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decoherence with quantum noise Motivated by experiments Widera et al., PRL (2008) Hofferberth et al., Nature (2007) + unpublished Vienna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

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