Magnetism in systems of ultracold atoms New problems

Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics Eugene Demler Harvard University 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) Collaboration with experimental groups of I. Bloch and J. Schmiedmayer

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

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

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 1 d chain Ramsey interference experiments in one dimensional systems - many-body decoherence

Superexchange and spin dynamics in optical lattices

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

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

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

Comparison to the Hubbard model

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

Beyond the basic Hubbard model

From two spins to a spin chain Spin oscillations ?

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

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

Behavior of the relaxation time with anisotropy See also: Sengupta, Powell & Sachdev (2004) - 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.

Ramsey interference in 1 d condensates Many-body decoherence

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

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

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

Interaction induced collapse of Ramsey fringes. Multimode analysis Low energy effective theory: Luttinger liquid approach 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

Interaction induced collapse of Ramsey fringes in one dimensional systems 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 Fundamental limit on Ramsey interferometry How to distinquish decoherence due to many-body dynamics?

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

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 1 d chain Ramsey interference experiments in one dimensional systems - many-body decoherence