Motivated by experiments of G.-B. Jo et al., Science (2009) Competing instabilitiesin ultracold Fermi gases 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)
U N(0) = 1 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 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
slow growth domains freeze domains coarsen u* 0 u Dynamics of magnetic domain formation near Stoner transition M. Babadi et al. (2009) Quench dynamics in D=3 Moving across transition at a finite rate 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 fewlF
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 Review: Duine and Stoof, 2004 Chin et al., 2009 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 ?
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
RPA with bare scattering length RPA with Cooperon Stoner instability Growth rate of magnetic Stoner instability Growth rate of pairing instability 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.