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The present study investigates the transient spectrum (TS) of a two-level system that interacts with a generalized squeezed state without using the rotating wave approximation (RWA). We consider the purity of the optical field, which is developed in a generalized squeezed state, utilizing the linear entropy. The analytic expressions of the TS and field purity (FP) of the bipartite system are evaluated. Moreover, the study exhibits the influence of the squeezed parameter and some photons transition on the TS and FP. We obtain that the control of the FP may be generated based on an adequate choice of the photons transition and squeezed parameter. Such results can be utilized in the understanding and development of various tasks of quantum physics and optics.

The emission spectrum of a qubit (two-level atom) system that interacts with a field in the framework of parity deformations is investigated in this paper. The model consists of a qubit coupled to a single-mode field within the parity deformed Jaynes-Cummings model (PDJCM) based on the λ-analog of the quantum harmonic oscillator algebra. We numerically evaluate the atomic emission spectrum (AES), by considering the influence of the deformed parameter and half-band-width of the spectrometer. Moreover, the dependence of the spectrum peaks on the detuning parameter is discussed. Finally, we study the variation of the geometric phase of the whole system state modelled by the PDJCM in terms of the main physical parameters.