Strongly Correlated Systems of Ultracold Atoms

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Strongly Correlated Systems of Ultracold Atoms
Theory work at CUA
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New Era in Cold Atoms Research
Focus 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)

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Quantum Simulations of Condensed Matter Systems
using Ultracold Atomic Gases
Preparation of many-body states
SYNERGY BETWEEN THEORY AND EXPERIMENT
Detection and Characterization
Phase Diagrams
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• Preparation of many-body states

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Doublon decay in a compressible state
How to get rid of the excess energy U?
Decay probability
Doublon can decay into a pair of quasiparticles
with many particle-hole pairs
Consider processes which maximize the number of
particle-hole excitations
Experiment ETH, Zurich Theory Harvard
Perturbation theory to order nU/t
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Observation of superexchange in a double well
potential
Theory A.M. Rey et al., PRL (2007)
Experiment S. Trotzky et al., Science (2008)
Experimental measurements of superexchange Jex.
Comparison to first principle calculations
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1D XXZ dynamics starting from the classical Neel
state
Coherent time evolution starting with
Equilibrium phase diagram
QLRO

• DMRG
• XZ model exact solution
• Dgt1 sine-Gordon
• Bethe ansatz solution

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Fermions in optical lattice surprise of the
attractive Hubbard model
Anomalous radius increase Experiments by I. Bloch
et al.
High temperature expansion of the Hubbard model
Theory MainzHarvard
Competition of attraction and entropy
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• DETECTION
• AND
• CHARACTERIZATION

PHASE DIAGRAMS
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Experiments with 1D Bose gas

Hofferberth et al. Nature Physics (2008)
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Interference of independent 1d condensates
S. Hofferberth et al., Nature Physics (2008)
Experiments Vienna Theory Harvard
Higher order correlation functions probed by
noise in interference
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• OUTLOOK
• NONEQUILIBRIUM DYNAMICS
• NEW PERSPECTIVE ON
• MANY-BODY SYSTEMS

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Dynamics in 1d Ramsey interference
Interaction induced collapse of Ramsey fringes.
Spin echo

• Experiments in 1d tubes
• Widera et al.
• PRL (2008)

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Interaction induced collapse of Ramsey fringesin
one dimensional systems
How to distinguish decoherence due to many-body
dynamics?
Luttinger liquid approach
Evolution of spin distribution functions
Only q0 mode shows complete spin echo Finite q
modes continue decay The net visibility is a
result of competition between q0 and other modes
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• OUTLOOK
• QUANTUM MANY-BODY SYSTEMS
• IN THE PRESENSE OF
• NONEQUILIBRIUM NOISE

NEW PERSPECTIVE ON MANY-BODY SYSTEMS
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Trapping ions and polar molecules
Trapped ions
Ultracold polar molecules
E
Noise spectrum is 1/f Monroe (2006), Chuang
(2008) Short range spatial correlations
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Effective coupling to external noise
(Quantum) Langevin dynamics
Thermal bath
External noise
Dissipative coupling to bath needed to ensure
steady state (removes the energy pumped in by the
external noise). Physical implementation
continuous cooling
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Wigner crystal correlations

• Decay of crystal correlations remains power-law.
  
• Decay exponent tuned by the 1/f noise power.

• Powerlaw correlations and response in the
  critical steady state
• Novel phase transitions tuned by acompetition of
  noise and quantum fluctuations

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Quantum Simulations of Condensed Matter Systems
using Ultracold Atomic Gases
Preparation of many-body states
SYNERGY BETWEEN THEORY AND EXPERIMENT
Detection and Characterization
Phase Diagrams
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