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## Strongly correlated many-body systems

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**Eugene Demler**Strongly correlated many-body systems Electronic materials Ultracold atoms Quantum Optics**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**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**U**t t The structure of La2CuO4 High Tc superconductors Microscopic description: Hubbard model**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)**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**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**Mott insulator**Superfluid t/U Superfluid to insulator transition in an optical lattice M. Greiner et al., Nature 415 (2002)**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)**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**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**Detection of fermion pairing**Quantum noise analysis of TOF images is more than HBT interference**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**Momentum correlations in paired fermions**Experiments: Greiner et al., PRL 94:110401 (2005)