Order and Correlations in Asymmetric Superfluid Matter

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Matter can behave in exotic, seemingly paradoxical ways. Take for instance the superfluid state: a state where matter conducts heat with infinite efficiency. A close relative is the superconducting state, in which materials conduct electricity without resistance. Both of these have now found their way into applications: cooling systems via superfluids and strong magnetic fields via superconductors. One of the most exciting open questions today is: Can superfluids be driven to ``crystallization" and can such a state be realized under extreme conditions as found in compact stars?Quantum particles are either bosons or fermions. Experiments with ultracold atoms indicate that so-called bosonic supercrystals may indeed exist. The possibility of fermionic supercrystals has also been intensely discussed for many years. While their realization remains elusive, it is of great interest to high-energy physics and astrophysics: for example, a crystalline color superconductor may be realized in the dense quark matter of compact stars.Currently, the most promising way to observe and analyze this exotic state of matter is via ultracold fermionic atoms. Corresponding experiments provide a clean environment to test our understanding of the formation of condensates and structure in the strongly interacting systems where supercrystals may form. Interestingly, ultracold gases of fermions share some important features with nuclear matter as well as with dense quark matter, in spite of their differences in orders of magnitude in density and temperature. The goal of this project is to exploit techniques developed intensively in the past years in the field of the theory of the strong interaction in order to elucidate, from first principles and in detail, the existence and properties of supercrystals in polarized fermionic matter under extreme conditions as modeled by ultracold gases of fermions.