Enhancing the atomic correlation dynamics under the effects of Stark shift and Kerr medium through multi-photon transitions

Enhancing and preserving the atomic correlation and entanglement is of significant utility in quantum information. To this aim, we study the temporal evolution of uncertainty-induced nonlocality (??) and logarithmic negativity (Script capital LMATHEMATICAL SCRIPT CAPITAL (LN) as measures of quantum correlations (QCs) and quantum entanglement (QE) between two effective atoms coupled to a bosonic reservoir in the absence of thermal fluctuations and in the presence of Kerr medium (KM) and Stark shift (SS) under which n-photon transitions are permitted. We explore how Markovian and non-Markovian regimes affect the temporal dynamics of atomic correlation and entanglement and its limitations. Our findings indicate that by adjusting the KM and SS parameters, the quantum correlations between the two atoms can be enhanced and maintained while displaying similar qualitative behavior. Notably, it was observed that the QCs and QE quantities are at their highest magnitudes in the non-Markovian regime when the strengths of both SS and KM are increased, implying that QCs and QE are well protected. In contrast to the typical view that protecting the QCs from decoherence that may be observed owing to environmental noise, we proposed a gainful way to reduce the atomic decoherence by adjusting the number of n-photon transitions. Our investigation reveals that in the non-Markovian regime, the considered system exhibits better resistance against decoherence in comparison to the Markovian regime, as evidenced by the significant amount of quantum correlations detected among the two effective atoms at a specific point in time.