合成维中高阶量子例外点的产生
Generating high-order quantum exceptional points in synthetic dimensions
摘要：
近年来，在耗散系统中提出并发展了各种构造高阶例外点（EPs）的方法。这些EP可以具有许多有趣的特性，例如，手性传输和增强的灵敏度。先前实现具有高阶EP的非厄米哈密顿（NHH）的提议主要基于耦合模式的空间网络的直接构造或利用合成维度，例如，将空间晶格映射到时间或光子数空间。这两种方法都依赖于构造有效的NHH来描述经典的或后选择的量子场，这忽略了量子跳跃的影响，因此，当量子跳跃的概率随着激发数和耗散率的增加而增加时，在{ \it量子态}中存在可扩展性问题。在这里，通过考虑一个二次Liouvillian超算子的全量子动力学，我们介绍了一个简单而有效的方法工程NHH与高阶量子EP，来自系统运营商矩的演化矩阵。也就是说，通过量化系统算子的高阶矩，例如，的二次双模系统，所得到的演化矩阵可以被解释为替代的NHH描述，例如，耦合谐振器的空间晶格，其中空间位点由场矩的合成空间中的高阶场矩表示。作为一个例子，我们考虑一个$U(1)$对称的二次Liouvillian描述了一个{ \it双峰}腔与非相干模式耦合，这也可以拥有反$\cal PT$对称性，其场矩动力学可以映射到一个NHH控制的空间{ \it网络}的耦合谐振器与高阶EP。
英文摘要：
Recently, there has been intense research in proposing and developing various methods for constructing high-order exceptional points (EPs) in dissipative systems. These EPs can possess a number of intriguing properties related to, e.g., chiral transport and enhanced sensitivity. Previous proposals to realize non-Hermitian Hamiltonians (NHHs) with high-order EPs have been mainly based on either direct construction of spatial networks of coupled modes or utilization of synthetic dimensions, e.g., of mapping spatial lattices to time or photon-number space. Both methods rely on the construction of effective NHHs describing classical or postselected quantum fields, which neglect the effects of quantum jumps, and which, thus, suffer from a scalability problem in the {\it quantum regime}, when the probability of quantum jumps increases with the number of excitations and dissipation rate. Here, by considering the full quantum dynamics of a quadratic Liouvillian superoperator, we introduce a simple and effective method for engineering NHHs with high-order quantum EPs, derived from evolution matrices of system operators moments. That is, by quantizing higher-order moments of system operators, e.g., of a quadratic two-mode system, the resulting evolution matrices can be interpreted as alternative NHHs describing, e.g., a spatial lattice of coupled resonators, where spatial sites are represented by high-order field moments in the synthetic space of field moments. As an example, we consider a $U(1)$-symmetric quadratic Liouvillian describing a {\it bimodal} cavity with incoherent mode coupling, which can also possess anti-$\cal PT$-symmetry, whose field moment dynamics can be mapped to an NHH governing a spatial {\it network} of coupled resonators with high-order EPs.
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