Functional renormalization group for ultracold atoms

超冷费米子原子气体中的凝聚和束缚现象构成了一个极其丰富的研究领域，其相关性从原子和凝聚态物理学延伸到核物质和天体物理学。该项目开发和应用相关的强耦合多体物理学的功能积分描述，以及在一个统一的框架，使用功能重整化群的少体物理学。本项目将讨论三个主要议题。(1)本文研究了二组分非平衡费米气体的相图随温度、平均化学势和非平衡参数的变化关系，特别注意了共振时的么正性极限。为了绘制完整的相图，超流性和费米子能隙的完整有效序参量的RG流是中心感兴趣的。超流相的性质和一阶过渡线的位置以及三临界点的位置应借助进入破碎相的功能RG流来确定。(2)三体复合材料在费米系统中的临界现象的作用还不太清楚，应在3组分费米气体的功能RG研究中进行探索。在低温和共振附近的预期三离子相是本研究的重点。此外，BCS或BEC配对及其对相结构和临界区位置的影响的三重修改将针对，作为执行一个前所未有的搜索三体主导的集体和临界现象。在第二步中，需要研究提升3-分量简并的显式非线性破缺项的影响，以便预测涉及错位Feshbach共振的潜在实验实现。(3)最近的进展，偶极原子和偶极分子在其旋转和振动的基态制备的动机，我们计划使用功能RG探索偶极费米气体，包括超导，超流，磁和可能更奇特的相的潜在丰富的相结构。虽然粒子-粒子通道是在几年前用二阶微扰理论研究的，但粒子-空穴通道中可能的不稳定性只是最近在平均场理论中讨论的。这些竞争渠道之间的竞争似乎对我们很有吸引力。通过玻色子Hubbard-Stratonovich场解耦长程各向异性费米子相互作用，我们的目标是描述对平均场理论的修正。事实上，通过使用仅在玻色子扇区平均场理论中具有截止的FRG作为初始条件，并且通过减少红外截止，我们逐步包括序参数波动。除了确定超流序参量和费米面的精确形状外，我们还将研究单粒子激发的光谱。

The condensation and binding phenomena in gases of ultracold fermionic atoms constitute an overwhelmingly rich field of research, the relevance of which extends from atomic and condensed-matter physics to nuclear-matter and astrophysics. This project develops and applies a functional integral description of the relevant strong-coupling many-body physics as well as few-body physics in a unified framework using the functional renormalization group. Three main topics shall be addressed within this project.(1) The phase diagram of a 2-component imbalanced Fermi gas is explored as a function of temperature, average chemical potential and the imbalance parameter, paying special attention to the unitarity limit at resonance. The RG flow of the full effective order-parameter for superfluidity and the fermionic gap are of central interest in order to map out the full phase diagram. The properties of the superfluid phases and the location of 1st-order transition lines as well as of the tri-critical point shall be determined with the aid of a functional RG flow into the symmetry-broken phases.(2) The role of 3-body composites for critical phenomena in fermi systems is little understood and shall be explored in a functional RG study of a 3-component Fermi gas. An expected trionic phase at low temperatures and near the resonance is at the focus of this study. Also, trionic modifications of BCS or BEC pairing and their influence on the phase structure and location of critical regimes will be aimed at, as to perform an unprecedented search for 3-body dominated collective and critical phenomena. In a second step, the influence of explicit symmetry-breaking terms lifting the 3-component degeneracy needs to be studied, in order to be predictive for potential experimental realizations involving dislocated Feshbach resonances.(3) Motivated by recent advances in the preparation of dipolar atoms and dipolar molecules in their rotational and vibrational ground state, we plan to use the functional RG to explore the potentially rich phase structure of dipolar Fermi gases,including nematic, superfluid, magnetic and possibly more exotic phases. While the particle-particle channel was investigated a couple of years back using second order perturbation theory a possible instability in the particle-hole channel was only discussed very recently within mean field theory. The competition between these competing channels seems very appealing to us. Decoupling the long range and anisotropic fermionic interaction by means of bosonic Hubbard-Stratonovich fields we are aiming at describing corrections to mean field theory. In fact, by using the FRG with a cutoff only in the bosonic sector mean field theory serves as an initial condition and by reducing the infrared cutoff we progressively include order parameter fluctuations. In addition to determining the superfluid order parameter and precise shape of the Fermi surface we are also going to study the spectrum of single particle excitations.