Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics

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Magnetism in systems of ultracold atomsNew
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
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Ferromagnetismin itinerant systems
Magnetism in condensed matter systems
Many-body magnetism. Equilibrium and ground state
Stoner instability. Double exchange
Frustrated magnetic systems
Antiferromagnetism
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Magnetism in atomic physics
Atomic clocks and Ramsey interference
Single atom magnetism. Quantum dynamics
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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
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Superexchange and spin dynamics in optical
lattices
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Two component Bose mixture in optical lattice
Example . Mandel et al., Nature
425937 (2003)
Two component Bose Hubbard model
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Quantum magnetism of bosons in optical lattices
Duan, Demler, Lukin, PRL 9194514 (2003)

• Ferromagnetic
• Antiferromagnetic

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Observation of superexchange in a double well
potential
Theory A.M. Rey et al., PRL 2008
Experiments S. Trotzky et al. Science 2008
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Comparison to the Hubbard model
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Beyond the basic Hubbard model
Basic Hubbard model includes only local
interaction
Extended Hubbard model takes into account
non-local interaction
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Beyond the basic Hubbard model
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From two spins to a spin chain
?
Spin oscillations
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1D XXZ dynamics starting from the classical Neel
state
P. Barmettler et al, PRL 2009
Ising-Order
Quasi-LRO
Equilibrium phase diagram
D
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• DMRG
• XZ model exact solution

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XXZ dynamics starting from the classical Neel
state
Dlt1, XY easy plane anisotropy
Oscillations of staggered moment, Exponential
decay of envelope
Except at solvable xx point where
Dgt1, Z axis anisotropy
Exponential decay of staggered moment
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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.

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Ramsey interference in 1d condensates
Many-body decoherence
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Interaction induced collapse of Ramsey fringes
Two component BEC. Single mode approximation
Ramsey fringe visibility
time
Experiments in 1d tubes A. Widera et al. PRL
100140401 (2008)
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Spin echo. Time reversal experiments
Single mode approximation
The Hamiltonian can be reversed by changing a12
Predicts perfect spin echo
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Spin echo. Time reversal experiments
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
No revival?
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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
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Interaction induced collapse of Ramsey fringesin
one dimensional systems
Only q0 mode shows complete spin echo Finite q
modes continue decay The net visibility is a
result of competition between q0 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?
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Interaction induced collapse of Ramsey fringes
Single mode analysis Kitagawa, Ueda, PRA 475138
(1993)
Multimode analysis evolution of spin distribution
functions
T. Kitagawa, S. Pielawa, A. Imambekov, et al.
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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
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