1. Quantum simulator theory
This talk: Harvard, Innsbruck-Stuttgart, Michigan, + Stanford experiments
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)
Dipolar interactions (Harvard, Innsbruck, Stuttgart)
Probing fermionic Hubbard model with
spin polarization (Harvard)

2. Experiments with 2D Bose gasz
Time of
flight
Experiments with 2D Bose gas
Hadzibabic, Dalibard et al., Nature 441:1118 (2006)
Experiments with 1D Bose gas
Hofferberth et al. Nature Physics (2008)

3. Interference of independent 1d condensates
S. Hofferberth, I. Lesanovsky, T. Schumm, J. Schmiedmayer,
A. Imambekov, V. Gritsev, E. Demler, Nature Physics (2008)
Higher order correlation functions
probed by noise in interference

4. Non-equilibrium spin dynamics in one dimensional systems
Ramsey interferometry and
many-body decoherence
Mainz, Harvard collaboration
Widera, Trotzky, Cheinet, Foelling, Gerbier, Bloch,
Gritsev, Lukin, Demler, PRL (2008)
+ Kitagawa, Pielawa, Imambekov, Demler, unpublished

5. Ramsey interference Atomic clocks and Ramsey interference:1
Ramsey interference is basically Larmor precession for spin ½ particles. If we take a state which is a superposition of spin
up and spin down state, the two states will evolve with different energies. So the spin rotates in the plane with the frequency determined
by the energy difference. Ramsey precession underlies atomic clocks and is done not with one atoms but with many.
Atomic clocks and Ramsey interference:
Working with N atoms improves
the precision by

6. Interaction induced collapse of Ramsey fringes
Two component BEC. Single mode approximation
Ramsey fringe visibility
time
Experiments in 1d tubes:
A. Widera et al. PRL 100: (2008)
What is the role of interaction on Ramsey precession?

7. Spin echo. Time reversal experiments
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
No revival?

8. Interaction induced collapse of Ramsey fringes in one dimensional systems
Low energy effective theory in 1D:
Luttinger liquid approach
Only q=0 mode shows complete spin echo
Finite q modes continue decay
The net visibility is a result of competition
between q=0 and other modes
Decoherence due to
many-body dynamics of
low dimensional systems
How to distinquish decoherence due to many-body dynamics?

9. Interaction induced collapse of Ramsey fringes
Single mode analysis
Kitagawa, Ueda, PRA 47:5138 (1993)
Multimode analysis
evolution of spin distribution functions
T. Kitagawa, S. Pielawa, A. Imambekov, et al.

10. Lattice models Nonequilibrium dynamics in 1d anisotropic Heisenberg spin systems
Barmettler, Punk, Altman, Gritsev, Demler, arXiv:0810:4845

11. 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

12. Nonequilibrium spin dynamics in 1d. Lattice
Spin dynamics in 1D starting from the classical Neel state
Coherent time evolution
starting with
Y(t=0) =
Equilibrium phase diagram
QLRO D
Time, Jt
Expected: critical slowdown near
quantum critical point at D=1
Observed: fast decay
at D=1

13. Experiment: 1D AF isotropic model prepared in the Neel state: decay of staggered magnetization S. Trotzky et al. (group of I. Bloch)

14. Quasi 2D condensates: From 2D BKT to 3D
Theory: Pekker, Gritsev, Demler (Harvard) B. Clark (UIUC)
Experiment: Kasevich et al. (Stanford)

15. Quasi 2D condensates at Stanford
Optical lattice array
~20 disks
~100 87Rb atoms/disk
each disk ~60 nm x 4 mm
10 mm
kbT/h ~ 1 kHz
m/h ~ 200 Hz
J/h ~ Hz
N ~ 100
Interlayer tunneling is a tunable parameter (with lattice depth). 15

16. Berezinskii–Kosterlitz–Thouless
T=TBKT
temperature
Fisher & Hohenberg, PRB (1988)
T=0

17. Modifications for multiple pancakes
3D Phonons
T=TC
T=TBKT
3D XY
temperature
T=2t
T=0

18. Comparison theory and experiment, 12 Er lattice
Theory: Classical Monte-Carlo of XY model (also RG analysis)
Temperature (nK)
12 ER
Experiment
RF cut frequency (kHz)

