Directionality in Engineered Quantum Systems

一般来说，两个量子系统之间的相互作用过程是可逆的。这意味着向前和向后的过程是固有的，两个系统都受到相互作用的影响。人们可能会问，是否有可能打破这种对称性，即，两个量子系统之间能否实现单向相互作用？这确实是可能的，因为如果与相应的耗散相互作用平衡，任何可因子分解的（相干的）哈密顿相互作用都可以呈现方向性。在这里，耗散是获得方向性的关键因素;耗散相互作用可以简单地通过将两个系统耦合到第三个系统来实现平衡相干相互作用与相应的耗散相互作用的强大概念可以用来设计用于量子信息处理的单向设备，计算和通信协议-例如，以实现对光子信号传播方向的控制，从而能够构建环行器、光隔离器或定向放大器。此外，控制两个系统之间相互作用的方向为量子态传输协议、隐形传态和反馈控制算法开辟了一条有趣的途径。基于这种方法，应研究非互易器件的新设计。其中包括一个级联的量子限制放大器，能够对弱信号进行鲁棒的定向放大。此外，还将引入一种新的非互易装置：定向挤压器，一种产生宽带压缩光的装置，是优于现有基于腔的压缩协议的有希望的候选者。除了实际应用，这项建议的目的是研究这个基本配方实现非互易性的高维系统，非线性相互作用的系统的推广，并回答重要的开放和基本的问题。例如，非互易系统产生有用纠缠的能力以及与非厄米哈密顿（PT对称）系统的关系还有待研究。该建议旨在探讨通过耗散工程的非互易性的概念是否也适用于实现光机械或超导阵列结构中的拓扑非平凡状态。此外，耗散工程和方向性的概念转移到费米子和热力学输运应进行探讨。

In general an interaction process between two quantum systems is reciprocal. This means that forward and backward processes are inherently present and both systems are influenced by the interaction. One may question whether it is possible to break this symmetry, i.e., can one realize a uni-directional interaction between two quantum systems? This is indeed possible, as any factorizable (coherent) Hamiltonian interaction can be rendered directional if balanced with the corresponding dissipative interaction. Here dissipation is the crucial element to obtain directionality; a dissipative interaction can be realized simply by coupling both systems to a third (highly damped) auxiliary system which mediates an indirect interaction between the two systems.The powerful concept of balancing a coherent interaction with the corresponding dissipative interaction can be exploited to engineer unidirectional devices for quantum information processing, computation and communication protocols - for example, to achieve control over the direction of propagation of photonic signals, enabling the construction of circulators, optical isolators or directional amplifiers. Moreover, having control over the direction of the interaction between two systems opens up an interesting route for quantum state transfer protocols, teleportation and feedback control algorithms.This recipe to realize nonreciprocity forms the basis of this research proposal. Based on this method, new designs for nonreciprocal devices shall be investigated. Among these is a cascaded quantum-limited amplifier enabling robust directional amplification of weak signals. Additionally, a new nonreciprocal device shall be introduced: the directional squeezer, a device generating broadband squeezed light and a promising candidate to outperform existing cavity-based squeezing protocols. Besides practical applications, this proposal aims to study the generalization of this basic recipe for achieving nonreciprocity to higher dimensional systems, systems with nonlinear interactions, and to answer important open and fundamental questions. For example, the nonreciprocal system's ability to generate useful entanglement and the relation to non-Hermitian Hamiltonian (PT-symmetric) systems has yet to be investigated. This proposal aims to explore whether concepts for nonreciprocity via dissipation engineering are also applicable to realize topologically non-trivial states in optomechanical or superconducting array structures. Additionally, the transfer of concepts of dissipation engineering and directionality to fermionic and thermodynamic transport shall be explored.