Description

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Introduction.- Part I Single-Site- and Single-Atom-Resolved Detection of Atomic Limit Mott Insulators.- Superfluid-Mott-Insulator Transition.- Overview of the Experimental Procedure.- Single-Site-Resolved Imaging and Thermometry of Atomic Limit Mott Insulators.- Part II Single-Site- and Single-Atom-Resolved Detection of Correlation Functions.- Detection of Particle-Hole Pairs Using Two-Site Correlation Functions.- Non-Local Correlations in One Dimension.- Non-Local Correlations in Two Dimensions, Duality and Distribution Functions.- Part III 'Higgs' Amplitude Mode.- Introduction to Amplitude and Phase Modes.- Detection of the Higgs Amplitude Mode at the 2d SF-Mott-Insulator Transition.- Outlook.- Part IV Appendix.- Appendix A Experimental Details.- Appendix B Numerical Methods for Correlation Functions.- Appendix C Calculation for Non-Local Correlations in One Dimension.- Appendix D Calculation for Non-Local Correlations in Two Dimensions.