Quantum metrology explores quantum features to ameliorate resolution, precision, and sensitivity beyond classical limits when the quantum theory determines the ultimate limit on the accuracy of any measurement. More recently, it is shown that entangled coherent states (ECSs) have the potential to perform robust sub-classical measurements considering only the case of a weak-coupling regime. In this paper, we examine the dynamics of the phase sensitivity for ECSs in the framework of the non-Markovian lossy channels and show how the non-Markovian features and reservoir parameters may be exploited for quantum-enhanced phase estimation. The influences of memory effects and the Ohmic reservoir with Lorentz–Drude regularization are examined under the following conditions: ${\omega }_c\ll {\omega }_0$, ${\omega }_c\approx {\omega }_0$, or ${\omega }_c\gg {\omega }_0$, where ${\omega }_0$ is the field mode frequency of interest and ${\omega }_c$ is the cutoff frequency of the Ohmic reservoir. In shape contract with results obtained in the presence of Markovian lossy, we obtain that the memory effects lead to an enhanced phase estimation while the ratio ${\omega }_c/{\omega }_0$ provides a way to control and improve the precision during the time evolution. We show that the smallest variance in the phase parameter highly depends on the combination of the ration ${\omega }_c/{\omega }_0$ and non-Markovian effects.

In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized field that is initially prepared in parity deformed coherent states (PDCSs). The dynamical features of the considered system are explored in the presence of parity deformed parameter (PDP) and time-dependent coupling (t-dc). In particular, we examine the amount of the entanglement formed in the qubit–field and qubit–qubit states. We find that the maximal amount of the entanglement may be occurred periodically during the time evolution. Finally, we investigate the influence of PDP on the Fisher information and the photon statistics of the deformed field with respect to the main parameters of the system.

We study the dynamics of two non-stationary qubits, allowing for dipole-dipole and Ising-like interplays between them, coupled to quantized fields in the framework of two-mode pair coherent states of power-low potentials. We focus on three particular cases of the coherent states through the exponent parameter taken infinite square, triangular and harmonic potential wells. We examine the possible effects of such features on the evolution of some quantities of current interest, such as population inversion, entanglement among subsystems and squeezing entropy. We show how these quantities can be affected by the qubit-qubit interaction and exponent parameter during the time evolution for both cases of stationary and non-stationary qubits. The obtained results suggest insights about the capability of quantum systems composed of nonstationary qubits to maintain resources in comparison with stationary qubits.