Quantum scrambling in a toy model of photodetectors

Quantum measurement is a process that involves the interaction between a quantum system and a macroscopic measurement apparatus containing many degrees of freedom. The photodetector is such an apparatus with many electrons interacting with the incoming quantum photon. Therefore the incoming photon will spread and get scrambled in the photodetector, that is, the operator of the initial incoming local photons will grow and becomes highly non-local through the interaction process. Investigating this scrambling process in detail is useful for understanding the interaction between the quantum system and the measurement apparatus. In this paper, we study the quantum scrambling process in an effective toy model of photodetectors in three different physical scenarios, by numerically simulating the evolution of the out-of-time correlators (OTOC). In particular, the integrability of the effective model is explored through level spacing statistics, and the effect of the spatially/temporarily distributed disorders on the system evolution is carefully investigated using the OTOC. Looking into these detailed dynamical processes paves the way to the quantum simulation and manipulation of photondetector, which would provide insights into understanding the wave-function collapse processes.