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
