Many-body quench dynamics in ultracold atoms Surprising applications to recent experiments $$ NSF,...
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Transcript of Many-body quench dynamics in ultracold atoms Surprising applications to recent experiments $$ NSF,...
Many-body quench dynamics in ultracold atoms
Surprising applications to recent experiments
$$ NSF, AFOSR MURI, DARPAHarvard-MIT
Eugene Demler (Harvard)
Outline
• Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances
Motivated by experiments, Jo et al., Science (2009)
• Ramsey interference experiments in 1d Probing many-body decoherence with quantum noise Motivated by experiments Widera et al., PRL (2008) Hofferberth et al., Nature (2007) + unpublished Vienna
experiments
Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances
arXiv:1005.2366
D. Pekker, M. Babadi, R. Sensarma, N. Zinner, L. Pollet, M. Zwierlein, E. Demler
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); …
Existence of Stoner type ferromagnetism in a single band model is still a subject of debate
Experiments weredone dynamically.What are implicationsof 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 attractiveEffective repulsion appears due to low energy bound states
Example:
scattering lengthV(x)
V0 tunable by the magnetic fieldCan tune through bound state
Feshbach resonanceTwo 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 ?
Many-body instabilitiesImaginary frequencies of collective modes
Magnetic Stoner instability
Pairing instability
= + + + …
Many body instabilities near Feshbach resonance: naïve picture
Pairing (BCS) Stoner (BEC)
EF=Pairing (BCS) Stoner (BEC)
Pairing instability regularized bubble isUV divergent
To keep answers finite, we must tune together:upper momentum cut-off interaction strength U
Instability to pairing even on the BEC side
Change from bare interaction to the scattering length
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
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
= + + + …= + + + …
Stoner instabilityRPA spin susceptibility
Interaction = Cooperon
Stoner instability
Pairing instability always dominates over pairing
If ferromagnetic domains form, they form at large q
Pairing instability vs experiments
Conclusions to part ICompetition of pairing and ferromagnetism near Feshbach resonance
Dynamics of competing orders is important for understanding experiments
Simple model with contact repulsive interactionsmay not be sufficient
Strong suppression of Stoner instability by Feshbach resonance physics + Pauli blocking
Alternative interpretation of experiments based on pair formation
Ramsey interference in one dimensional systems: The full distribution function of fringe
contrast as a probe of many-body dynamics
T. Kitagawa, S. Pielawa, A. Imambekov, J.Schmiedmayer, V. Gritsev, E. Demler
arXiv:0912.4643
Working with N atoms improves the precision by .
Ramsey interference
t0
1
Atomic clocks and Ramsey interference:
Ramsey Interference with BEC
Single modeapproximation
time
Am
plit
ude
of
Ra
mse
y fr
ing
es
Interactions shouldlead to collapse andrevival of Ramsey fringes
1d systems in microchips
Treutlein et.al, PRL 2004
Two component BEC in microchip
Ramsey Interference with 1d BEC
1d systems in opticallattices
Ramsey interference in 1d tubes: A.Widera et al.,B. PRL 100:140401 (2008)
Ramsey interference in 1d condensates
Collapse but no revivals
A. Widera, et al, PRL 2008
Ramsey interference in 1d condensates
A. Widera, et al, PRL 2008
Only partial revival after spin echo!
Spin echo experiments
Expect full revival of fringes
Spin echo experiments in 1d tubes
Single mode approximation does not apply.Need to analyze the full model
Ramsey interference in 1dTime evolution
Technical noise could also lead to the absence of echo
Need “smoking gun” signaturesof many-body decoherece
Luttinger liquid provides good agreement with experiments.A. Widera et al., PRL 2008. Theory: V. Gritsev
Dis
trib
uti
on
Probing spin dynamics using distribution functions
Distribution contains informationabout all the moments
→ It can probe the system Hamiltonian
Joint distribution function can also be obtained!
Distribution function of fringe contrastas a probe of many-body dynamics
Short segments
Long segments
Radius =Amplitude
Angle =Phase
Distribution function of fringe contrastas a probe of many-body dynamics
Preliminary results by J. Schmiedmayer’s group
Splitting one condensate into two.
Short segments Long segments
l =20 m l =110 m
Expt Theory Data: Schmiedmayer et al., unpublished
Summary of Part II• Suggested unique signatures of the multimode
decoherence of Ramsey fringes in 1d
• Ramsey interferometer combined with study of distribution function is a useful tool to probe many-body dynamics
Harvard-MIT