Low dimensional systems 1d: spin dynamics of two component Bose mixture Harvard, Mainz collaboration

1d: dynamics of spin chains Harvard, Mainz collaboration (+Weizmann, Munich, Fribourg)

2d: interference of weakly coupled pancakes Harvard, Stanford collaboration

Microscopic parameters of low-D systems (Michigan)

Probing fermionic Hubbard model with spin polarization (Harvard)

Quantum simulator theoryThis talk: Harvard, Innsbruck-Stuttgart, Michigan,

+ Stanford experiments

Dipolar interactions (Harvard, Innsbruck, Stuttgart)

x

z

Time of

flight

Experiments with 2D Bose gasHadzibabic, Dalibard et al., Nature 441:1118 (2006)

Experiments with 1D Bose gas Hofferberth et al. Nature Physics (2008)

Interference of independent 1d condensatesS. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer, A. Imambekov, V. Gritsev, E. Demler, Nature Physics (2008)

Higher order correlation functionsprobed by noise in interference

Non-equilibrium spin dynamicsin one dimensional systemsRamsey interferometry and many-body decoherence

Mainz, Harvard collaborationWidera, Trotzky, Cheinet, Foelling, Gerbier, Bloch, Gritsev, Lukin, Demler, PRL (2008)+ Kitagawa, Pielawa, Imambekov, Demler, unpublished

Working with N atoms improves the precision by .

Ramsey interference

t0

1

Atomic clocks and Ramsey interference:

Two component BEC. Single mode approximation

Interaction induced collapse of Ramsey fringes

time

Ramsey fringe visibility

Experiments in 1d tubes: A. Widera et al. PRL 100:140401 (2008)

Spin echo. Time reversal experiments

No revival?

A. Widera et al., PRL (2008)

Experiments done in array of tubes. Strong fluctuations in 1d systems.Single mode approximation does not apply.Need to analyze the full model

Interaction induced collapse of Ramsey fringesin one dimensional systems

Decoherence due to many-body dynamics of low dimensional systems

How to distinquish decoherence due to many-body dynamics?

Low energy effective theory in 1D: Luttinger liquid approach

Only q=0 mode shows complete spin echoFinite q modes continue decayThe net visibility is a result of competition between q=0 and other modes

Single mode analysisKitagawa, Ueda, PRA 47:5138 (1993)

Multimode analysisevolution of spin distribution functions

T. Kitagawa, S. Pielawa, A. Imambekov, et al.

Interaction induced collapse of Ramsey fringes

Lattice modelsNonequilibrium dynamics in 1d

anisotropic Heisenberg spin systems

Barmettler, Punk, Altman, Gritsev, Demler, arXiv:0810:4845

Superexchange in Mott state.Spin dynamics in double well systems

Jex Mainz, Harvard collaboration (+BU)A.M. Rey et al., PRL (2007)S. Trotzky et al., Science (2008)

Experimental measurements of superexchange Jex.

Comparison to first principle calculations

Nonequilibrium spin dynamics in 1d. Lattice Spin dynamics in 1D starting from the classical Neel state

Equilibrium phase diagram

(t=0) =Coherent time evolution starting with

QLRO

Expected: critical slowdown near quantum critical point at =1

Observed: fast decay at =1

Time, Jt

Experiment: Experiment: 1D AF isotropic model 1D AF isotropic model prepared in the Neel state: decay of prepared in the Neel state: decay of

staggered magnetizationstaggered magnetization S. Trotzky et al. (group of I. Bloch) S. Trotzky et al. (group of I. Bloch)

Quasi 2D condensates:From 2D BKT to 3D

Theory: Pekker, Gritsev, Demler (Harvard) B. Clark (UIUC)

Experiment: Kasevich et al. (Stanford)

Quasi 2D condensates at StanfordOptical lattice array

• ~20 disks• ~100 87Rb

atoms/disk• each disk ~60 nm x

4 m

10 m

kbT/h ~ 1 kHz

/h ~ 200 Hz

J/h ~ 5-500 Hz

N ~ 100

Interlayer tunneling is a tunable parameter (with lattice depth).

Berezinskii–Kosterlitz–Thoulesste

mpe

ratu

re

T=0

T=TBKT

Fisher & Hohenberg, PRB (1988)

Modifications for multiple pancakes

3D XY

3D Phonons

tem

pera

ture

T=0

T=TBKT

T=TC

T=2t

Comparison theory and experiment, 12 Er lattice

RF cut frequency (kHz)

Temperature (nK)

12 ER

Theory: Classical Monte-Carlo of XY model (also RG analysis)

Experiment

Response vs. Correlations

TKT

What is typically being measured?• Condensed matter

• response function (e.g. superfluid density)• Cold atoms

• correlations (peak shapes and heights) • also possible to do response now

Ulrtacold atoms in low dimensionsUlrtacold atoms in low dimensions

Realization of Low dimensions: atoms in strong transverse traps

• Projection to the transverse ground state

• Weakly interacting atoms:

Luming Duan

• Multi-level effects

• Strongly interacting atoms near Feshbach resonance

Simple Projection does not work!

