1. The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advisory Committee Visit, May 13-14, 2010

2. Collaboration with experimental groups Stability of superfluid currents in optical lattices Theory: Harvard. Experiment: MIT Dynamics of crossing the ferromagnetic Stoner transition Theory: Harvard. Experiment: MIT Dynamic crossing of the superfluid to Mott transition in optical lattices Theory: Harvard. Experiment: Harvard Explore new systems that are not yet studied experimentally but may be realized in the future Adiaibatic preparation of magnetic and d-wave paired states in lattices Collaboration of groups by Lukin, Demler, Greiner Phase sensitive detection of nontrivial pairing Collaboration of groups of Demler, Greiner Tonks-Girardeau gas of photons in hollow fibers Collaboration of groups by Lukin, Demler, Vuletic Subwavelength resolution Collaboration of groups by Lukin, Greiner Connection to experimental groups all over the world Role of theory in the CUA

3. Bose-Einstein condensation of weakly interacting atoms Scattering length is much smaller than characteristic interparticle distances. Interactions are weak Density 10 13 cm -1 Typical distance between atoms 300 nm Typical scattering length 10 nm

4. New Era in Cold Atoms Research Focus on Systems with Strong Interactions Low dimensional systems. Strongly interacting regimes at low densities Feshbach resonances. Scattering length comparable to interparticle distances Optical lattices. Suppressed kinetic energy. Enhanced role of interactions Ketterle, Zwierlein Greiner, Ketterle Greiner

5. Theoretical work in the CUA New challenges and new opportunities Fermionic Hubbard model. Old model new questions Novel temperature regime, New probes, e.g. lattice modulation experiments Nonequilibrium phenomena New questions of many-body nonequilibrium dynamics Important for reaching equilibrium states Convenient time scales for experimental study Fundamental open problem Expansion of interacting fermions Photon fermionization New systems Alkali-Earth atoms. Systems with SU(N) symmetry

6. Fermionic Hubbard model New questions posed by experiments with cold atoms

7. Antiferromagnetic and superconducting Tc of the order of 100 K Atoms in optical lattice Antiferromagnetism and pairing at sub-micro Kelvin temperatures Same microscopic model Quantum simulations with ultracold atoms

8. Energy scales of the half-filled Hubbard model U and Antiferro Mott state Paramagnetic Mott phase. Charge fluctuations suppressed, no spin order current experiments Half-filling n=1 and TNTN

9. Lattice Modulation as a probe of the Mott state Experiment: Modulate lattice intensity Measure number Doublons Original Experiment: R. Joerdens et al., Nature 455:204 (2008) Theory: Sensarma, Pekker, Lukin, Demler, PRL 103, 035303 (2009) Latest spectral data ETH

10. Reduced probability to find a singlet on neighboring sites Radius Density P singlet D. Pekker, L. Pollet Temperature dependence

11. What can we learn from lattice modulation experiments?

12. Low Temperature Rate of doublon production in linear response approximation Fine structure due to spinwave shake-off Sharp absorption edge from coherent quasiparticles Signature of AFM! q k-q

13. Open problems: Develop theoretical approaches for connecting high and low temperature regimes Other modulation type experiments: e.g. oscillation of the Optical Lattice phase Intermediate temperature regime for spinful bosons.

14. Nonequilibrium phenomena Equilibration of different degrees of freedom Adiabatic preparation. Understand time scales for preparation of magnetically ordered states

15. Nonequilibrium phenomena in fermionic Hubbard model Doublons – repulsively bound pairs What is their lifetime? Excess energy U should be converted to kinetic energy of single atoms Decay of doublon into a pair of quasiparticles requires creation of many particle-hole pairs Direct decay is not allowed by energy conservation

16. Doublon decay in a compressible state Perturbation theory to order n=U/6t Decay probability To calculate the decay rate: consider processes which maximize the number of particle-hole excitations N. Strohmaier, D. Pekker, et al., PRL (2010) Expt: ETHZ Theory: Harvard

17. New systems that are not yet studied experimentally but may be realized in the future Alkali-Earth atoms. Systems with SU(N) symmetry

18. [Picture: Greiner (2002)] Two-Orbital SU(N) Magnetism with Ultracold Alkaline-Earth Atoms Alkaline-Earth atoms in optical lattice: Ex: 87 Sr (I = 9/2) |g  = 1 S 0 |e  = 3 P 0 698 nm 150 s ~ 1 mHz orbital degree of freedom ⇒ spin-orbital physics → Kugel-Khomskii model [transition metal oxides with perovskite structure] → SU(N) Kondo lattice model [for N=2, colossal magnetoresistance in manganese oxides and heavy fermion materials] Nuclear spin decoupled from electrons SU(N=2I+1) symmetry → SU(N) spin models ⇒ valence-bond-solid & spin-liquid phases A. Gorshkov, et al., Nature Physics, in press

19. Nonequilibrium many-body dynamics Important for reaching equilibrium states Convenient time scales for experimental study Fundamental open problem Expansion of interacting fermions

20. Experiment: I. Bloch et al., Theory: A. Rosch, E. Demler, et al. New dynamical symmetry: identical slowdown of expansion for attractive and repulsive interactions Expansion of interacting fermions in optical lattice

21. Photon fermionization Nonequilibrium many-body dynamics

22. Strongly correlated systems of photons Nature Physics (2008)

23. Self-interaction effects for one-dimensional optical waves BEFORE : two level systems and insufficient mode confinement Interaction corresponds to attraction. Physics of solitons Weak non-linearity due to insufficient mode confining Limit on non-linearity due to photon decay NOW: EIT and tight mode confinement Sign of the interaction can be tuned Tight confinement of the electromagnetic mode enhances nonlinearity Strong non-linearity without losses can be achieved using EIT

24. Experimental detection of the Luttinger liquid of photons Control beam off. Coherent pulse of non-interacting photons enters the fiber. Control beam switched on adiabatically. Converts the pulse into a Luttinger liquid of photons. “Fermionization” of photons detected by observing oscillations in g 2 c K – Luttinger parameter In equilibrium in a Luttinger liquid

25. Non-equilibrium dynamics of strongly correlated many-body systems g 2 for expanding Tonks-Girardeau gas with adiabatic switching of interactions 100 photons after expansion

26. Do we have universality in nonequilibrium dynamics of many-body quantum systems? Universaility in dynamics of nonlinear classical systems Solitons in nonlinear wave propagation Bernard cells in the presence of T gradient Universality in quantum many- body systems in equilibrium Broken symmetries Fermi liquid state