Disorder and Quantum Magnetism in Ultracold Atom Systems

该项目的目的是在强相互作用的玻色和费米气体与多个组件的量子磁性和无序效应的理论描述。近年来，冷气体实验取得了令人瞩目的进展，无序三维玻色-哈伯德模型已经可以在实验室中模拟，费米子的Mott绝缘态已经实现，实现长程磁有序是该领域目前的主要目标之一。因此，量子相及其临界参数的定量理论预测对于进一步指导实验变得至关重要。然而，对这些系统的可靠描述，特别是在更高维度下，仍然是一个重大的理论挑战。基于第一个资助期间成功的方法开发，我们现在能够定量描述费米子和玻色子量子晶格气体，在存在外部势和/或无序的情况下，在任何相关强度下，我们在第二个资助期的重点是在本研究单位的实验组中实现的系统：旋量玻色子，异质结分子和质量不平衡的费米-费米混合物。我们的目标是定量描述的相位与长程有序，如可调反铁磁性，超固体和极化相，以及它们的修改实验上可实现的斑点无序或无公度超晶格的存在下，在定性的新阶段，如玻色玻璃或自旋液体可以出现。本项目的主要目标是提取这些量子相位的光谱特征，这些特征可以通过双光子布拉格散射、射频光谱或受激拉曼散射来测量。我们将在基于动力学平均场理论的非微扰技术中计算相关的1-和2-粒子响应量。通过这种方式，我们希望有助于实验检测相关的多体相位，也是他们的前体效应的临界温度以上。

This project aims at a theoretical description of quantum magnetism and disorder effects in strongly interacting Bose- and Fermi gases with multiple components. Due to impressive progress in experiments on cold gases during the last few years, the disordered three-dimensional Bose-Hubbard model can now be simulated in the laboratory, Mott-insulating states of fermions have been realized, and achieving long-range magnetic order is currently one of the major goals in the field. Quantitative theoretical predictions on quantum phases and their critical parameters are therefore becoming essential for further guidance of experiments. However, a reliable description of these systems especially in higher dimensions is still a major theoretical challenge.Based on successful method development during the first funding period, we are now able to quantitatively describe fermionic and bosonic quantum lattice gases, in the presence of external potentials and/or disorder, at any correlation strength, and for experimentally realistic system sizes.Our focus in the second funding period is on systems which are realized in the experimental groups of this research unit: spinor bosons, heteronuclear molecules, and Fermi-Fermi mixtures with mass imbalance. We aim at quantitatively describing phases with long-range order such as tunable antiferromagnetism, supersolids and polaronic phases, and their modification in the presence of experimentally realizable speckle disorder or incommensurate superlattices, where qualitatively new phases such as Bose glasses or spin liquids can emerge. The crucial influence of different lattice geometries such as triangular, or spin-dependent hexagonal will be studied as well.A major goal of this project is to extract spectroscopic signatures of these quantum phases, which are measurable in 2-photon Bragg scattering, RF spectroscopy or by stimulated Raman scattering. We will calculate the associated 1- and 2-particle response quantities within our non-perturbative techniques based on dynamical mean-field theory. In this way we hope to aid experimental detection of correlated many-body phases and also their precursor effects above the critical temperature.