Manifestation of strong and ultra-strong coupling in high-order correlation functions

Strong and ultra-strong coupling in a “cavity–single atom” system is of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to the ultra-strong coupling regime. In this paper, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequences for the correlation functions of different orders. We show that for n-th order correlation functions, the transition to the strong coupling regime requires a coupling strength approximately n2/3 times greater than the one for first order correlation functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlation functions at less coupling strength than in the dynamics of first order correlation functions. As a result, the measurement of high-order correlation functions makes it easier to observe the ultra-strong coupling in “cavity mode–single atom.”