Interaction-induced transition in quantum many-body detection probability

With the advent of digital and analog quantum simulation experiments, it is now possible to experimentally simulate dynamics of quantum many-body lattice systems and make site-resolved measurements. These experiments make it pertinent to consider the probability of getting any specific measurement outcome, which we call the `signal', on placing multiple detectors at various sites while simulating dynamics of a quantum many-body lattice system. In this work, we formulate and investigate this problem, introducing the concept of quantum many-body detection probability (QMBDP), which refers to the probability of detecting a chosen signal at least once in a given time. We show that, on tuning some Hamiltonian parameters, there can be sharp transition from a regime where QMBDP $\approx 1$, to a regime, where QMBDP $\approx 0$. Most notably, the effects of such a transition can be observed at a single trajectory level. This is not a measurement-induced transition, but rather a non-equilibrium transition reflecting opening of a specific type of gap in the many-body spectrum. We demonstrate this in a single-impurity non-integrable model, where changing the many-body interaction strength brings about such a transition. Our findings suggest that instead of measuring expectation values, single-shot stroboscopic measurements could be used to observe non-equilibrium transitions.