Entanglement maintenance of classically pumped qubits and calibration aspects with the resonator tomography under the Stark shift effect inside a coherent resonator

We present a scheme for the investigation of entanglement of a similar qubits-pair along with the coherent resonator tomography under two-photon processes. Our discussion is focusing on the effect of the classical power amplitude along with Stark shift width and the conditions under which they have a constructive role in protecting the initial-state entanglement and the corresponding field tomography evolution. We observe that the entanglement between the qubits does maximally peak below a critical value and can be determined by suitable measurements on the resonator tomography. Interestingly, above the critical value, the tomography profile either shows an annular structure or exhibits quantumness which could be largely diminished by controlling the driving power intensity as well as the shift width. Particularly and for a detuned interaction, the critical values can be largely exceeded for sufficiently large values of the driving intensity and Stark shift, hence, more regions in the plane of parameters can be occupied by the qubits correlation. In this case, the pronounced fluctuations exhibited by entanglement dynamics due to phase variations could be highly interrupted. Additionally, preserving the field tomography showing a multi-component Schrödinger cat state via field-field detuning, robust, periodical and close to unity entanglement between the qubits could be highly possible. Moreover, in particular situations, the field tomography dynamics show the Fourier transform of the original field wave packet one-quarter period after initial, accordingly, entanglement maxima are reached frequently per a quarter period of rotation.