19. 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

20. Ulrtacold atoms in low dimensions
Luming Duan
Realization of Low dimensions: atoms in strong transverse traps
Weakly interacting atoms:
Projection to the transverse ground state
Strongly interacting atoms near Feshbach resonance
Simple Projection does not work!
Multi-level effects

21. Description 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 length
Not adequate yet near Resonance
Reason:
Existence of two-body bound-state at any detuning in low-D
Effective low-D atomic scattering length does not include this bound state

22. Effective Hamiltonian for low-D strongly interacting gas
Effective interaction between atoms and dressed molecules (model II)
(Kestner, Duan, PRA, 06)
Atoms in transverse ground level
Dressed molecules,
accounting for atomic
population in excited
transverse levels.

23. Comparison of predictions of model I and model II
Comparison of Tomas-Fermi Radius of 2D gas in a weak planar trap
Fails to reproduce
a shrinking radius at the
BEC side
BCS side
BEC side
Zhang, Lin, Duan, PRA 08

24. Dipolar interactions
R. Cherng, E. Demler (Harvard) D.W. Wang (Tsing-Hua Univ)
H.P. Buchler (Stuttgart), P. Zoller (Innsbruck)

25. - + Dipolar interactions in low dimensional systems
Attractive interaction head-to-tail
Repulsive interaction side-by-side
Dipole-Dipole Interactions in 2D pancake
Attractive at short distances
Repulsive at long distances
Roton-maxon spectrum and roton softening
Santos, Shlyapnikov, Lewenstein (2000)
Fischer (2006)

26. 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:
Roton softening for
10, 20, and 100 layers
Growth rate of unstable modes
Decoherence of Bloch oscillations
In agreement with expts on 39K: Fattori et al, PRL (2008)
momentum
out of plane
momentum
in the plane

27. B F Spin-dipolar interactions for ultracold atoms
Larmor Precession (100 kHz) dominates
over all other energy scales.
Effective interaction based on
averaging over precession B F
Quasi 2D system of 87Rb. Spin-roton softening
Wide range of instabilities tuned by quadratic Zeeman, AC Stark shift, initial spiral spin winding

28. Dipolar instabilities in spinor condensates
Fourier spectrum
Spontaneously
modulated
textures in Rb
condensates
Vengalattore et al.,
PRL (2008)
Dipolar spin
instabilities
R. Cherng, E. Demler,
arXiv:
Checkerboard pattern
observed in experiments
reflects unstable
spin modes

29. Polar molecules Objectives: Polar molecules rotation of the molecule
dipole
moment
rotation of
the molecule
Objectives:
- control and design the
interactions potentials
- derive extended Hubbard models
Polar molecules
- permanent dipole
moment:
- polarizable with static electric
field, and microwave fields
- interactions are increased by
compared to magnetic dipole interactions

30. Polar molecules Three-body interactions Repulsive shield Spin toolbox
- 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
Spin toolbox
- polar molecules with spin
- realization of Kitaev model
(A. Micheli, G. Brennen, P. Zoller,
Nature Physics 2006)

31. Probing fermionic Hubbard model with spin polarization
B. Wunsch, E. Demler (Harvard)
E. Manousakis (FSU)

32. Antiferromagnetic Mott state and spin imbalance
Do we have spin separation in parabolic trap?
Perfect AF
Mott state
Spin
polarized
edges
Spin
polarized
edges
Canted antiferromagnetic
phase in the Mott plateau
W. Hofstetter et al., NJP(2008)
Hartree-Fock approximation

33. Antiferromagnetic Mott state and spin imbalance
Both states are self-consistent solutions of the HF equations
Canted antiferromagnetic phase is lower in energy

34. Quantum simulator theory
This talk: Harvard, Innsbruck-Stuttgart, Michigan
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)
Dipolar interactions (Harvard, Innsbruck, Stuttgart)
Probing fermionic Hubbard model with
spin polarization (Harvard)