Strongly Correlated Systems of Ultracold Atoms

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. 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

4. Preparation of many-body states

5. 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 n=U/t

6. Jex Use magnetic field gradient to prepare a state Observe oscillations between and states 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

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

8. 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: Mainz+Harvard Competition of attraction and entropy

9. DETECTION AND CHARACTERIZATION PHASE DIAGRAMS

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

11. 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

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

13. Ramsey fringe visibility time Dynamics in 1d: Ramsey interference Interaction induced collapse of Ramsey fringes. Spin echo • Experiments in 1d tubes: • Widera et al. • PRL (2008)

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

17. 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

18. 2D superfluid 1D critical 2D crystal Kc 2 F0 /h 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

19. 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