Transcript Competing instabilities in strongly correlated electron

Competing instabilities
in ultracold Fermi gases
David Pekker (Harvard)
Details in arXiv:1005.2366
Mehrtash Babadi (Harvard)
Lode Pollet (Harvard)
Rajdeep Sensarma (Harvard/JQI Maryland)
Nikolaj Zinner (Harvard/Niels Bohr Institute)
Antoine Georges (Ecole Polytechnique)
Martin Zwierlein (MIT)
Eugene Demler (Harvard)
Special thanks to W. Ketterle, G.B. Jo,
and other members of the MIT group
Harvard-MIT
$$ NSF, AFOSR MURI, DARPA ARO
Outline
• Introduction. Stoner instability
• Possible observation of Stoner instability in MIT
experiments. G.B. Jo et al., Science (2009)
• Dynamics vs equilibrium: pairing and magnetism
• Dynamics of molecule formation near
Feshbach resonance
• Magnetic Stoner instability near Feshbach resonance
• Comparison of two instabilities and relation to
experiments
Stoner instability
E. Stoner, Phil. Mag. 15:1018 (1933)
Stoner model of ferromagnetism
Spontaneous spin polarization
decreases interaction energy
but increases kinetic energy of
electrons
Mean-field criterion
U N(0) = 1
U – interaction strength
N(0) – density of states at Fermi level
Theoretical proposals for observing Stoner instability with cold
gases: Salasnich et. al. (2000); Sogo, Yabu (2002); Duine, MacDonald
(2005); Conduit, Simons (2009); LeBlanck et al. (2009); …
Recent work on hard sphere potentials: Pilati et al. (2010); Chang et al. (2010)
Experiments were
done dynamically.
What are implications
of dynamics?
Why spin domains could
not be observed?
Is it sufficient to consider effective model with
repulsive interactions when analyzing
experiments?
Feshbach physics beyond effective repulsive
interaction
Feshbach resonance
Interactions between atoms are intrinsically attractive
Effective repulsion appears due to low energy bound states
Example:
V(x)
V0 tunable by the magnetic field
Can tune through bound state
scattering length
Feshbach resonance
Two particle bound state
formed in vacuum
Stoner instability
BCS instability
Molecule formation
and condensation
This talk: Prepare Fermi state of weakly interacting atoms.
Quench to the BEC side of Feshbach resonance.
System unstable to both molecule formation
and Stoner ferromagnetism. Which instability dominates ?
Pair formation
Two-particle scattering in vacuum
p
k
Lippman-Schwinger equation
-k
-p
k
k
-k
p
-p
k
p
-k
-p
k
p’
-p’
p
-p
On-shell T-matrix. Universal low energy expression
For positive scattering length bound state at
appears as a pole in the T-matrix
Cooperon
p
k
Two particle scattering in the
presence of a Fermi sea
-k
-p
Cooperon equation
k
k
-k
p
-p
k
p
-k
-p
k
p’
-p’
p
-p
Cooper channel response function
Linear response theory
Induced pairing field
Response function
Poles of the Cooper channel response function
are given by
Cooper channel response function
Linear response theory
Poles of the response function
describe collective modes
Time dependent dynamics
When the mode frequency has imaginary part,
the system is unstable to formation of paired state
Pairing instability regularized
BCS side
Instability rate coincides with the equilibrium gap
(Abrikosov, Gorkov, Dzyaloshinski)
Instability to pairing even on the BEC side
Pairing instability
Intuition: two body collisions do not lead to molecule
formation on the BEC side of Feshbach resonance.
Energy and momentum conservation laws can not
be satisfied.
This argument applies in vacuum. Fermi sea prevents
formation of real Feshbach molecules by Pauli blocking.
Molecule
Fermi sea
Pairing instability
Pairing instability
at different temperatures
Three body recombination
as in Shlyapnikov et al., 1996;
Petrov, 2003; Esry 2005
From wide to
narrow resonances
Magnetic instability
Stoner instability. Naïve theory
Spin response function
Relates induced spin polarization
to external Zeeman field
Spin collective modes are given by the poles of response function
Imaginary frequencies correspond to magnetic instability
Quench dynamics across Stoner instability
Magnetic Stoner instability
For U>Uc unstable collective modes
Unphysical divergence at unitarity
Stoner instability
=
+
+
Stoner instability is determined by two particle
scattering amplitude
Divergence in the scattering amplitude arises
from bound state formation. Bound state is
strongly affected by the Fermi sea.
+ …
Stoner instability
RPA spin susceptibility
Interaction = Cooperon
Stoner instability
Pairing dominates over magnetic instability
If ferromagnetic domains form, they form at large q
Relation to experiments
Pairing instability vs experiments
Pairing and magnetism
in strongly correlated systems.
Quantum dynamics
Quantum simulations with ultracold atoms
Atoms in optical lattice
Antiferromagnetic and
superconducting Tc
of the order of 100 K
Antiferromagnetism and
pairing at sub-micro Kelvin
temperatures
Same microscopic model
Nonequilibrium dynamics in quantum
many-body systems of ultracold atoms
Long intrinsic time scales
- Interaction energy and bandwidth ~ 1kHz
- System parameters can be changed over this time scale
Decoupling from external environment
- Long coherence times
Can achieve highly non equilibrium quantum many-body states
Equilibrium properties of many-body systems. Many open questions but
known paradigms: order parameters, universal fixed points (e.g. Fermi liquid)
Nonequilibrium properties of many-body systems. We do not even have
paradigms or understanding of universality
Competing instabilities in strongly correlated
electron systems
Heavy fermion
materials
Organic materials.
Bechgaard salts
High Tc
superconductors
temperature (K)
400
300
200
100
0
doping
This talk is also about competition between pairing and
magnetism. Instabilities rather than ground states.
Summary
Competition of pairing and ferromagnetism
near Feshbach resonance
Dynamics of competing orders is important for understanding
experiments
Simple model with repulsive interactions
may not be sufficient
Strong suppression of Stoner instability
by Feshbach resonance physics + Pauli blocking
Alternative interpretation of experiments based on pair formation
Harvard-MIT