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The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advisory Committee Visit, May 13-14, 2010

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The Center for Ultracold Atomsat MIT and Harvard

Strongly Correlated Many-Body Systems

Theoretical work in the CUA

Advisory Committee Visit, May 13-14, 2010

- Collaboration with experimental groups
- Stability of superfluid currents in optical lattices
- Theory: Harvard. Experiment: MIT
- Dynamics of crossing the ferromagnetic Stoner transition
- Theory: Harvard. Experiment: MIT
- Dynamic crossing of the superfluid to Mott transition in optical lattices
- Theory: Harvard. Experiment: Harvard
- Explore new systems that are not yet studied experimentally but may be realized in the future
- Adiaibatic preparation of magnetic and d-wave paired states in lattices
- Collaboration of groups by Lukin, Demler, Greiner
- Phase sensitive detection of nontrivial pairing
- Collaboration of groups of Demler, Greiner
- Tonks-Girardeau gas of photons in hollow fibers
- Collaboration of groups by Lukin, Demler, Vuletic
- Subwavelength resolution
- Collaboration of groups by Lukin, Greiner
- Connection to experimental groups all over the world

Bose-Einstein condensation of weakly interacting atoms

Density 1013 cm-1

Typical distance between atoms 300 nm

Typical scattering length 10 nm

Scattering length is much smaller than characteristic interparticle distances.

Interactions are weak

New Era in Cold Atoms Research

Focus on Systems with Strong Interactions

- Feshbach resonances.
- Scattering length comparable
- to interparticle distances

Ketterle,

Zwierlein

- Optical lattices.
- Suppressed kinetic energy.
- Enhanced role of interactions

Greiner,

Ketterle

- Low dimensional systems.
- Strongly interacting regimes
- at low densities

Greiner

Fermionic Hubbard model. Old model new questions

- Novel temperature regime,
- New probes, e.g. lattice modulation experiments
- Nonequilibrium phenomena

Theoretical work in the CUA

New challenges and new opportunities

New systems

Alkali-Earth atoms. Systems with SU(N) symmetry

- New questions of many-body nonequilibrium dynamics
- Important for reaching equilibrium states
- Convenient time scales for experimental study
- Fundamental open problem
- Expansion of interacting fermions
- Photon fermionization

New questions posed by experiments with cold atoms

Antiferromagnetic and superconducting Tc

of the order of 100 K

Quantum simulations with ultracold atoms

Atoms in optical lattice

Antiferromagnetism and

pairing at sub-micro Kelvin

temperatures

Same microscopic model

and

and

Energy scales of the half-filled Hubbard modelHalf-filling n=1

Paramagnetic Mott phase.

Charge fluctuations suppressed,

no spin order

and

current

experiments

Antiferro

Mott state

U

Lattice Modulation as a probe of the Mott state

- Experiment:
- Modulate lattice intensity
- Measure number Doublons

Latest spectral data ETH

Original Experiment:

R. Joerdens et al.,

Nature 455:204 (2008)

Theory: Sensarma, Pekker, Lukin, Demler,

PRL 103, 035303 (2009)

Density

Psinglet

Radius

Radius

D. Pekker,

L. Pollet

Reduced probability to find a singlet on neighboring sites

lattice modulation experiments?

Low Temperature

q

k-q

Rate of doublon production in linear response approximation

Fine structure due to spinwave shake-off

Sharp absorption edge from coherent quasiparticles

Signature of AFM!

Develop theoretical approaches for connecting

high and low temperature regimes

Other modulation type experiments:

e.g. oscillation of the Optical Lattice phase

Intermediate temperature regime for spinful

bosons.

Equilibration of different

degrees of freedom

Adiabatic preparation.

Understand time scales for preparation of

magnetically ordered states

Nonequilibrium phenomena in fermionic Hubbard model

Doublons – repulsively bound pairs

What is their lifetime?

Direct decay is

not allowed by

energy conservation

Excess energy U should be converted to kinetic energy of single atoms

Decay of doublon into a pair of quasiparticles requires creation of many particle-hole pairs

Doublon decay in a compressible state

N. Strohmaier, D. Pekker, et al., PRL (2010)

Perturbation theory to order n=U/6t

Decay probability

To calculate the decay rate: consider processes which maximize the number of particle-hole excitations

Expt: ETHZ

Theory: Harvard

New systems that are not yet studied experimentally but may be realized in the future

Alkali-Earth atoms. Systems with SU(N) symmetry

Two-Orbital SU(N) Magnetism with

Ultracold Alkaline-Earth Atoms

|e> = 3P0

698 nm

150 s ~ 1 mHz

Ex: 87Sr(I = 9/2)

|g> = 1S0

[Picture: Greiner (2002)]

A. Gorshkov, et al., Nature Physics, in press

Alkaline-Earth atoms in optical lattice:

Nuclear spin decoupled from electrons SU(N=2I+1) symmetry

→ SU(N) spin models ⇒ valence-bond-solid & spin-liquid phases

• orbital degree of freedom ⇒ spin-orbital physics

→ Kugel-Khomskii model [transition metal oxides with perovskite structure]

→ SU(N) Kondo lattice model [for N=2, colossal magnetoresistance in manganese oxides and heavy fermion materials]

Nonequilibrium many-body dynamics

Important for reaching equilibrium states

Convenient time scales for experimental study

Fundamental open problem

Expansion of interacting fermions

Expansion of interacting fermions in optical lattice

Experiment: I. Bloch et al.,

Theory: A. Rosch, E. Demler, et al.

New dynamical symmetry:

identical slowdown of expansion

for attractive and repulsive

interactions

Nonequilibrium many-body dynamics

Photon fermionization

Strongly correlated systems of photons

Nature Physics (2008)

Self-interaction effects for one-dimensional optical waves

BEFORE: two level systems and

insufficient mode confinement

NOW: EIT and tight

mode confinement

Interaction corresponds to attraction.

Physics of solitons

Sign of the interaction can be tuned

Tight confinement of the

electromagnetic mode

enhances nonlinearity

Weak non-linearity due to insufficient

mode confining

Limit on non-linearity due to

photon decay

Strong non-linearity without losses

can be achieved using EIT

Experimental detection of the Luttinger liquid of photons

Control beam off.

Coherent pulse of

non-interacting photons

enters the fiber.

Control beam switched on adiabatically.

Converts the pulse into a Luttinger liquid

of photons.

“Fermionization” of photons detected by observing oscillations in g2

In equilibrium in

a Luttinger liquid

K – Luttinger parameter

Non-equilibrium dynamics of strongly

correlated many-body systems

g2 for expanding Tonks-Girardeau gas

with adiabatic switching of interactions

100 photons after expansion

nonlinear classical systems

Universality in quantum many-body systems in equilibrium

Do we have universality in nonequilibrium dynamics of many-body quantum systems?Solitons in nonlinear wave propagation

Broken symmetries

Bernard cells in the presence of T gradient

Fermi liquid state

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