Order and Correlations in Asymmetric Superfluid Matter

物质可以以奇异的、看似自相矛盾的方式表现。以超流体状态为例：物质以无限的效率传导热量的状态。一个近亲是超导状态，在这种状态下，材料在没有电阻的情况下导电。这两种技术现在都已进入应用领域：通过超流体实现冷却系统，通过超导体实现强磁场。今天最令人兴奋的悬而未决的问题之一是：超流体能被驱动到“结晶”吗？这种状态能像致密恒星那样在极端条件下实现吗？量子粒子要么是玻色子，要么是费米子。用超冷原子进行的实验表明，所谓的玻色子超晶可能确实存在。多年来，费米子超晶的可能性也得到了激烈的讨论。虽然它们的实现仍然难以捉摸，但它对高能物理和天体物理学非常感兴趣：例如，晶体颜色超导体可能在致密恒星的致密夸克物质中实现。目前，观察和分析这种奇异物质状态的最有希望的方法是通过超冷费米子原子。相应的实验提供了一个干净的环境来测试我们对凝聚体的形成和在可能形成超晶体的强相互作用系统中的结构的理解。有趣的是，费米子的超冷气体与核物质和致密夸克物质有一些重要的共同特征，尽管它们在密度和温度的数量级上有所不同。这个项目的目标是利用过去几年在强相互作用理论领域密集发展的技术，以便从第一原理和详细说明在极端条件下由费米子超冷气体模拟的极化费米子物质中超晶的存在和性质。

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.