1. Strongly Correlated Systems of Ultracold Atoms Theory work at CUA

2. 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)

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

4. Preparation of many-body states

5. Decay probability Doublon decay in a compressible state How to get rid of the excess energy U? Doublon can decay into a pair 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, Zurich Theory: Harvard

6. Observation of superexchange in a double well potential Use magnetic field gradient to prepare a stateObserve oscillations between and states J ex Experimental measurements of superexchange J ex. Comparison to first principle calculations Experiment: S. Trotzky et al., Science (2008) Theory: A.M. Rey et al., PRL (2007)

7. 1D: XXZ dynamics starting from the classical Neel state DMRG XZ model: exact solution D >1: sine-Gordon Bethe ansatz solution Time, Jt D Equilibrium phase diagram Y (t=0) = Coherent time evolution starting with QLRO

8. Fermions in optical lattice: surprise of the attractive Hubbard model Anomalous radius increase Experiments by I. Bloch et al. Theory: Mainz+Harvard Competition of attraction and entropy High temperature expansion of the Hubbard model

9. DETECTION AND CHARACTERIZATION PHASE DIAGRAMS

10. x z Time of flight Experiments with 2D Bose gas Hadzibabic, Dalibard et al., Nature 441:1118 (2006) Experiments with 1D Bose gas Hofferberth et al. Nature Physics (2008)

11. Interference of independent 1d condensates S. Hofferberth et al., Nature Physics (2008) Higher order correlation functions probed by noise in interference Experiments: Vienna; Theory: Harvard

12. OUTLOOK: NONEQUILIBRIUM DYNAMICS NEW PERSPECTIVE ON MANY-BODY SYSTEMS

13. 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

14. Interaction induced collapse of Ramsey fringes in one dimensional systems How to distinguish decoherence due to many-body dynamics? Luttinger liquid approach Evolution of spin distribution functions 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

15. OUTLOOK: QUANTUM MANY-BODY SYSTEMS IN THE PRESENSE OF NONEQUILIBRIUM NOISE NEW PERSPECTIVE ON MANY-BODY SYSTEMS

16. Trapped ions Ultracold polar molecules E Trapping ions and polar molecules Noise spectrum is 1/f Monroe (2006), Chuang (2008) Short range spatial correlations

17. Effective coupling to external noise + - + - + - + - + - + - + - + - + - + - (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

18. Wigner crystal correlations - Decay of crystal correlations remains power-law. - Decay exponent tuned by the 1/f noise power. 2 KcKc F 0 /  2D superfluid 2D crystal 1D critical Powerlaw correlations and response in the critical steady state Novel phase transitions tuned by a competition of noise and quantum fluctuations

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