In this thesis, the generation of entanglement is studied in a controlled environment. The model system of interest includes a cavity field interacting with a pair of atoms. The cavity field is heavily damped and it is pumped in order to maintain a steady state field population. Thus, we can eliminate the cavity field adiabatically and obtain the master equation describing only the qubits evolution in time. At first, this system is analyzed in the steady state, without making any measurement on the photons leaking through the cavity walls. In this way, the ideal physical parameter set for maximum entanglement in this model is investigated. In the second step, we assume a direct measurement on the leaking cavity photons, and observe the evolution of entanglement in a quantum trajectories approach. We simulate quantum trajectories approach by applying Monte Carlo method. The amount of entanglement is obtained as a function of time and number of photon detections.