Transcript ppt - Condensed Matter Theory at Harvard University

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)
Experiments with 2D Bose gas
Hadzibabic, Dalibard et al., Nature 441:1118 (2006)
z
Time of
flight
x
Experiments with 1D Bose gas
Hofferberth et al. Nature Physics (2008)
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
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+ Kitagawa, Pielawa, Imambekov, Demler, unpublished
Ramsey interference
1
0
Atomic clocks and Ramsey interference:
Working with N atoms improves
the precision by
.
t
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 100:140401 (2008)
Spin echo. Time reversal experiments
A. Widera et al., PRL (2008)
No revival?
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 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?
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.
Lattice models
Nonequilibrium 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
Coherent time evolution
starting with
Y(t=0) =
Equilibrium phase diagram
QLRO
D
Expected: critical slowdown near
quantum critical point at D=1
Observed: fast decay
at D=1
Time, Jt
Experiment: 1D AF isotropic model
prepared in the Neel state: decay of
staggered magnetization
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 Stanford
Optical lattice array
10
mm
• ~20 disks
• ~100 87Rb
atoms/disk
• each disk ~60 nm x
4 mm
kbT/h ~ 1 kHz
m/h ~ 200 Hz
J/h ~ 5-500 Hz
N ~ 100
Interlayer tunneling
is a tunable
parameter (with
lattice depth).
Berezinskii–Kosterlitz–Thouless
temperature
T=TBKT
Fisher & Hohenberg, PRB (1988)
T=0
Modifications for multiple pancakes
3D Phonons
T=TC
temperature
T=TBKT
T=2t
T=0
3D XY
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)
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 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
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
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.
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
BEC side
BCS side
Zhang, Lin, Duan, PRA 08
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
+ +
-
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)
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
Decoherence of Bloch oscillations
In agreement with expts on
39K: Fattori et al, PRL (2008)
momentum
out of plane
momentum
in the plane
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
Dipolar instabilities in spinor condensates
Spontaneously
modulated
textures in Rb
condensates
Vengalattore et al.,
PRL (2008)
Dipolar spin
instabilities
R. Cherng, E. Demler,
arXiv:0806.1991
Fourier spectrum
Checkerboard pattern
observed in experiments
reflects unstable
spin modes
Polar molecules
Objectives:
rotation of
the molecule
- control and design the
interactions potentials
- derive extended Hubbard models
dipole
moment
Polar molecules
- permanent dipole
moment:
- polarizable with static electric
field, and microwave fields
- interactions are increased by
compared to magnetic dipole interactions
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
Spin toolbox
- polar molecules with spin
- realization of Kitaev model
(A. Micheli, G. Brennen, P. Zoller,
Nature Physics 2006)
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?
Perfect AF
Mott state
Spin
polarized
edges
Spin
polarized
edges
W. Hofstetter et al., NJP(2008)
Hartree-Fock approximation
Canted antiferromagnetic
phase in the Mott plateau
Antiferromagnetic Mott state and spin imbalance
Both states are self-consistent solutions of the HF equations
Canted antiferromagnetic phase is lower in energy
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)