1. Collaboration: L. Santos (Hannover) Former post doctorates : A. Sharma, A. Chotia Former Students: Antoine Reigue A. de Paz (PhD), B. Naylor (PhD), J. Huckans (visitor), O. Gorceix, E. Maréchal, L. Vernac, P. Pedri, B. Laburthe-Tolra Spin Exchange with ultra cold chromium atoms

2. Outline Magnetism due to dipolar spin exchange with ultracold bosons Production of a chromium Fermi sea Dipolar physics with chromium atoms

3. dipole-dipole interactionspermanent magnetic dipole moment = 6 µ B S=3 anisotrope 52 Cr long range New Physics compared to "usual" BECs Stuttgart group Villetaneuse group Cr Stuttgart group Stanford group Dy Innsbruck group Er Van der Walls interactions

4. Dipolar physics with chromium atoms dipole-dipole interactionspermanent magnetic dipole moment = 6 µ B S=3 anisotropic excitation spectra 52 Cr 1 mG 0.5 mG 0.25 mG « 0 mG » -3-20123 (a) (b) (c) (d) allow spin changing collisions magnetization becomes free spontaneous depolarization of a Cr BEC at low B field B. Pasquiou et al., PRL 106, 255303 (2011) G. Bismut et al, Phys. Rev. Lett. 109, 155302 (2012 )

5. Dipolar physics with chromium atoms dipole-dipole interactionspermanent magnetic dipole moment = 6 µ B S=3 52 Cr allow spin exchange processes at a distance 0 +1 Phys. Rev. Lett. 92, 140403 (2004) spin 1spin 1/2 observed with contact (van der Walls) interactions

6. Dipolar Spin Exchange: a tool for Quantum Magnetism Ising term Exchange term DDIs provide a Heisenberg-like Hamiltonian with direct spin-spin interactions: Spin Exchange can be obtained through Van der Walls interactions… … for atoms closeby (contact interactions) Specific study of dipolar Spin Exchange in separated geometries 3D lattices with one atom per site double well trap

7. Quantum Magnetism with cold atoms tunneling assisted super exchange U Heisenberg Hamiltonian Magnetism ie quantum phases not set by ddi but by exchange interactions What is (are) the (quantum) phase(s) of a given crystal at "low" T ? anti ferromagneticferromagnetic Quantum Magnetism: what is it about?

8. Quantum Magnetism with a dipolar species in a 3D lattice long range = beyond the next neighbor direct spin-spin interaction real spin magnetic dipole moment S=3 quantum regime, high filling factor V dd = 10-20 Hz T < 1 nK Spin dynamics in an out of equilibrium system V dd to reach ground state similar work in Jun Ye group but there are many differences Heisenberg like Hamiltonian

9. Cr BEC loaded in a 3D lattice: a Mott state spin preparation in the excited Zeeman state ms=-2 -2 0 1 2 3 -3 Quantum Magnetism with a chromium BEC in a 3D lattice -2 0 1 2 3 -3 constant magnetization magnetization = spin exchange? S=3 measurement of the evolution of the Zeeman states populations

10. expected Mott distribution Different Spin exchange dynamics in a 3D lattice Contact interaction (intrasite) -2 -3

11. expected Mott distribution doublons removed = only singlons Different Spin exchange dynamics in a 3D lattice dipolar relaxation with Contact interaction (intrasite) Dipole-dipole interaction (intersite) no spin changing term -2 -3 -2 -3

12. Spin exchange dynamics in a 3D lattice: with only singlons the spin populations change! time (ms) P -3 /P -2

13. Spin exchange dynamics in a 3D lattice: with only singlons 3*3 sites, 8 sites containing one atom + 1 hole quadratic light shift and tunneling taken into account Proof of intersite dipolar coupling Many Body system E(m s ) = q m S 2 measured with interferometry comparison with a plaquette model (Pedri, Santos) A. de paz et al Phys. Rev. Lett. 111, 185305 ( 2013)

