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的、非常有用的实验系统，在其中可以探索多体环境中的强关联物理效应。在这样的系统中，基本模型哈密顿量的几乎一对一的实现允许人们通过实验在最先进的固态分析和数值方法之间执行从头算比较，从而在许多情况下使得能够对这样的理论进行第一次定量测试。此外，超冷量子气体为研究强关联量子系统中的非平衡动力学提供了独特的机会，使我们能够将关于强关联效应的知识从静态扩展到动态。在这个研究方案中，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。对于相互排斥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，以达到两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制备和分析费米子量子气体的磁有序，特别是在Tnéel周围有趣的温度区域，在那里发生向反铁磁体的相变。在我们之前关于费米子量子气体混合物吸引相互作用的工作的基础上，我们计划在光学晶格的最低能带内演示超流相。最近的理论工作表明，使用吸引相互作用的费米气体混合物可以提供实验优势，甚至可以深入研究排斥相互作用的哈伯德模型。此外，我们计划将最近对费米子量子气体混合物的输运测量扩展到受控无序方向，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。这里，除了变量相互作用外，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-费米混合物，我们计划实现极化子，其中单个费米子杂质原子可以通过玻色量子气体的声子激发来修饰。通过调节费米子和玻色子之间的相互作用强度，应该可以研究这种新的准粒子在输运中的根本变化。作为第二个主要项目部分，我们计划继续我们的工作，用光学超晶格实现一维玻色子量子气梯系统的非平衡物理。在这里，我们计划研究如何将众所周知的量子力学二能级系统的动力学概念，如Landau-Zener扫描，扩展到多体量子系统。我们将特别关注在系统中调整相互作用和关联的情况。在相同的实验装置中，我们计划将超晶格装置扩展到实现耦合的平板系统，并用这些装置来研究超流-莫特绝缘体相变中的重入现象，这些现象已经被证明在解释无序玻色量子气体中的无序诱导重入行为中起到了至关重要的作用。

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.