Competing instabilities in ultracold Fermi gases

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Competing instabilities in ultracold Fermi gases
David Pekker (Harvard) 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)
Details in arXiv1005.2366
Special thanks to W. Ketterle, G.B. Jo, and
other members of the MIT group
NSF, AFOSR MURI, DARPA ARO
Harvard-MIT
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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

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Stoner instability
E. Stoner, Phil. Mag. 151018 (1933)
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Stoner model of ferromagnetism
Spontaneous spin polarization decreases
interaction energy but increases kinetic energy
of electrons
Mean-field criterion
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)
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Experiments were done dynamically. What are
implications of dynamics? Why spin domains could
not be observed?
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• Is it sufficient to consider effective model
  with repulsive interactions when analyzing
  experiments?
• Feshbach physics beyond effective repulsive
  interaction

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Feshbach resonance
Interactions between atoms are intrinsically
attractive Effective repulsion appears due to low
energy bound states
Example
scattering length
V0 tunable by the magnetic field Can tune through
bound state
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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 ?
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Pair formation
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Two-particle scattering in vacuum
Lippman-Schwinger equation
On-shell T-matrix. Universal low energy
expression
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Cooperon
Two particle scattering in the presence of a
Fermi sea
Cooperon equation
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Cooper channel response function
Linear response theory
Induced pairing field
Response function
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Cooper channel response function
Time dependent dynamics
When the mode frequency has imaginary part, the
system is unstable to formation of paired state
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Pairing instability regularized
BCS side
Instability rate coincides with the equilibrium
gap (Abrikosov, Gorkov, Dzyaloshinski)
Instability to pairing even on the BEC side
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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
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Pairing instability
From wide to narrow resonances
Pairing instability at different temperatures
Three body recombination as in Shlyapnikov et
al., 1996 Petrov, 2003 Esry 2005
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Magnetic instability
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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
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Quench dynamics across Stoner instability
Magnetic Stoner instability
For UgtUc unstable collective modes
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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.
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Stoner instability
RPA spin susceptibility
Interaction Cooperon
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Stoner instability
Pairing dominates over magnetic instability If
ferromagnetic domains form, they form at large q
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Relation to experiments
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Pairing instability vs experiments
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Pairing and magnetism in strongly correlated
systems. Quantum dynamics
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Quantum simulations with ultracold atoms
Atoms in optical lattice
Antiferromagnetism and pairing at sub-micro
Kelvin temperatures
Same microscopic model
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Nonequilibrium dynamics in quantum many-body
systems of ultracold atoms
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
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Competing instabilities in strongly correlated
electron systems
Organic materials. Bechgaard salts
High Tc superconductors
Heavy fermion materials
This talk is also about competition between
pairing and magnetism. Instabilities rather than
ground states.
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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
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