14. Spin exchange dynamics in a 3D lattice: perspective A giant Entanglement? How to prove it? Entanglement witness entangled separable EW = condition fulfilled by all full separable sates If EW violated, then state is entangled example: Vitagliano, Hyllus, Egusquiza, and Toth PRL 107, 240502 (2011) Collaboration with Perola Milman and Thomas Coudreau group from Paris 7 separable two atoms: yes ! No Yes Problem: find one relevant for your system

15. Dipolar Spin exchange dynamics with a new playground: a double well trap -3 +3 N atoms R idea: direct observation of spin exchange with giant spins, "two body physics" compensating the increase in R by the number of atomsrealization: load a Cr BEC in a double well trap + selective spin flip frequency of the exchange: precession of one spin in the B field created by N spins at R R = 4 µmj = 3 B field created by one atom N = 5000 Hz

16. Dipolar Spin exchange dynamics in a double well trap: realization realizing a double well spin preparation N atoms in -3 RF spin flip in a non homogeneous B field non polarizing lateral displacement beam splitter N atoms in +3

17. Spin exchange dynamics in a double well trap: results No spin exchange dynamics! Hz -3+3 Spin analysis by Stern Gerlach: as long as no m s =0 are detected, negative m s belong to one well, positive m s to the other

18. Inhibition of Spin exchange dynamics in a double well trap: interpretation What happens for quantum magnets in presence of an external B field when S increases? Ising termExchange term 2S+1 intermediate states "half period" of the exchange grows exponentially Ising contribution gives different diagonal terms S half period (au) fast slow -2 -3 -3 +3

19. Inhibition of Spin exchange dynamics in a double well trap: interpretation Evolution of two coupled magnetic moments if no more exchange possible It is as if we had two giant spins interacting Transition from quantum to classical magnetism  in presence of an external B field A. de paz et al, arXiv:1407.8130 (2014) accepted at Phys Rev A

20. Dipolar Spin exchange observed in 3D lattice frozen for double well

21. Production of a degenerate quantum gas of fermionic chromium the Fermi sea family: 6 Li 3 He* 173 Yb 161 Dy 87 Sr 167 Er 53 Cr dipolar cooling strategies: - sympathetic cooling - cooling of a spin mixture - "dipolar" evaporative cooling 40 K non applicable for us

22. Production of a degenerate quantum gas of fermionic chromium Loading a one beam Optical Trap with ultra cold chromium atoms direct accumulation of atoms from the MOT in metastable states RF sweep to cancel the magnetic force of the MOT coils for 53 Cr : finding repumping lines crossed dipole trap

23. Production of a degenerate quantum gas of fermionic chromium Strategy to start sympathetic cooling make a fermionic MOT, load the IR trap with 53 Cr make a bosonic MOT, load the IR trap with 52 Cr more than 10 5 53 Cr about 10 6 52 Cr inelastic interspecies collisions limits to 3.10 4 53 Cr + 6.10 5 52 Cr not great, we tried anyway… sympathetic cooling

24. Production of a degenerate quantum gas of fermionic chromium Evaporation

25. Production of a degenerate quantum gas of fermionic chromium Why such a good surprise? evaporation one body losses

26. Production of a degenerate quantum gas of fermionic chromium Results N at In situ images parametric excitation of the trap trap frequencies Expansion analysis slightly degenerated

27. Production of a degenerate quantum gas of fermionic chromium What can we study with our gas? Fermionic magnetism very different from bosonic magnetism ! T=200 nK T=50 nK T=10 nK Larmor frequency (kHz) Population in m F =-9/2 Fermi T=0 Boltzmann minimize E tot -2 0 1 2 3 -3 Picture at T= 0 and no interactions -7/2 -5/2 -3/2 -1/2 1/2 3/2 -9/2 5/2 7/2 9/2

28. thank you for your attention!

