# Entanglement Control of Two-Level Atoms in Dissipative Cavities
## 1 Introduction
Thus, before reaching the center of the cavity, many molecules are lost by spontaneous emission to levels other than the target level, thereby spoiling efficiency and selectivity. After model calculations had confirmed the validity of that view, a remedy was quickly found: remove the cavity and bring in a second external laser S, with its center shifted upstream of the axis of laser P. The molecules would then be interacting with a strong S field as they reached the wings of the P laser. Therefore, the rate of stimulated emission, induced by the S field, would be sufficiently large to compete with spontaneous emission as soon as molecules have traveled far enough to be excited by the P laser. Modification of the molecular-beam-laser modeling code (using a density-matrix approach) [35] to include the spatial shift of the two laser fields (a timing offset between the two fields affecting the molecules) confirmed that fully transfer efficiency should be achievable. This prediction was in fact experimentally demonstrated soon afterwards [36], where it was noted that the proposed and demonstrated technique does not require laser intensity modulation, laser frequency chirping, or level shifting. STIRAP has been explained chemically and physically [37], and its protocols have been applied to various models to speed up adiabatic passage techniques and achieve fast and robust population control in two-level atomic systems [38; 39], in a three-level system STIRAP [40; 41; 42] can be used to transfer population from the ground state \(|0\rangle\) to the second excited state \(|2\rangle\) without having excitations in state \(|1\rangle\) during the process. In this situation, it is possible to realize \(0-2\) population transfer even in systems where that would otherwise be a forbidden transition, as is the case of the transmon [43], and four-level atom [44]. The system in [45] consisted of a fixed-frequency transmon qubit embedded in a three-dimensional superconducting aluminium cavity and if the coupling strength is much smaller than the qubit-cavity detuning, the undriven qubit-cavity system is well described by the dispersive Jaynes-Cummings Hamiltonian. The authors of [46] measured the modulation response of several QC lasers, packaged and processed as just described, by driven them with the output of synthesized signal generator and light output was detected with a GaAs/AlGaAs quantum-well infrared photodetector(QWIP), also packaged for high-speed operation and the resulting photocurrent was amplified and fed to a microwave spectrum analyzer, where the modulation amplitude was measured. In [47], the authors review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically, with the simple two-state model providing an inexhaustible source of novel concept. The choice of initial system parameters as we propose is related to the artificial phase jumps of Pancharatnam phase. Phase jumps are promising points such that they generate better entanglement degrees, and its successive repetition inside any system dynamics reflects a good sign of system capability to transfer information, as the geometric phases can be altered by changing the relative delay of the laser pulses [48]. Our work here is oriented around the interaction of an open quantum system of two independent two-level atoms with a quantization (non-classical) of electromagnetic field in a dissipative cavity in the multi-photon process. In Section 2, the considered physical scenario is introduced, the corresponding Hamiltonian is investigated, and the mathematical procedure for obtaining the solution of the wave equation is clearly given. In Section 3, we discuss the proposed technique to control the entanglement by properly choosing the initial values of the atomic state.