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相互的。这意味着向前和向后的过程是内在存在的，两个系统都受到相互作用的影响。人们可能会质疑是否有可能打破这种对称性，即人们能否实现两个量子系统之间的单向相互作用？这确实是可能的，因为如果与相应的耗散相互作用相平衡，任何可因式分解(相干)的哈密顿相互作用都可以是定向的。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(高度衰减的)辅助系统来实现，该辅助系统调节两个系统之间的间接相互作用。平衡相干相互作用和相应的耗散相互作用的强大概念可以被用来设计用于量子信息处理、计算和通信协议的单向设备-例如，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路线。这种实现非互易性的秘诀构成了本研究方案的基础。在此方法的基础上，研究非互易器件的新设计。其中之一是级联量子限制放大器，能够对微弱信号进行稳健的定向放大。此外，还将引入一种新的非互易器件：定向压缩器，这是一种产生宽带压缩光的器件，是一种有希望超越现有基于腔的压缩协议的候选器件。除了实际应用，这一建议的目的是研究这一基本配方的推广，以实现非互易到高维系统，具有非线性相互作用的系统，并回答重要的开放和基本问题。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。该方案旨在探索耗散工程中的非互易性概念是否也适用于实现光学机械或超导阵列结构中的拓扑非平凡状态。此外，还应探讨如何将耗散工程和方向性的概念转移到费米子和热力学输运中。

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.