Interaction, Disorder and Dynamical Effects in Strongly Correlated Bosonic and Fermionic Ultracold Quantum Gases

光学晶格中的超冷玻色子和费米子量子气体已被证明是一类新颖而非常有用的实验系统，在这些实验系统中可以探索多体环境中强相关物理的影响。在这样的系统中，基本模型哈密顿量几乎是一对一的实现，这使得人们可以在最先进的固态分析方法和数值方法之间进行从头比较，从而在许多情况下能够对这些理论进行第一次定量测试。此外，超冷量子气体为研究强相关量子系统中的非平衡动力学提供了独特的机会，使我们能够将强相关效应的知识从静态扩展到动态。在这项研究计划中，我们计划重点研究光学晶格中的费米子量子气体混合物，以及光学晶格中具有可变多体相互作用的玻色-费米混合物的行为。对于排斥性相互作用的费米子量子气体混合物，我们小组在研究小组资助的第一阶段已经达到了费米子莫特绝缘阶段。我们现在计划通过实施新的冷却方案来扩展这项工作，以达到双组分自旋混合物的反铁磁有序相。光学超晶格的实现将使我们能够准备和分析费米子量子气体的磁有序，特别是在tnsamel周围有趣的温度区，在那里发生了向反铁磁体的相变。在我们之前关于相互作用的费米子量子气体混合物的研究基础上，我们计划在光学晶格的最低带内展示超流体相。最近的理论工作表明，使用具有吸引力的相互作用的费米气体混合物可以提供实验优势，甚至可以深入了解相互作用的哈伯德模型的研究。此外，我们计划扩展最近对费米子量子气体混合物的输运测量，在这些测量中，我们研究了相互作用对系统输运行为的作用，朝着受控无序的方向发展。这里，除了可变的相互作用外，我们还将在输运测量过程中引入可控的静态无序势。对于玻色子-费米混合物，我们计划实现极化子，其中单个费米杂质原子可以通过玻色子量子气体的声子激发来修饰。通过调整费米子和玻色子之间的相互作用强度，应该有可能研究这些新准粒子输运的根本变化。作为项目的第二个主要部分，我们计划继续研究利用光学超晶格实现的一维玻色子量子气体阶梯系统的非平衡物理。在这里，我们计划研究如何将量子力学双能级系统中众所周知的动力学概念，如朗道-齐纳扫描，扩展到多体量子系统。我们将特别关注系统中相互作用和相关性被调整的情况。在相同的实验设置中，我们计划将超晶格设置扩展到耦合斑块系统的实现，并使用这些系统来研究超流体-莫特绝缘体跃迁中的再入口现象，这些现象已被证明对解释无序玻色子量子气体中无序诱导的再入口行为起着至关重要的作用。

Ultracold bosonic and fermionic quantum gases in optical lattices have proven to be a novel and highly useful class of experimental systems in which the effect of strong correlation physics in a many-body setting can be explored. The almost one-to-one implementation of fundamental model Hamiltonians in such systems has allowed one to perform ab-initio comparisons between state of the art solid-state analytical and numerical methods with experiments, thus enabling in many cases a first quantitative test of such theories. In addition, ultracold quantum gases offer unique opportunities for the investigation of non-equilibrium dynamics in strongly correlated quantum systems that enable the extension of our knowledge about strong correlation effects from a static to a dynamic regime.Within this research proposal we plan to focus on the investigation of fermionic quantum gas mixtures in an optical lattice, as well as on the behaviour of Bose-Fermi mixtures with variable many-body interactions in optical lattices. For repulsively interacting fermionic quantum gas mixtures our group has reached a fermionic Mott insulating phase during the first phase of the research group funding. We now plan to extend this work by implementing novel cooling schemes to reach an antiferromagneticly ordered phase for the two-component spin mixture. The realization of optical superlattices in this setup will allow us to prepare and analyze the magnetic ordering of the fermionic quantum gas especially in the interesting temperature regime around TNéel, where the phase transition to an antiferromagnet occurs. Building on our previous work on attractively interacting fermionic quantum gas mixtures, we plan to demonstrate a superfluid phase within the lowest band of an optical lattice. Recent theoretical work has shown that the use of an attractively interacting Fermi gas mixture can provide experimental advantages, and can even yield insight into the investigation of the repulsively interacting Hubbard model. Furthermore, we plan to extend recent transport measurements for fermionic quantum gas mixtures, in which we have investigated the role of interactions on the transport behaviour of the system, towards the direction of controlled disorder. Here, in addition to variable interactions, we will introduce controllable static disorder potentials during the transport measurement. For Bose-Fermi mixtures we plan to realize polarons, in which single fermionic impurity atoms can be dressed by phononic excitations of the bosonic quantum gas. By tuning the interation strength between the fermions and bosons it should be possible to investigate the fundamental change in transport of such new quasiparticles.As a second main project part, we plan to continue our work on the non-equilibrium physics of one-dimensional bosonic quantum gas ladder systems realized using optical superlattices. Here we plan to investigate how dynamical concepts well known for a quantum mechanical twolevel system, such as a Landau-Zener sweep, can be extended to many-body quantum systems. We will focus especially on the case where the interactions and the correlations are tuned in the system. In the same experimental setup, we plan to extend the superlattice setup towards the realization of coupled plaquette systems and use these to study re-entrance phenomena in the superfluid-Mott insulator transition that have been shown to play a crucial to explain disorder induced re-entrance behaviour in disordered bosonic quantum gases.