Quantum Magnetism with 7 Li Niklas Jepsen, Ivana Dimitrova, Jesse Amato-Grill, Michael Messer, Graciana Puentes, David Weld, David Pritchard, Wolfgang Ketterle MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics Department of Physics, Massachusetts Institute of Technology, Cambridge Introduction The Need 4 Speed Two-component Bose-Hubbard Hamiltonian H = - X hij i,σ =↑,↓ t σ a † i σ a j σ + h .c . + 1 2 X i ,σ =↑,↓ U σ n i σ (n i σ - 1)+ U ↑↓ X i n i ↑ n i ↓ Super-exchange dominated spin-interactions J = t 2 /U (a) Neighboring atoms U T (b) Virtual Excitation of energy U T (c) Particle tunnels back are enabled by (1) Light mass of Li-7 (2) Green optical lattice (3) Feshbach resonance E R = 2 k 2 2m U ≈ a · 8 π k (V 0 /E R ) 3/4 E R t ≈ E R · 4 √ π (V 0 /E R ) 3/4 e − √ V 0 /E R ⇒ Higher critical temperature for magnetic ordering (k B T c ∼ t 2 /U ) ⇒ Faster spin dynamics within experimentally relevant timescales Possible Experiments Spin Dynamics I Spin transport by super-exchange interactions (d) Prepare a 50-50 spin mixture (e) Separate spins by magnetic field gradient (f) Apply optical lattice (g) Allow spins to mix (by decreasing magnetic field gradient) Quantum Simulation I Realization of 2-component Spin Hamiltonians I Anisotropic Heisenberg Model (XXZ model) H = X <i ,j > [λ z s z i s z j - λ xy (s x i s x j + s y i s y j )] - B z X i s z i λ z = t 2 ↑ t 2 ↓ 2U ↑↓ - t 2 ↑ U ↑↑ - t 2 ↓ U ↓↓ λ xy = t ↑ t ↓ 2U ↑↓ I Magnetic phase diagram L.-M. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. Anti-Ferromagnet Z-Ferromagnet XY-Ferromagnet z ? Magnetic field gradient Particle Interactions U "# <U "" ,U ## U "" ,U ## <U "# λ z /λ ? Magnetic field h z /6λ xy λ z /λ xy L.-M. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. 91, 090402 (2003) Experimental Realization Experimental Model I Two-component Hamiltonian realized by 7 Li atoms in two hyperfine states placed in an optical lattice I Freely tunable experimental parameters: I Energy ratio t /U by optical lattice depth I On-site interaction energy U by a Feshbach resonance I Spin separating potential by a magnetic field gradient I Temperature by evaporation time Experimental Sequence 1. Zeeman-slowing and Magneto-optical trapping 2. Evaporative cooling in a plug trap 3. BEC in a dipole trap supported by a Feshbach resonance 4. Green lattice plus dipole trap Machine Table Design Realization Performance of the Magneto-optical Trap I Atom number: 3 · 10 10 I Loading time: 5s I Decay constants: 13s , 75s I Temperature: 10mK I Velocity: 1ms -1 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1 Time in seconds Trapped fraction Loading 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 Time in seconds Trapped fraction Lifetime Funding Acknowledgements