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Eugene Demler Strongly correlated many-body systems Electronic materials Ultracold atoms Quantum Optics “Standard” model of electrons in solids High density of electrons. Band theory. Description in terms of weakly interacting Landau electrons. Au, Cu, Si, GaAs, … First semiconductor transistor Intel 386DX microprocessor Strongly correlated electron systems Low density of electrons. Interactions localize electrons. Hubbard bands. Unusual U thermodynamic and transport properties. Spin and orbital ordering. Energy EF Quantum magnetism. Phase diagram of La 1-x Ca x MnO3 Ordered state for x=0.5 High Tc superconductors The structure of La2CuO4 Microscopic description: Hubbard model U t t 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) Atoms in optical lattice Antiferromagnetism and pairing at sub-micro Kelvin temperatures Antiferromagnetic and superconducting Tc of the order of 100 K Same microscopic model U t t Detection of many body states ? Quantum noise analysis E. Altman, A. Polkovnikov, A. Imambekov, V. Gritsev, T. Kitagawa, R. Cherng, M. Lukin Quantum noise Classical measurement: collapse of the wavefunction into eigenstates of x Histogram of measurements of x 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 Superfluid to insulator transition in an optical lattice M. Greiner et al., Nature 415 (2002) U Mott insulator Superfluid n 1 t/U Time of flight experiments Quantum noise interferometry of atoms in an optical lattice Second order coherence Second order coherence in the insulating state of bosons. Hanburry-Brown-Twiss experiment Experiment: Folling et al., Nature 434:481 (2005) Hanburry-Brown-Twiss stellar interferometer Second order coherence in the insulating state of bosons Bosons at quasimomentum expand as plane waves with wavevectors First order coherence: Oscillations in density disappear after summing over Second order coherence: Correlation function acquires oscillations at reciprocal lattice vectors Second order coherence in the insulating state of bosons. Hanburry-Brown-Twiss experiment Experiment: Folling et al., Nature 434:481 (2005) Second order coherence in the insulating state of fermions. Hanburry-Brown-Twiss experiment Experiment: Tom et al. Nature 444:733 (2006) Probing spin order in optical lattices Correlation Function Measurements Extra Bragg peaks appear in the second order correlation function in the AF phase Quantum noise analysis of TOF images is more than HBT interference Detection of fermion pairing Second order interference from the BCS superfluid Theory: Altman et al., PRA 70:13603 (2004) n(k) n(r’) kF k n(r) BCS BEC n(r, r' ) n(r) n(r' ) n(r,r) BCS 0 Momentum correlations in paired fermions Experiments: Greiner et al., PRL 94:110401 (2005)