Strongly correlated many-body systems

1. Eugene Demler Strongly correlated many-body systems Electronic materials Ultracold atoms Quantum Optics

2. First semiconductor transistor “Standard” model of electrons in solids High density of electrons. Band theory. Description in terms of weakly interacting Landau electrons. Au, Cu, Si, GaAs, … Intel 386DX microprocessor

3. U EF Energy Strongly correlated electron systems Low density of electrons. Interactions localize electrons. Hubbard bands. Unusual thermodynamic and transport properties. Spin and orbital ordering. Quantum magnetism. Phase diagram of La1-x Cax MnO3 Ordered state for x=0.5

4. U t t The structure of La2CuO4 High Tc superconductors Microscopic description: Hubbard model

5. Artificial crystals: optical lattices Theory: Jaksch et al. PRL (1998) Experiment: Greiner et al., Nature (2001) and many more Motivation: quantum simulations of strongly correlated electron systems including quantum magnets and unconventional superconductors. Hofstetter et al. PRL (2002)

6. U t t 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

7. Detection of many body states ? Quantum noise analysis E. Altman, A. Polkovnikov, A. Imambekov, V. Gritsev, T. Kitagawa, R. Cherng, M. Lukin

8. Quantum noise Classical measurement: collapse of the wavefunction into eigenstates of x Histogram of measurements of x

9. Second order coherence: HBT experiments Classical theory Hanburry Brown and Twiss (1954) Quantum theory Glauber (1963) For bosons For fermions Used to measure the angular diameter of Sirius HBT experiments with matter

10. Mott insulator Superfluid t/U Superfluid to insulator transition in an optical lattice M. Greiner et al., Nature 415 (2002)

11. Time of flight experiments Quantum noise interferometry of atoms in an optical lattice Second order coherence

12. Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment Experiment: Folling et al., Nature 434:481 (2005)

13. Hanburry-Brown-Twiss stellarinterferometer

14. Bosons at quasimomentum expand as plane waves with wavevectors Second order coherence in the insulating state of bosons First order coherence: Oscillations in density disappear after summing over Second order coherence: Correlation function acquires oscillations at reciprocal lattice vectors

15. Second order coherence in the insulating state of bosons.Hanburry-Brown-Twiss experiment Experiment: Folling et al., Nature 434:481 (2005)

16. Second order coherence in the insulating state of fermions.Hanburry-Brown-Twiss experiment Experiment: Tom et al. Nature 444:733 (2006)

17. Probing spin order in optical lattices Correlation Function Measurements Extra Bragg peaks appear in the second order correlation function in the AF phase

18. Detection of fermion pairing Quantum noise analysis of TOF images is more than HBT interference

19. n(r’) k F n(r) Second order interference from the BCS superfluid Theory: Altman et al., PRA 70:13603 (2004) n(k) k BCS BEC

20. Momentum correlations in paired fermions Experiments: Greiner et al., PRL 94:110401 (2005)