Exploring quantum magnetism in a Chromium Bose-Einstein Condensate

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1 CLEO Europe - IQEC Munich May 14th 013 Olivier GORCEIX Exploring quantum magnetism in a Chromium Bose-Einstein Condensate Laboratoire de Physique des Lasers Université Paris 13, SPC Villetaneuse - France

2 GPE / NLSE: Contact interactions in a standard condensate (one single internal state) m V ext g c Van der Waals Interaction dd Local mean field description g 4 c a s m The non-linear term spawns various interesting effects vortex, solitons, Josephson-like physics, squeezing, non-linear (atomic) optics

3 Two types of interactions between cold atoms Interactions Van der Waals / contact : short range and isotropic Effective potential a S d(r), where a S = scattering length, Dipole-dipole interactions : long range and anisotropic magnetic atoms Cr, Er, Dy ; dipolar molecules ; Rydberg atoms Chromium atoms carry a magnetic moment of 6µ B MDDI are 36 times greater than in alkali BECs e dd (Cr)=0,159 compared to e dd (Rb)=0,0044 e dd 0 mm 1 a V V dd VdW e dd = ratio : dipolar interactions / contact interactions if e dd 1 a 3D condensate is unstable

4 head to tail attraction Dipole-dipole interactions Side to side repulsion Links with magnetism, Phases, Frustration, R Coupling Between spin and rotation Least energy configuration

5 GPE / NLSE: The two types of interactions in a single state condensate Contact interaction g 4 c a s m Local mean field V ext g c m V dd dipole-dipole interactions ( r) dd dd ( r) 4 V dd ( r r') 0 13cos m 3 J m g J B r n( r') d 3 r' B Non local Anisotropic mean field m m1 R r Non-linear non-local and anisotropic terms enlarge the possible research opportunities.

6 Spin Exchange and dipolar relaxation DR in a multi-componant condensate - SPINOR dipole-dipole interaction and spin operators : Various types of collisions: Elastic collisions 1 S 1 z S z 3 zs 1 4r z zs r z / S 1 r S S 1 r S x iy S 1 r S S 1 r S +3 + Spin Exchange m S tot Inelastic collisions m S tot B 0 1, -1 - Magnetisation is constant except for inelastic collisions ms 1 ms ms ms f 1 i ms tot +1 Cr BEC M= 3 Strong heating -3 FORBIDDEN or not energetically (depending on T)

7 Inelastic Collisions Induced rotation B Two channels are open for two atoms in m = ,3 S 3,,3 with m 1 3,3, with m s 1 or m S m l 0 Angular momentum conservation implies rotation? Spontaneous creation of vortices? Einstein-de-Haas effect

8 Why do we care for spinors? «spinor» physics: combines On one hand, superfluidity and On the other hand, magnetism

9 well Part of it!! The experimental setup

10 INHIBITION OF DIPOLAR RELAXATION Stabilisation of the spinor gas by confinement in optical lattices

11 Inelastic Collisions dipolar relaxation DR E m S g B B Zeeman energy ladder in B field DR causes heating and losses ; B controls DR rate To start with one must prepare BEC in m = -3. When atoms are brought to +3 or any combinaison of m s > -3, one loses the BEC in a few milliseconds? How could we get a stable spinor? Set B extremely low (< 0,5 mg = 5 nt) Or trap the BEC in optical lattices (D, 1D or even 0D ie at the nodes of 3D OL)?

12 Rate parameter (10 m s ) Loss rate in log Scale!! D 3 D PRA 81, pancakes D 0.01 tubes 1 D Phys. Rev. Lett. 106, Magnetic field (G) Below threshold: a metastable quantum gas in a spin excited state (energy >> chemical potential) is produced ; Spinor Physics, spin excitations in 1D

13 Relaxation and band excitation Inhibition mechanism B 40 mg Atoms whose spin flips are promoted from the fondamental band to the excited band as B becomes greater than the threshold value set by gbb Below relaxation is forbidden. L B 3 L 1

14 Magnetism in a 3D optical lattice - Coherent vs incoherent spin dynamics We load the BEC into anisotropic 3D lattices

15 A NEW dipolar effect Dipolar relaxation resonances with (or more) atoms in m = +3 per site The combined anisotropies of the lattice and of the dipolar interaction account for the anisotropy of the relaxation spectra = remaining atoms vs B for two orthogonal orientations g BB L Dipolar relaxation occurs when the released energy matches a band excitation. Hold time 30 ms Here y / = 55 khz It couples -3, -3> to different bands depending on B orientation.

16 Dipolar relaxation resonance with atoms per site m=3 fraction Dipolar relaxation occurs when the released energy matches the band excitation g BB L Magnetic field (khz) Hold time 1 ms Here y / = 4 khz

17 Dipolar relaxation resonance with, 3 or more atoms per site

18 S = 3 Spinor physics From now, we forbid dipolar relaxation By setting B below 15 mg (lowest resonance in the deep OL) Magnetization remains constant All interactions are elastic Spin dynamics is coherent We study a S=3 spinor in a 3D lattice Typically 40 x 40 x 40 sites

19 Adiabatic preparation of a condensate in m = - with two atoms par site We monitor spin composition as time goes Interactions redistribute populations t

20 Spin Exchange within doubly occupied sites due to contact interactions Preparation : atoms per site Hold time - ; -> = a 6, -4> + b 4, -4> 4 B BG c na a m 6 4 (period 0 µs) Tunneling causes damping (still to fully analyse) (theory 50 µs)

21 Spin dynamics in a 3D lattice with 1 single atom per site (or less) Hold time populations m=-3 m=- Intersite spin redistribution 1 S1 S S1 S Time (ms) 15 0 (time scale 5 to 10 ms)

22 1.4 Preparation : atoms per site Coherent evolution at long time inter-site coupling by dipolar interaction pop(m=-3)/pop(m=-) Preparation : 1 single atom per site 5 10 time (ms) 15 0 For doublons the oscillation time scale rules out intra-site interactions A toy model with atoms in wells + dipolar interaction accounts for this time scale

23 Summary Inhibition of Dipolar Relaxation in reduced dimensions SPINOR Physics with S = 3 Coherent spin dynamics + inter-site dipolar interactions Spontaneous demagnetization -phase transition; -thermodynamics of a spin 3 gas with free magnetization Outlook In situ imaging Spin Textures dynamics of magnetic domains quantum magnetism simulation (in D + lattice) Einstein-de-Haas effect in a gas Production of a dipolar Fermi sea with 53 Cr New exotic magnetic phases

24 Cold Atom Team (GQD) in Villetaneuse - Paris Nord PhD students: Aurélie De Paz and Benjamin Pasquiou Post-docs: Amodsen Chotia and Arijit Sharma Permanent members: Bruno Laburthe-Tolra, Etienne Maréchal, Paolo Pedri (theory), Laurent Vernac and O. G. Collaborations: Mariusz Gajda and Luis Santos

25 Dipolar Quantum Gas Team www-lpl.univ-paris13.fr:808 OG, L. Vernac, J. Huckans (invited), P. Pedri, B. Laburthe, A. de Paz (PhD), A. Chotia (postdoc), A.Sharma (postdoc), E.Maréchal