The dynamic Stark shift results from the interaction of an atom with the electromagnetic field. We show how a propagating single-photon wave packet can induce a time-dependent dynamical Stark shift on a two-level system (TLS). A non-perturbative fully quantum treatment is employed, where the quantum dynamics of both the field and the TLS are analyzed. We also provide the means to experimentally access such time-dependent frequency by measuring the interference pattern in the electromagnetic field inside a 1D waveguide. The effect we evidence here may find applications in the autonomous quantum control of quantum systems without classical external fields, which can be useful for quantum information processing as well as for quantum thermodynamical tasks.
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