The Center for Ultracold Atoms at MIT and Harvard Strongly Correlated Many-Body Systems Theoretical work in the CUA Advi

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

2. Role of theory in the CUA • 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

3. Bose-Einstein condensation of weakly interacting atoms Density 1013 cm-1 Typical distance between atoms 300 nm Typical scattering length 10 nm Scattering length is much smaller than characteristic interparticle distances. Interactions are weak

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

5. Fermionic Hubbard model. Old model new questions • Novel temperature regime, • New probes, e.g. lattice modulation experiments • Nonequilibrium phenomena Theoretical work in the CUA New challenges and new opportunities New systems Alkali-Earth atoms. Systems with SU(N) symmetry • 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

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

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

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

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

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

11. What can we learn from lattice modulation experiments?

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

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? Direct decay is not allowed by energy conservation 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

16. Doublon decay in a compressible state N. Strohmaier, D. Pekker, et al., PRL (2010) Perturbation theory to order n=U/6t Decay probability To calculate the decay rate: consider processes which maximize the number of particle-hole excitations 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. Two-Orbital SU(N) Magnetism with Ultracold Alkaline-Earth Atoms |e> = 3P0 698 nm 150 s ~ 1 mHz Ex: 87Sr(I = 9/2) |g> = 1S0 [Picture: Greiner (2002)] A. Gorshkov, et al., Nature Physics, in press Alkaline-Earth atoms in optical lattice: Nuclear spin decoupled from electrons SU(N=2I+1) symmetry → SU(N) spin models ⇒ valence-bond-solid & spin-liquid phases • 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]

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

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

21. Nonequilibrium many-body dynamics Photon fermionization

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 NOW: EIT and tight mode confinement Interaction corresponds to attraction. Physics of solitons Sign of the interaction can be tuned Tight confinement of the electromagnetic mode enhances nonlinearity Weak non-linearity due to insufficient mode confining Limit on non-linearity due to photon decay Strong non-linearity without losses can be achieved using EIT

24. c 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 g2 In equilibrium in a Luttinger liquid K – Luttinger parameter

25. Non-equilibrium dynamics of strongly correlated many-body systems g2 for expanding Tonks-Girardeau gas with adiabatic switching of interactions 100 photons after expansion

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