Ultracold atoms in periodically modulated optical potentials: A quantum metamaterial to explore nonequilibrium dynamics and tosimulate relativistic effect

这个联合实验理论项目的主要目标是研究交流驱动的超冷原子气体，为非平衡量子动力学和相对论物理效应提供一个新的实验平台。为了实现这一目标，我们将使用量子Floquet形式和高性能计算进行理论研究，并在时间调制的光学晶格势中进行超冷原子气体的实验。该项目分为两个连续步骤。首先，我们将集中在交流驱动的光学晶格势的非平衡量子制度。我们要解决的具体问题是：（i）避免不同Floquet态之间的交叉引起的传输共振和（ii）在强粒子间相互作用和强驱动的限制下，量子多体效应对原子传输的影响。下一步是研究交流驱动的光学势作为可调谐量子“超材料”。其核心思想是通过在指定的Floquet态之间可控地避免交叉，在经调制的量子系统的准能谱中产生狄拉克锥。为了测试这些狄拉克锥的物理性质，我们计划对相对论性克莱因隧穿和Veselago透镜进行实验量子模拟，将超冷原子云置于驱动光势中。我们预期成果的可能应用包括基于Floquet态的新量子工具，其操作原理将依赖于非平衡物理学，并可用于对相对论多体波动方程进行量子模拟。

The main objective of this joint experiment-theory project is to study ac-driven ultracold atomic gases towards the goal of developing a new testing-ground for non-equilibrium quantum dynamics and relativistic physics effects. To reach this goal we will perform both theoretical studies, by using the quantum Floquet formalism and high-performance computing, and experiments with ultra-cold atomic gases in temporally modulated optical lattice potentials.The project is subdivided into two consecutive steps. Starting out we will focus on the non-equilibrium quantum regime of ac-driven optical lattice potentials. The specific questions we want to address are (i) transport resonances induced by avoided crossings between different Floquet states and (ii) uantum many-body effects on the atom transport in the limit of strong interparticle interactions and strong driving. The next step is to study ac-driven optical potentials as tunable quantum “metamaterials”. The key idea is to create Dirac cones in the quasienergy spectrum of a periodically-modulated quantum system through controllable avoided crossings between designated Floquet tates. To test the physics that follows from these Dirac cones we plan to carry out an experimental quantum simulation of relativistic Klein tunneling and also Veselago lensing with a cloud of ultracold atoms placed in driven optical potentials. Among possible applications of our anticipated outcomes are new Floquet-state based quantum tools, whose operational principles will rely on non-equilibrium physics and can be used to carry out quantum simulations of the relativistic manybody wave equation.