Transcript ppt - Condensed Matter Theory at Harvard University

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 1d 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
?
1D: XXZ dynamics starting from the classical Neel state
P. Barmettler et al, PRL 2009
Y(t=0
)
=
Ising-Order
Quasi-LRO
Equilibrium phase diagram:
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 1d condensates
Many-body decoherence
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 100:140401 (2008)
Spin echo. Time reversal experiments
Single mode approximation
The Hamiltonian can be reversed by changing a12
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 1d 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 1d chain
Ramsey interference experiments in one
dimensional systems
- many-body decoherence