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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

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. 151018 (1933)

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)

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

scattering length

V0 tunable by the magnetic field Can tune through

bound state

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

Lippman-Schwinger equation

On-shell T-matrix. Universal low energy

expression

Cooperon

Two particle scattering in the presence of a

Fermi sea

Cooperon equation

Cooper channel response function

Linear response theory

Induced pairing field

Response function

Cooper channel response function

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

From wide to narrow resonances

Pairing instability at different temperatures

Three body recombination as in Shlyapnikov et

al., 1996 Petrov, 2003 Esry 2005

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 UgtUc unstable collective modes

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

Antiferromagnetism and pairing at sub-micro

Kelvin temperatures

Same microscopic model

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

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.

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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