Description of Strongly interacting atoms in low dimensionsDescription of Strongly interacting atoms in low dimensions

• Renormalization of atom-atom scattering length (model I) (Olshanni etc., 1D, PRL; Petrov, Shlyapnikov, etc., 2D, PRL)

Effective low-D scattering lengthNot adequate yet near Resonance

• Effective low-D atomic scattering length does not include this bound state

• Existence of two-body bound-state at any detuning in low-D

Reason:

Effective Hamiltonian for low-D strongly interacting gasEffective Hamiltonian for low-D strongly interacting gas

• Effective interaction between atoms and dressed molecules (model II)

Atoms in transverse ground level Dressed molecules,accounting for atomic population in excited transverse levels.

(Kestner, Duan, PRA, 06)

Comparison of predictions of model I and model IIComparison of predictions of model I and model II

Comparison of Tomas-Fermi Radius of 2D gas in a weak planar trap

Fails to reproducea shrinking radius at the BEC side

Zhang, Lin, Duan, PRA 08BEC side BCS side

Dipolar interactions

R. Cherng, E. Demler (Harvard) D.W. Wang (Tsing-Hua Univ)

H.P. Buchler (Stuttgart), P. Zoller (Innsbruck)

Dipolar interactions in low dimensional systems

Roton-maxon spectrum and roton softening

++-- Attractive interaction head-to-tail

Repulsive interaction side-by-side

Dipole-Dipole Interactions in 2D pancake

Attractive at short distancesRepulsive at long distances

Santos, Shlyapnikov, Lewenstein (2000)Fischer (2006)

Enhancement of roton softening in multi-layer systems

Amplification of attractive interaction for dipoles in different layers on top of each other

Wang, Demler, arXiv:0812.1838

Roton softening for 10, 20, and 100 layers

Growth rate of unstable modes

momentumout of plane

momentumin the plane

Decoherence of Bloch oscillations

In agreement with expts on 39K: Fattori et al, PRL (2008)

Spin-dipolar interactions for ultracold atoms

BF

Larmor Precession (100 kHz) dominatesover all other energy scales.Effective interaction based on averaging over precession

Quasi 2D system of 87Rb. Spin-roton softening

Wide range of instabilities tuned by quadratic Zeeman, AC Stark shift, initial spiral spin winding

Dipolar instabilities in spinor condensates

Vengalattore et al., PRL (2008)

Fourier spectrumSpontaneously modulated textures in Rb condensates

Dipolar spin instabilitiesR. Cherng, E. Demler,arXiv:0806.1991

Checkerboard patternobserved in experimentsreflects unstable spin modes

Polar molecules

Objectives:

- control and design the interactions potentials

- derive extended Hubbard models

dipole moment

rotation of the molecule

Polar molecules

- permanent dipole moment:

- polarizable with static electric field, and microwave fields

- interactions are increased by compared to magnetic dipole interactions

Spin toolbox

- polar molecules with spin- realization of Kitaev model (A. Micheli, G. Brennen, P. Zoller, Nature Physics 2006)

Polar molecules

Three-body interactions

- systematic approach to strong many-body interactions (H.P. Büchler, A. Micheli, and P. Zoller, Nature Physics 2007)

Repulsive shield

- crystalline phases (H.P. Büchler, E. Demler, M. Lukin, A. Micheli, G. Pupillo, P. Zoller, PRL 2007)- design of a repulsive potential between polar molecules- quenches inelastic collisions

Probing fermionic Hubbard model with spin polarization

B. Wunsch, E. Demler (Harvard)

E. Manousakis (FSU)

Antiferromagnetic Mott state and spin imbalance

Do we have spin separation in parabolic trap?

W. Hofstetter et al., NJP(2008)

Spin polarizededges

Spin polarizededges Canted antiferromagnetic

phase in the Mott plateau

Perfect AF Mott state

Hartree-Fock approximation

Antiferromagnetic Mott state and spin imbalanceBoth states are self-consistent solutions of the HF equations

Canted antiferromagnetic phase is lower in energy

Low dimensional systems 1d: spin dynamics of two component Bose mixture Harvard, Mainz collaboration

1d: dynamics of spin chains Harvard, Mainz collaboration (+Weizmann, Munchen,Fribourg)

2d: interference of weakly coupled pancakes Harvard, Stanford collaboration

Microscopic parameters of low-D systems (Michigan)

Probing fermionic Hubbard model with spin polarization (Harvard)

Quantum simulator theoryThis talk: Harvard, Innsbruck-Stuttgart, Michigan

Dipolar interactions (Harvard, Innsbruck, Stuttgart)