magnetism in ultracold fermi gases and new physics with ultracold ions: many-body systems with...
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Magnetism in ultracold Fermi gasesand
New physics with ultracold ions: many-body systems with non-equilibrium noise
$$ NSF, AFOSR MURI, DARPAHarvard-MIT
David Pekker (Harvard),Rajdeep Sensarma (Harvard/JQI Maryland), Mehrtash Babadi (Harvard), Nikolaj Zinner (Harvard/Niels Bohr Institute), Antoine Georges (Ecole Polytechnique),Ehud Altman (Weizmann),Emanuele Dalla Torre (Weizmann),Thierry Giamarchi (Geneva),Eugene Demler (Harvard)
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Outline
• Stoner instability in ultracold atomsMotivated by experiments of G.-B. Jo et al., Science (2009) Introduction to Stoner instability. Possible observation of Stoner instability in MIT experiments. Domain formation.Competition of molecule formation and Stoner instabilityRef: M. Babadi et al., arXiv:0909.3483 and unpublished
• New physics with ultracold ionsQuantum many-body systems in the presence of non-equilibrium noiseRef: Dalla Torre et al., arXiv:0908.0868
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Stoner model of ferromagnetismSpontaneous spin polarizationdecreases interaction energybut increases kinetic energy ofelectrons
Mean-field criterion
U N(0) = 1
U – interaction strengthN(0) – density of states at Fermi level
Theoretical proposals for observing Stoner instabilitywith ultracold Fermi gases:Salasnich et. al. (2000); Sogo, Yabu (2002); Duine, MacDonald (2005); Conduit, Simons (2009); LeBlanck et al. (2009); …
Kanamori’s counter-argument: renormalization of U
then
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Magnetic domainscould not be resolved.Why? T.L. Ho (2009)
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Stoner InstabilityNew feature of cold atoms systems: non-adiabatic crossing of Uc
Screening of U (Kanamori) occurs on times 1/EF
Two timescales in the system: screening and magnetic domain formation
Magnetic domain formation takes place on much longer time scales: critical slowing down
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Quench dynamics across Stoner instability
Find collective modes
Unstable modes determine characteristic lengthscale of magnetic domains
For U>Uc unstable collective modes
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For MIT experiments domain
sizes of the order of a few F
Quench dynamics in D=3
Dynamics of magnetic domain formation near Stoner transition
Moving across transition at a finite rate
0 uu*
domains coarsen
slowgrowth
domainsfreeze
Growth rate of magnetic domains
Domain size
Domains freeze when
Domain size at “freezing” point
M. Babadi et al. (2009)
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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 resonanceReview: Duine and Stoof, 2004 Chin et al., 2009
Two particle bound state formed in vacuum
BCS instabilityStoner instability
Molecule formationand 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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Many-body instabilitiesImaginary frequencies of collective modes
Magnetic Stoner instability
Pairing instability
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Change from bare interaction to the scattering length
Instability to pairing even on the BEC side
Pairing instability
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Pairing instabilityIntuition: two body collisions do not lead to molecule formation on the BEC side of Feshbach resonance.Energy and momentum conservation laws can notbe satisfied.
This argument applies in vacuum. Fermi sea preventsformation of real Feshbach molecules by Pauli blocking.
Molecule Fermi sea
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Pairing instabilityTime dependent variational wavefunction
Time dependence of uk(t) and vk(t) due to BCS(t)
For small BCS(t):
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Pairing instabilityFrom wide to narrow resonances
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Stoner vs pairing
Does Stoner instability really exceed molecule formation rate?
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Stoner instability
=
Divergence in the scattering amplitude arises from bound state formation. Bound state is strongly affected by the Fermi sea.
Stoner instability is determined by two particlescattering amplitude
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Stoner instabilitySpin susceptibility
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Growth rate of pairing instability
Growth rate of magneticStoner instability
RPA with barescattering length
RPA with Cooperon
Changing from scattering length to Cooperon gives strong suppressionof the Stoner instability
Stoner instability suppressedwhen using a Cooperon. Strong suppression due to Pauli blocking
Stoner instability
?
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Stoner vs pairing
G.B. Jo et al., Science (2009)
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Stoner vs pairing
Increase in the kinetic energy:consistent with pairing.In the BCS state kineticenergy goes up and the interaction energy goes down
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Conclusions for part I
Competition of pairing and Stoner instabilities
New features due to dynamical character of experiments
Simple model with contact repulsive interactionsmay not be sufficient to understand experiments
Strong suppression of Stoner instability by Fechbach resonance physics + Pauli blocking
Possible ways to recover Stoner instability:many-body correlations, e.g. effective mass renormalization.Interesting questions beyond linear instability analysis.
