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

Stoner instability. Double exchange

Ferromagnetismin itinerant systems

AntiferromagnetismFrustrated magneticsystems

?

Magnetism in condensed matter systemsMany-body magnetism. Equilibrium and ground state

t0

1

Atomic clocks and Ramsey interference

Magnetism in atomic physics

Single atom magnetism.Quantum dynamics

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

Superexchange and spin dynamics in optical lattices

t

t

Two component Bose mixture in optical latticeExample: . Mandel et al., Nature 425:937 (2003)

Two component Bose Hubbard model

Quantum magnetism of bosons in optical lattices

Duan, Demler, Lukin, PRL 91:94514 (2003)

• Ferromagnetic• Antiferromagnetic

J

J

Use magnetic field gradient to prepare a state

Observe oscillations between and states

Observation of superexchange in a double well potentialTheory: A.M. Rey et al., PRL 2008

Experiments:S. Trotzky et al.Science 2008

Comparison to the Hubbard model

Basic Hubbard model includesonly local interaction

Extended Hubbard modeltakes into account non-localinteraction

Beyond the basic Hubbard model

Beyond the basic Hubbard model

From two spins to a spin chain

Spin oscillations ?

1D: XXZ dynamics starting from the classical Neel state

• DMRG

• XZ model: exact solution

Time, Jt

Equilibrium phase diagram:

(t=0) =

Quasi-LRO

1

Ising-Order

P. Barmettler et al, PRL 2009

XXZ dynamics starting from the classical Neel state

<1, XY easy plane anisotropy

Oscillations of staggered moment, Exponential decay of envelope

>1, Z axis anisotropy

Exponential decay of staggered moment

Except at solvable xx point where:

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)

Ramsey interference in 1d condensates Many-body decoherence

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)

Spin echo. Time reversal experiments

Single mode approximation

Predicts perfect spin echo

The Hamiltonian can be reversed by changing a12

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

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 oscillatorscan be analyzed exactly

Low energy effective theory: Luttinger liquid approach

Interaction induced collapse of Ramsey fringesin one dimensional systems

Fundamental limit on Ramsey interferometry

Only q=0 mode shows complete spin echoFinite 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?

Single mode analysisKitagawa, Ueda, PRA 47:5138 (1993)

Multimode analysisevolution of spin distribution functions

T. Kitagawa, S. Pielawa, A. Imambekov, et al.

Interaction induced collapse of Ramsey fringes

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