Transcript 2010_utrecht - Harvard University

Competing instabilities
in ultracold Fermi gases
Motivated by experiments of G.-B. Jo et al., Science (2009)
David Pekker (Harvard),
Mehrtash Babadi (Harvard),
Rajdeep Sensarma (Harvard/Maryland),
Nikolaj Zinner (Harvard/Niels Bohr Institute),
Antoine Georges (Ecole Polytechnique),
Eugene Demler (Harvard)
Harvard-MIT
$$ NSF, AFOSR MURI, DARPA
Outline
• Introduction. Stoner instability
• Possible observation of Stoner
instability in MIT experiments.
G.B. Jo et al., Science (2009)
• Spin domains. Nonequilibrium dynamics
across Stoner transition
• Competition of molecule formation and
Stoner instability (motivated by discussions
with Sandro Stringari)
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
Kanamori’s counter-argument: renormalization of U
then
Theoretical proposals for observing Stoner instability
with ultracold Fermi gases:
Salasnich et. al. (2000); Sogo, Yabu (2002); Duine, MacDonald (2005);
Conduit, Simons (2009); LeBlanck et al. (2009); …
Magnetic domains
could not be resolved.
Why? T.L. Ho (2009)
Stoner Instability
New feature of cold atoms
systems: non-adiabatic
crossing of Uc
Two timescales in the system:
screening and magnetic
domain formation
Screening of U (Kanamori) occurs on times 1/EF
Magnetic domain formation takes place on
much longer time scales: critical slowing down
Quench dynamics across Stoner instability
For U>Uc unstable collective modes
Unstable modes determine characteristic
lengthscale of magnetic domains
Find collective modes
Dynamics of magnetic domain formation
M. Babadi et al. (2009)
near Stoner transition
Quench dynamics in D=3
Moving across transition at a finite rate
slow
growth
0
domains
freeze
domains
coarsen
u*
Domains freeze when
Growth rate of magnetic domains
Domain size at “freezing” point
Domain size
For MIT experiments domain
sizes of the order of a few lF
u
Is it sufficient to consider effective model
with repulsive interactions when analyzing
experiments?
Feshbach physics beyond effective
repulsive interaction
Feshbach resonance
Two particle bound state
formed in vacuum
Stoner instability
Review: Duine and Stoof, 2004
Chin et al., 2009
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 ?
Many-body instabilities
Imaginary frequencies of collective modes
Magnetic Stoner instability
Pairing instability
Pairing instability
Change from bare interaction to the scattering length
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
Time dependent variational wavefunction
Time dependence of uk(t) and vk(t) due to DBCS(t)
For small DBCS(t):
Pairing instability
From wide to narrow resonances
Stoner vs pairing
Does Stoner instability really exceed
molecule formation rate?
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
Spin susceptibility
Stoner instability
Growth rate of magnetic
Stoner instability
Growth rate of
pairing instability
RPA with bare
scattering length
RPA with
Cooperon
Changing from scattering length to
T-matrix gives appreciable suppression
of the Stoner instability
Additional suppression due to Pauli
blocking
Stoner vs pairing
G.B. Jo et al., Science (2009)
Stoner vs pairing
Increase in the kinetic energy:
consistent with pairing.
In the BCS state kinetic
energy goes up and the
interaction energy goes down
Conclusions
Competition of pairing and Stoner instabilities
New features due to dynamical character of
experiments
Simple model with contact repulsive interactions
may not be sufficient to understand experiments
Strong suppression of Stoner instability
by Fechbach resonance physics + Pauli blocking
Interesting questions beyond linear instability
analysis.