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QUANTUM MANY-BODY SYSTEMS
IN THE PRESENSE OF
NONEQUILIBRIUM NOISE
NEW PHYSICS WITH ULTRACOLD IONS
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Question:
What happens to low dimensional quantum systems when they are subjected to external non-equilibrium noise?
Ultracold polar moleculesTrapped ions
E
One dimensional Luttinger state can evolve into a new critical state. This new state has intriguing interplay of quantum critical and external noise driven fluctuations
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A brief review:Universal long-wavelength theory of 1D systems
Displacement field:
Long wavelength density fluctuations (phonons):
Haldane (81)
Weak interactions: K >>1Hard core bosons: K = 1Strong long range interactions: K < 1
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1D review cont’d: Wigner crystal correlations
No crystalline order !
Scale invariant critical state (Luttinger liquid)
Wigner crystal order parameter:
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1D review cont’d:Effect of a weak commensurate lattice potential
How does the lattice potential change under rescaling ?
Quantum phase transition: K<2 – Pinning by the lattice (“Mott insulator”) K>2 – Critical phase (Luttinger liquid)
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New systems more prone to external disturbance
+-
+-
+-
+-
+-
+-
+-
+-
+- E+
-
Ultracold polar molecules
Trapped ions R. Blatt’s talk at this conference
(from NIST group )
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Linear ion trap
Linear coupling to the noise:
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Measured noise spectrum in ion trap
f
From dependence of heating rate on trap frequency.
- Direct evidence that noise spectrum is 1/f
- Short range spatial correlations (~ distance from electrodes)
Monroe group, PRL (06), Chuang group, PRL (08)
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Ultra cold polar molecules
+-
+-
+-
+-
+-
+-
+-
+-
+- E
Polarizing electric field:
+-
System is subject to electric field noise from the electrodes !
Molecule polarizability
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Long wavelength description of noisy low D systems
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
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Effective coupling to external noise
Long wavelength component of noise
Component of noise at wavelengths near the inter-particle spacing
The “backscattering” can be neglected if the distance to the noisy electrode is much larger than the inter-particle spacing.
>>
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
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Effective harmonic theory of the noisy system
+- +- +- +-+-+- +-+- +-+-
Dissipative coupling to bath needed to ensure steady state (removes the energy pumped in by the external noise)
Implementation of bath: continuous cooling
(Quantum) Langevin dynamics:
Thermal bath
External noise
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Wigner crystal correlations
1/f noise is a marginal perturbation ! Critical steady state
Case of local 1/f noise:
- Decay of crystal correlations remains power-law.
- Decay exponent tuned by the 1/f noise power.
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Effect of a weak commensurate lattice potential
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-
How does the lattice change under a scale transformation?
Without lattice: Scale invariant steady state.
Phase transition tuned by noise power
(Supported also by a full RG analysis within the Keldysh formalism)
Kc
F0 /
Localized
Critical state2
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1D-2D transition of coupled tubes
+- +- +- +-+-+- +-+- +-+-+- +- +- +-+-+- +-+- +-+-
+- +- +- +-+-+- +-+- +-+-+- +- +- +-+-+- +-+- +-+-
+- +- +- +-+-+- +-+- +-+-
Scaling of the inter-tube hopping:Kc
F0 /1/4
2D superfluid
1D critical
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Global phase diagram
Kc
F0 /
2D crystal
Critical state1
Kc
F0 /1/4
2D superfluid
1D critical
Inter-tube interactionsInter-tube tunneling
Both perturbations
2
Kc
F0 /
2D superfluid
2D crystal
1D critical
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Conclusions for part II
New perspectives on many-body physics fromchains of ions and polar molecules
Effects of external noise on quantum critical states- new critical state- new phases and phase transitions tuned by noise
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Summary
• Stoner instability in ultracold atomsMotivated by experiments of G.-B. Jo et al., Science (2009) Introduction to Stoner instability. Possible observation of Stoner instability in MIT experiments. Domain formation.Competition of molecule formation and Stoner instabilityRef: M. Babadi et al., arXiv:0909.3483 and unpublished
• New physics with ultracold ionsQuantum many-body systems in the presence of non-equilibrium noiseRef: Dalla Torre et al., arXiv:0908.0868
Harvard-MIT