We show that the topological phase transition for a Kitaev chain embedded in a cavity can be identified by measuring experimentally accessible photon observables such as the Fano factor and the cavity quadrature amplitudes. Moreover, based on density matrix renormalization group numerical calculations, endorsed by an analytical Gaussian approximation for the cavity state, we propose a direct link between those observables and quantum entropy singularities. We study two bipartite entanglement measures, the von Neumann and Rényi entanglement entropies, between light and matter subsystems. Even though both display singularities at the topological phase transition points, remarkably only the Rényi entropy can be analytically connected to the measurable Fano factor. Consequently, we show a method to recover the bipartite entanglement of the system from a cavity observable. Thus, we put forward a path to experimentally access the control and detection of a topological quantum phase transition via the Rényi entropy, which can be measured by standard low noise linear amplification techniques in superconducting circuits. In this way, the main quantum information features of Majorana polaritons in photon-fermion systems can be addressed in feasible experimental setups.

中文翻译：

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Rényi熵奇异性是耦合光子-费米子系统中拓扑临界性的标志

我们表明，可以通过测量实验可访问的光子可观测值（例如Fano因子和腔正交振幅）来识别嵌入腔中的Kitaev链的拓扑相变。此外，基于密度矩阵重归一化组的数值计算，并通过对腔态的解析高斯近似的认可，我们提出了这些可观测值与量子熵奇点之间的直接联系。我们研究了光与物质子系统之间的两个二分纠缠测度，即冯·诺依曼和雷尼纠缠熵。即使两个都在拓扑相变点都显示出奇异性，但只有Rényi熵可以解析地连接到可测量的Fano因子上。所以，我们展示了一种从可观察到的腔中恢复系统二分纠缠的方法。因此，我们提出了一条途径，可以通过Rényi熵实验地访问对拓扑量子相变的控制和检测，这可以通过超导电路中的标准低噪声线性放大技术来测量。这样，可以在可行的实验装置中解决光子-费米子系统中马约拉纳极化子的主要量子信息特征。