Quantum chaos is usually characterized through its statistical implications on the energy spectrum of a given system. In this work we propose a decoherent mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum system is sensed by studying the implications that it produces in the long-time dynamics of a probe coupled to it under a dephasing interaction. By introducing the notion of an effective averaged decoherence factor, we show that the correction to the geometric phase acquired by the probe with respect to its unitary evolution can be exploited as a robust tool for sensing the integrable to chaos transition of the many-body quantum system to which it is coupled. This sensing mechanism is verified for several systems with different types of symmetries, disorder and even in the presence of long-range interactions, evidencing its universality.

量子混沌通常通过其对给定系统能谱的统计意义来表征。在这项工作中，我们提出了一种用于感知量子混沌的退相干机制。多体量子系统的混沌性质是通过研究它在移相相互作用下耦合到它的探针的长期动力学中产生的影响来感知的。通过引入有效平均退相干因子的概念，我们表明对探测器获得的几何相位的校正相对于其幺正演化可以用作感知多体量子可积到混沌转变的强大工具与之耦合的系统。这种传感机制已针对具有不同类型对称性、无序甚至存在长距离相互作用的多个系统进行了验证，