1. Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard, Freiburg), A. Imambekov (Yale), T. Kitagawa (Harvard), M. Lukin (Harvard), S. Pielawa (Harvard), A. Polkovnikov (BU), M. Punk (TU Munich), A.M. Rey (Harvard, CU Boulder, JILA) Eugene Demler Harvard University Collaboration with experimental groups of I. Bloch and J. Schmiedmayer

2. Stoner instability. Double exchange Ferromagnetism in itinerant systems Antiferromagnetism Frustrated magnetic systems ? Magnetism in condensed matter systems Many-body magnetism. Equilibrium and ground state

3. t 0 1 Atomic clocks and Ramsey interference Magnetism in atomic physics Single atom magnetism. Quantum dynamics

4. Magnetism of ultracold atoms: Quantum many-body dynamics Superexchange and spin dynamics in optical lattices - superexchange interactions in Mott state - observation of superexchange in double wells - spin dynamics of 1d chain Ramsey interference experiments in one dimensional systems - many-body decoherence

5. Superexchange and spin dynamics in optical lattices

6. t t Two component Bose mixture in optical lattice Example:. Mandel et al., Nature 425:937 (2003) Two component Bose Hubbard model

7. Quantum magnetism of bosons in optical lattices Duan, Demler, Lukin, PRL 91:94514 (2003) Ferromagnetic Antiferromagnetic

8. J J Use magnetic field gradient to prepare a stateObserve oscillations between and states Observation of superexchange in a double well potential Theory: A.M. Rey et al., PRL 2008 Experiments: S. Trotzky et al. Science 2008

9. Comparison to the Hubbard model

10. Basic Hubbard model includes only local interaction Extended Hubbard model takes into account non-local interaction Beyond the basic Hubbard model

12. From two spins to a spin chain Spin oscillations ?

13. 1D: XXZ dynamics starting from the classical Neel state DMRG XZ model: exact solution Time, Jt D Equilibrium phase diagram: Y (t=0 ) = Quasi-LRO 1 Ising-Order P. Barmettler et al, PRL 2009

14. XXZ dynamics starting from the classical Neel state D<1, XY easy plane anisotropy Oscillations of staggered moment, Exponential decay of envelope D>1, Z axis anisotropy Exponential decay of staggered moment Except at solvable xx point where:

15. Behavior of the relaxation time with anisotropy - Moment always decays to zero. Even for high easy axis anisotropy - Minimum of relaxation time at the QCP. Opposite of classical critical slowing. - Divergent relaxation time at the solvable XX point. See also: Sengupta, Powell & Sachdev (2004)

16. Ramsey interference in 1d condensates Many-body decoherence

17. Two component BEC. Single mode approximation Interaction induced collapse of Ramsey fringes time Ramsey fringe visibility Experiments in 1d tubes: A. Widera et al. PRL 100:140401 (2008)

18. Spin echo. Time reversal experiments Single mode approximation Predicts perfect spin echo The Hamiltonian can be reversed by changing a 12

19. Spin echo. Time reversal experiments No revival? A. Widera et al., PRL 2008 Experiments done in array of tubes. Strong fluctuations in 1d systems. Single mode approximation does not apply. Need to analyze the full model

20. Interaction induced collapse of Ramsey fringes. Multimode analysis Luttinger model Changing the sign of the interaction reverses the interaction part of the Hamiltonian but not the kinetic energy Time dependent harmonic oscillators can be analyzed exactly Low energy effective theory: Luttinger liquid approach

21. Interaction induced collapse of Ramsey fringes in one dimensional systems Fundamental limit on Ramsey interferometry Only q=0 mode shows complete spin echo Finite q modes continue decay The net visibility is a result of competition between q=0 and other modes Decoherence due to many-body dynamics of low dimensional systems How to distinquish decoherence due to many-body dynamics?

22. Single mode analysis Kitagawa, Ueda, PRA 47:5138 (1993) Multimode analysis evolution of spin distribution functions T. Kitagawa, S. Pielawa, A. Imambekov, et al. Interaction induced collapse of Ramsey fringes

23. Magnetism of ultracold atoms: Quantum many-body dynamics Superexchange and spin dynamics in optical lattices - superexchange interactions in Mott state - observation of superexchange in double well systems - spin dynamics of 1d chain Ramsey interference experiments in one dimensional systems - many-body decoherence