 1
- Operate near B=0. Investigate absolute many-body ground-state
- We do not (cannot ?) reach those new ground state phases
Thermal excitations probably dominate
Phases set by contact interactions,
magnetization dynamics set by
dipole-dipole interactions
« quantum magnetism »
Also new physics in 1D:
Polar phase is a singlet-paired phase
arXiv: (Shlyapnikov-Tsvelik) 23

24. Only thermal gas depolarizes…
Prospect : new cooling method using the spin degrees of freedom -3 -2 -1 2 1 3
Above Bc:
Only thermal gas depolarizes…
get rid of it ?
(Bragg excitations
or field gradient)

25. Conclusion
Dipolar relaxation in BEC – new measurement of Cr scattering lengths
non-local correlations
Dipolar relaxation in reduced dimensions - towards Einstein-de-Haas
rotation in lattice sites
Spontaneous demagnetization in a quantum gas
- New phase transition
– first steps towards spinor ground state
(Spinor thermodynamics with free magnetization
– application to thermometry)
(Collective excitations – effect of non-local mean-field)

26. …one open Post-doc position in our group…
G. Bismut (PhD), B. Pasquiou (PhD) , A. de Paz
B. Laburthe, E. Maréchal, L. Vernac,
P. Pedri, M. Efremov (Theory),
O. Gorceix (Group leader)
…one open Post-doc position in our group… 26 26 26 26

27. Thermal effect: (Partial) Loss of BEC when demagnetization
Spin degree of freedom is released ; lower Tc
B=0
B=20 mG
PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000)
Dipolar interaction opens the way to spinor thermodynamics with free magnetization 27

28. Single component Bose thermodynamics

29. Multi-component Bose thermodynamics-3 -2 -1 2 1 3
Multi-component Bose thermodynamics -2 -1 1 2 3 -3
7 Zeeman states; all trapped
PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000)
temperature
magnetization

30. Non interacting spinor
Double phase transition at constant magnetization
Condensate fraction
temperature
temperature
magnetization
Magnetization
Magnetic field
No demagnetization at low temperature
Temperature

31. How to make a Chromium BEC
An atom: 52Cr
An oven
A Zeeman slower
425 nm
427 nm
650 nm
7S3
5S,D
7P3
7P4
A small MOT
Oven at 1425 °C
N = 4.106
T=120 μK
750
700
650
600
550
500
450
(1)
(2) Z
A dipole trap
All optical evaporation
A BEC
A crossed dipole trap

32. 32

33. BEC with Cr atoms in an optical trap
PRA 73, (2006)
PRA 77, (2008)
PRA 77, (R) (2008) 33

34. Thermal effect: (Partial) Loss of BEC when demagnetization
Spin degree of freedom is released ; lower Tc
temperature
Normal
« A phase »
A BEC in majority component
« B phase »
A BEC in each component
magnetization
PRA, 59, 1528 (1999) J. Phys. Soc. Jpn,   69, 12, 3864 (2000)
lower Tc: a signature of decoherence 34

35. Thermodynamics of a spinor gas with free magnetization
Above Bc, magnetization well accounted for by non interacting model
Above Bc, thermal gas depolarizes, but BEC remains polarized

36. Spin population and thermometry (above Bc)
BEC in m=-3
Depolarized thermal gas
A new thermometry ?
(limits to be checked)
« bi-modal » spin distribution

37. Threshold for dipolar relaxation in 1D:
(almost) complete suppression of dipolar relaxation in 1D at low field in 2D lattices
B. Pasquiou et al., Phys. Rev. Lett. 106, (2011) 37