Collaborations: L. Santos (Hannover) Students: Antoine Reigue, Ariane A.de Paz (PhD), B. Naylor, A. Sharma (post-doc), A. Chotia (post doc), J. Huckans (visitor), O. Gorceix, E. Maréchal, L. Vernac, P. Pedri, B. Laburthe-Tolra Recent results with ultra cold chromium atoms

Outline Quantum Magnetism with ultracold bosons Production of a chromium Fermi sea

Quantum Magnetism: what is it about? 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 ferromagnetic ferromagnetic

Quantum Magnetism with cold atoms tunneling assisted super exchange U

Quantum Magnetism with a dipolar species in a 3D lattice dipole-dipole interactions long range = beyond the next neighbor direct spin-spin interaction real spin magnetic dipole moment S=3 quantum regime, high filling factor V dd = Hz T < 1 nK Spin dynamics in an out of equilibrium system V dd to reach ground state Ising term Exchange term

Cr BEC loaded in a 3D lattice: a Mott state spin preparation, measurement of the evolution of the Zeeman states populations Quantum Magnetism with a chromium BEC in a 3D lattice constant magnetization magnetization = dipolar relaxation change of the magnetization different spin dynamics induced by dipole-dipole interactions spin exchange S=3

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)

-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 0 10 mG Stern Gerlach analysis

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

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) without spin changing term

Spin exchange dynamics in a 3D lattice: with only singlons the spin populations change! comparison with a plaquette model (Pedri, Santos) 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

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

Dipolar Spin exchange dynamics with a new playground: a double well trap 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 filp 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

Spin exchange dynamics in a double well trap: realization realizing a double well spin preparation RF spin flip in a non homogeneous B field

Spin exchange dynamics in a double well trap: results No spin exchange dynamics

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 

Inhibition of Spin exchange dynamics in a double well trap: interpretation (2) It is as if we had two giant spins interacting What happens for quantum magnets in presence of an external B field when S increases? Evolution of two coupled magnetic moments in presence of an external B field if no more exchange possible Ising termExchange term no spin changing terms 2S+1 states Ising contribution gives different diagonal terms no complete exchange "half period" of the exchange grows exponentially

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

Production of a degenerate quantum gas of fermionic chromium Two very different quantum statistics T < T c T > T c a quantum gas at T<T c or T<<T F a quantum gas at T<<T F

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

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

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 mestastable states RF sweep to cancel the magnetic force of the MOT coils for 53 Cr : finding repumping lines crossed dipole trap

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: /-10 MHz Deduced value for the isotopic shift: Center value = = MHz Uncertainty: +/-(10+10) MHz (our experiment) +/-8 MHz (HFS of 7 P 3 ) isotopic shift: -mass term -orbital term isotopic shifts unknown

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 Cr about Cr inelastic interspecies collisions limits to Cr Cr not great, we tried anyway…

Production of a degenerate quantum gas of fermionic chromium Evaporation

Production of a degenerate quantum gas of fermionic chromium Why such a good surprise? Maybe we reach the hydrodynamic regime for the fermions… If collisions with bosons set the mean free path of fermions below the trap radius How to measure Fermion-Boson collision cross section? By heating selectively and quickly the bosons and then measure fermions thermalization then fermions are trapped by collisions very preliminary measurements + analysis support this interpretation

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

Production of a degenerate quantum gas of fermionic chromium What can we study with our gas? Phase separation requires good in situ imaging 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 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

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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

Preparation in an atomic excited state --  -3 Raman transition laser power m S = -2 A  - polarized laser Close to a J  J transition (100 mW nm) creation of a quadratic light shift energy quadratic effect (laser power) transfer in -2 ~ 80% transfer adiabatic

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

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

-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)

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'

-2 -3 the Cr BEC can depolarize at low B fields from the ground state spin changing collisions become possible 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 » (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