# Entanglement Control of Two-Level Atoms in Dissipative Cavities
## 1 Introduction  
Quantum systems promise enhanced capabilities in sensing, communications, and computing beyond what can be achieved with classical-based conventional technologies rather than quantum physics. Mathematical models are essential for analyzing these systems and building suitable quantum models from empirical data is an important research topic. In [PERSON] theory of radiation [1], he considered atoms and the radiation field with which they interact as a single system whose energy is represented by the frequency/energy of each atom solely, the frequency/energy of every mode of the applied laser field alone, and a small term is to the coupling energy between atoms and field modes. The interaction term is necessary if atoms and field modes are to affect each other. A simple model is that we consider a pendulum of resonant frequency \(\omega_{0}\), which corresponds to an atom, and a vibrating string of resonant frequency \(\omega_{1}\) which corresponds to the radiation field. Jaynes-Cummings model (JCM) [2] is the first solvable analytical model to represent the atom-field interaction with experimental verification [3]. JCM has been subjected to intensive research in the last decades with many interesting phenomena explored [4; 5; 6; 7]. The matter-field coupling term may be constant [8; 9; 10] or time-dependent [11; 12], and that depends on the considered physical situation. Parametric couplingfor superconducting qubits [13; 14] is studied [15]. In our case, the atoms are moving while interacting with the laser field, this topic has been investigated for different quantum systems [16; 17; 18; 19; 20]. Using a non-Hermitian generalization of the Hamiltonian (NHH) is now considered as a model to describe an open quantum system [21; 22; 23], we may obtain complex-energy eigenvalues. These NHHs are justified as an approximate and phenomenological description of an open quantum system such as radioactive decay processes [24]. Driving a quantum system with the output field from another driven quantum system, and a quantum trajectory theory for cascaded open systems were studied by proposing NHH in [25; 26], respectively. Investigating the dynamics of three-level systems has allowed the discussion of teleportation and non-classical properties [27; 28], concurrence, and Shannon information entropy [29; 30]. Entanglement is robust under decoherence, independent of the initial state of the qubits, is relatively easy to generate, and has a system-independent value, such systems could be used as \"entanglement batteries\". This entanglement can be harvested and further transmitted in a quantum circuit [31]. The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonance-like behaviour [32]. In this work, we propose a new technique to control the entanglement. Stimulated Raman adiabatic passage (STIRAP) is a process that allows transfer of a population between two states via at least two coherent field pulses by inversely engineering the Hamiltonian parameters via Lewis-Riesenfeld phases [33]. To investigate the essential requirements, such as, efficiency, selectivity robustness and flexibility, one may use what is called STIRAP [34]. The goal was reached after implementing changes which were motivated by the following consideration, based again on a rate-equation picture. The laser beam S, generated by optical pumping, is necessarily confined to the axis of the cavity, and thus, the driving laser-field P must also propagate along that axis. New molecules traveling towards the cavity to further feed the laser action find themselves first in the wings of these two lasers, P and S. The P laser is already strong enough to excite molecules in level 1 to the upper laser level (level 2), but the S laser is not yet strong enough for the rate of stimulated emission to the target level to compete successfully with the rate of spontaneous emission.