Strongly Correlated Systems of Ultracold Atoms

Strongly Correlated Systems of Ultracold Atoms

Theory work at CUA

New Era in Cold Atoms ResearchFocus on Systems with Strong Interactions

• Optical lattices

• Feshbach resonances

• Low dimensional systems

• Systems with long range interactions (Coulomb interaction for trapped ions, dipolar interactions for polar molecules)

SYNERGYBETWEEN THEORYANDEXPERIMENT

Phase Diagrams

Detection andCharacterization

Preparation of many-body states

Quantum Simulations of Condensed Quantum Simulations of Condensed Matter Systems using Ultracold Matter Systems using Ultracold

Atomic GasesAtomic Gases

Preparation of many-body states

Decay probability

Doublon decay in a compressible stateHow to get rid of the excess energy U?

Doublon can decay into apair of quasiparticles with many particle-hole pairs

Consider processes which maximize the number of particle-hole excitations

Perturbation theory to order n=U/t

Experiment:ETH, ZurichTheory:Harvard

Observation of superexchange in a double well potential

Use magnetic field gradient to prepare a state

Observe oscillations between and states

Jex

Experimental measurements of superexchange Jex.

Comparison to first principle calculations

Experiment: S. Trotzky et al., Science (2008)

Theory: A.M. Rey et al., PRL (2007)

1D: XXZ dynamics starting from the classical Neel state

• DMRG• XZ model: exact solution• >1: sine-Gordon Bethe ansatz solution

Time, Jt

Equilibrium phase diagram

(t=0) =Coherent time evolution starting with

QLRO

Fermions in optical lattice: surprise of the attractive Hubbard model

Anomalous radius increaseExperiments by I. Bloch et al.

Theory: Mainz+Harvard

Competition of attraction and entropy

High temperature expansion of the Hubbard model

DETECTION

AND

CHARACTERIZATION

PHASE DIAGRAMS

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 et al., Nature Physics (2008)

Higher order correlation functionsprobed by noise in interference

Experiments: Vienna; Theory: Harvard

OUTLOOK:

NONEQUILIBRIUM DYNAMICS

NEW PERSPECTIVE ON

MANY-BODY SYSTEMS

Dynamics in 1d: Ramsey interference

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

Interaction induced collapse of Ramsey fringes. time

Ramsey fringe visibility

Spin echo

Interaction induced collapse of Ramsey fringesin one dimensional systems

How to distinguish decoherencedue to many-body dynamics?Luttinger liquid approach

Evolution of spin distribution functions

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

OUTLOOK:

QUANTUM MANY-BODY SYSTEMS

IN THE PRESENSE OF

NONEQUILIBRIUM NOISE

NEW PERSPECTIVE ON

MANY-BODY SYSTEMS

Trapped ions Ultracold polar molecules

E

Trapping ions and polar molecules

Noise spectrum is 1/f

Monroe (2006), Chuang (2008)

Short range

spatial correlations

Effective coupling to external noise

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(Quantum) Langevin dynamics:

Dissipative coupling to bath needed to ensure steady state (removes the energy pumped in by the external noise).

Physical implementation: continuous cooling

Thermal bath

External noise

Wigner crystal correlations

- Decay of crystal correlations remains power-law.

- Decay exponent tuned by the 1/f noise power.

2Kc

F0 /

2D superfluid

2D crystal1D critical

• Powerlaw correlations and response in the critical steady state

• Novel phase transitions tuned by acompetition of noise and quantum fluctuations

SYNERGYBETWEEN THEORYANDEXPERIMENT

Phase Diagrams

Detection andCharacterization

Preparation of many-body states

Quantum Simulations of Condensed Quantum Simulations of Condensed Matter Systems using Ultracold Matter Systems using Ultracold

Atomic GasesAtomic Gases