Correlated Quantum Dynamics of a Single Atom Collisionally Coupled to an Ultracold Finite Bosonic Ensemble

We explore the correlated quantum dynamics of a single atom with a spatio-temporally localized coupling to a finite bosonic ensemble [{\it arXiv:1410.8676}]. The single atom is initially prepared in a coherent state of low energy and oscillates in a harmonic trap. An ensemble of $N_A$ interacting bosons is held in a displaced trap such that it is periodically penetrated by the single atom. The non-equilibrium quantum dynamics of the total system is simulated by means of an {\it ab-initio} method. Here, we focus on characterizing the impact of the peculiar inter-species coupling and the thereby induced inter-species correlations on the subsystem states: At instants of not too imbalanced excess energy distribution among the subsystems, inter-species correlations prove to be significant. A phase-space analysis for the single atom reveals that these correlations manifests themselves in short phases of strong deviations from a coherent state. In the bosonic ensemble, the single atom mainly induces singlet and delayed doublet excitations, for which we offer analytical insights with a stroboscopic time-dependent perturbation theory approach. When increasing the ensemble size, its maximal dynamical quantum depletion is shown to decrease faster than $1/N_A$ for a fixed excess energy.