False signals of chaos from quantum probes

We demonstrate that two-time correlation functions, which are generalizations of out-of-time-ordered correlators (OTOCs), can show 'false-flags' of chaos by exhibiting behaviour predicted by random matrix theory even in a system with classically regular dynamics. In particular, we analyze a system of bosons trapped in a double-well potential and probed by a quantum dot which is coupled to the bosons dispersively. This is an integrable system (considered both as separate parts and in total). Despite the continuous time evolution generated by the actual Hamiltonian, we find that the n-fold two-time correlation function for the probe describes an effective stroboscopic or Floquet dynamics whereby the bosons appear to be alternately driven by two different non-commuting Hamiltonians in a manner reminiscent of the Trotterized time evolution that occurs in digital quantum simulation. The classical limit of this effective dynamics can have a nonzero Lyapunov exponent, while the effective level statistics and return probability show traditional signatures of chaotic behaviour. In line with several other recent studies, this work highlights the fact that the behavior of OTOCs and their generalizations must be interpreted with some care.