29. dipole – dipole interactions Anisotropic Long Range comparison of the interaction strength Dipolar Quantum gases alcaline for 87 Rb chromium dysprosium forthe BEC can become unstable polar molecules van-der-Waals Interactions Isotropic Short range R erbium T c = few 100 nK BEC

30. -2 -3 +3 +2 +1 the Cr BEC can depolarize at low B fields from the ground statefrom 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 m S At low B field the Cr BEC is a S=3 spinor BECCr BEC in a 3D optical lattice: coupling between magnetic and band excitations Spin changing collisions dipole-dipole interactions induce a spin-orbit coupling rotation induced dipolar relaxation V -V V' -V'

31. -2 -3 from the ground state spin changing collisions can depolarize the BEC at low B field At low B field the Cr BEC is a S=3 spinor BEC Spin changing collisions V -V V' -V' 1 mG 0.5 mG 0.25 mG « 0 mG » -3-20123 (a) (b) (c) (d) As a 6 > a 4, it costs no energy at B c to go from m S =-3 to m S =-2 : stabilization in interaction energy compensates for the Zeeman excitation

32. Dipolar relaxation in a 3D lattice - observation of resonances width of the resonances: tunnel effect + B field, lattice fluctuations n x, n y, n z kHz 1 mG = 2.8 kHz (Larmor frequency)

33. -3 -2 Spin exchange dynamics in a 3D lattice vary time Load optical lattice state preparation in -2 B dipolar relaxation suppressed evolution at constant magnetization experimental sequence: spin exchange from -2 first resonance of the 3D lattice 0 10 mG Stern Gerlach analysis

34. Preparation in an atomic excited state -3 -2 --  -3 Raman transition -2 -3 laser power m S = -2 A  - polarized laser Close 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 (laser power) -3 -2 0 1 -2 -3 transfer in -2 ~ 80% transfer adiabatic

35. Dipolar Relaxation in a 3D lattice dipolar relaxation is possible if: + selection rules E c is quantized -3 -2 0 1 2 3 kinetic energy gain If the atoms in doubly occupied sites are expelled

36. Spin exchange dynamics in a 3D lattice with doublons at short time scale initial spin state onsite contact interaction: spin oscillations with the expected period strong damping contact spin exchange in 3D lattice: Bloch PRL 2005, Sengstock Nature Physics 2012

37. result of a two site model: Spin exchange dynamics in a 3D lattice with doublons at long time scale two sites with two atoms dipolar rate raised (quadratic sum of all couplings) our experiment allows the study of molecular Cr2 magnets with larger magnetic moments than Cr atoms, without the use of a Feshbach resonance intersite dipolar coupling not fast enough: the system is many body

38. -3 -2 expected Mott distribution doublons removed = only singlons Different Spin exchange dynamics with a dipolar quantum gas in a 3D lattice intrasite contact intersite dipolar Heisenberg like hamiltonian quantum magnetism with S=3 bosons and true dipole-dipole interactions de Paz et al, Arxiv (2013)

39. Inhibition of Spin exchange dynamics in a double well trap: interpretation (1) What happens for classical magnets? evolution in a constant external B fieldevolution of two coupled magnetic moments 

40. Contact Spin exchange dynamics from a double well trap after merging after merging without merging Spin exchange dynamics due to contact interactions Fit of the data with theory gives an estimate of a 0 the unknown scattering length of chromium

41. Production of a degenerate quantum gas of fermionic chromium 53 Cr MOT : Trapping beams sketch Lock of Ti:Sa 2 is done with an ultrastable cavity 53 Cr MOT : laser frequencies production So many lasers… 7S37S3 7P47P4

42. Production of a degenerate quantum gas of fermionic chromium Spectroscopy and isotopic shifts 5 D J=3 → 7 P° J=3 for the 52 // 5 D J=3 F=9/2 → 7 P° J=3 F=9/2 for the 53 Shift between the 53 and the 52 line: 1244 +/-10 MHz Deduced value for the isotopic shift: Center value = 1244 -156.7 + 8 = 1095.3 MHz Uncertainty: +/-(10+10) MHz (our experiment) +/-8 MHz (HFS of 7 P 3 ) isotopic shift: -mass term -orbital term isotopic shifts unknown

43. Production of a degenerate quantum gas of fermionic chromium Results N at In situ images parametric excitation of the trap trap frequencies Expansion analysis Temperature slightly degenerated

44. Production of a degenerate quantum gas of fermionic chromium Degeneracy criteria A quantum gas ? 3D harmonic trap Chemical Potential