Collaboration: L. Santos (Hannover) Former post doctorates : A. Sharma, A. Chotia

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

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

3. Dipolar physics with chromium atoms 52Cr S=3 permanent magnetic dipole moment = 6 µB dipole-dipole interactions anisotrope Van der Walls interactions long range New Physics compared to "usual" BECs Stuttgart group Villetaneuse group Cr Stanford group Stuttgart group Dy Innsbruck group Er

4. Dipolar physics with chromium atoms 52Cr S=3 permanent magnetic dipole moment = 6 µB dipole-dipole interactions anisotropic excitation spectra allow spin changing collisions magnetization becomes free spontaneous depolarization of a Cr BEC at low B field 1 mG (a) 0.5 mG (b) 0.25 mG (c) G. Bismut et al, Phys. Rev. Lett. 109, 155302 (2012 ) « 0 mG » (d) -3 -2 -1 0 1 2 3 B. Pasquiou et al., PRL 106, 255303 (2011)

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

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

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

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

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

10. Different Spin exchange dynamics in a 3D lattice Contact interaction (intrasite) -1 -2 -3 expected Mott distribution

11. Different Spin exchange dynamics in a 3D lattice Contact interaction (intrasite) Dipole-dipole interaction (intersite) -1 -2 no spin changing term -1 -2 -2 -3 -3 dipolar relaxation with doublons removed = only singlons expected Mott distribution

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

13. Spin exchange dynamics in a 3D lattice: with only singlons comparison with a plaquette model (Pedri, Santos) E(ms) = q mS2 3*3 sites , 8 sites containing one atom + 1 hole quadratic light shift and tunneling taken into account measured with interferometry Proof of intersite dipolar coupling Many Body system A. de paz et al Phys. Rev. Lett. 111, 185305 ( 2013)

14. Spin exchange dynamics in a 3D lattice: perspective two atoms: yes ! 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 No Yes example: separable Collaboration with Perola Milman and Thomas Coudreau group from Paris 7 Vitagliano, Hyllus, Egusquiza, and Toth PRL 107, 240502 (2011) Problem: find one relevant for your system

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

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

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

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? 2S+1 intermediate states Ising contribution gives different diagonal terms Ising term Exchange term "half period" of the exchange grows exponentially -2 -2 -3 -1 fast half period (au) slow -3 +3 +3 -3 S

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

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

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

23. Production of a degenerate quantum gas of fermionic chromium Strategy to start sympathetic cooling make a fermionic MOT, load the IR trap with 53Cr more than 10553Cr about 10652Cr make a bosonic MOT, load the IR trap with 52Cr + 6.10552Cr 3.10453Cr inelastic interspecies collisions limits to 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? one body losses evaporation

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

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

28. thank you for your attention!

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

30. Spin changing collisions V' V -V -V' from the ground state from the highest energy Zeeman state -1 +3 dipolar relaxation -2 +2 -3 +1 after an RF transfer to ms=+3 study of the transfer to the others mS spin changing collisions become possible at low B field dipole-dipole interactionsinduce a spin-orbitcoupling rotation induced the Cr BEC can depolarizeat low B fields At low B field the Cr BEC is a S=3 spinor BEC Cr BEC in a 3D optical lattice: coupling between magnetic and band excitations

31. Spin changing collisions V' V -V -V' from the ground state -1 1 mG (a) -2 0.5 mG (b) 0.25 mG -3 (c) « 0 mG » (d) spin changing collisions can depolarize the BEC at low B field -3 -2 -1 0 1 2 3 As a6 > a4 , it costs no energy at Bc to go from mS=-3 to mS=-2 : stabilization in interaction energy compensates for the Zeeman excitation At low B field the Cr BEC is a S=3 spinor BEC

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

33. Spin exchange dynamics in a 3D lattice 10 mG B 0 first resonance of the 3D lattice dipolar relaxation suppressed evolution at constant magnetization spin exchange from -2 experimental sequence: -1 -2 Load optical lattice -3 state preparation in -2 vary time Stern Gerlach analysis

34. mS = -2 Preparation in an atomic excited state -3 energy creation of a quadratic light shift Raman transition s- p -3 -2 -1 0 1 2 3 -1 A s- polarized laser Close to a JJ transition (100 mW 427.8 nm) -2 -1 -3 1 quadratic effect (laser power) -2 -3 laser power 0 -1 -3 -2 -2 transfer adiabatic transfer in -2 ~ 80% -3

35. Dipolar Relaxation in a 3D lattice kinetic energy gain Ec is quantized 3 dipolar relaxation is possible if: 2 1 0 -1 + selection rules -2 -3 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. Spin exchange dynamics in a 3D lattice with doublons at long time scale intersite dipolar coupling result of a two site model: 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 not fast enough: the system is many body

38. Different Spin exchange dynamics with a dipolar quantum gas in a 3D lattice -1 -2 -3 intrasite contact intersite dipolar expected Mott distribution Heisenberg like hamiltonian quantum magnetism with S=3 bosons and true dipole-dipole interactions doublons removed = only singlons intersite dipolar 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 field evolution of two coupled magnetic moments q

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 a0 the unknown scattering length of chromium

41. Production of a degenerate quantum gas of fermionic chromium So many lasers… 7P4 53Cr MOT : Trapping beams sketch 53Cr MOT : laser frequencies production 7S3 Lock of Ti:Sa 2 is done with an ultrastable cavity

42. Production of a degenerate quantum gas of fermionic chromium Spectroscopy and isotopic shifts isotopic shifts unknown 5D J=3 →7P° J=3 for the 52    //  5D J=3 F=9/2 →7P° 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 7P3) • isotopic shift: • mass term • orbital term

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

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