Quantum-limited tomographic detection of correlations in a strongly interacting atomic Fermi gas

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One of the greatest challenges of physics is the realisation of materials with properties that can be changed at will. Historically, this field of research was mainly pursued in condensed matter physics. This has lead to the development of complex materials whose performance is dominated by quantum correlations and strong interactions. Some of these discoveries have found their way into applications of our daily life. The prime examples are high-temperature superconductivity which is used in medical instrumentation and telecommunications and giant magneto-resistance which has revolutionized computer hard disks. However, from a fundamental perspective an understanding of the underlying mechanism is often lacking. Without this understanding a further optimization or targeted search for even more advanced materials is quite difficult.In recent years, a promising new route to study fundamental properties of strongly correlated materials has emerged: atomic gases at Nanokelvin temperatures - firstly Bose-Einstein condensates and later degenerate Fermi gases - realize quantum many-body systems of unprecedented purity and tunability. Materials with complex properties can now be assembled from atoms in a bottom-up approach. The key ingredient which allows for a particularly good conceptual relation between cold atomic gases and solid state physics is the optical lattice. Optical lattices are crystals of light formed by three pairs of counter-propagating laser beams. This complex arrangement of intense laser light fields provides a periodic potential for atoms resembling the crystal lattice of a solid. Fermionic atom gases in an optical lattice simulate the physics of electrons in a solid yet being an extremely well controlled model system. They thus pave the way to understand the quantum behaviour of electrons in a solid under much purer and even tunable conditions. For example, it has been proposed that cold atomic gases in optical lattices could unravel the physics underlying high-temperature superconductivity. With our experiments we will investigate quantum many-body physics from first principles. We plan to realize complex quantum phases of fermionic atoms in a three-dimensional optical lattice including the analogue of a high-temperature superconducting phase. This would allow to identify the mechanism of how the electrons in as superconductor pair and why high-temperature superconductors are different from metals or metallic superconductors. To characterize the strongly correlated quantum many-body state as precisely as possible we will perform a novel three-dimensional tomographic imaging with single atom resolution. This new technique is based on the progress in atomic physics over the past decade to achieve single atom detection of near 100% efficiency. Equipped with this experimental capability we will be able to uncover even the smallest correlation effects at the quantum limit to observe the correlated motion of pairs of atoms. This will unambiguously reveal novel superconducting or magnetically ordered states.