Effects of thermal fluctuation when an optical cavity possesses neutral atoms and a two-mode laser system

Quantum-based experiments and their applications in lasers and magnetic fields have long been paramount, yet how to achieve exact stability for a long time is a merely answered question. This article develops a coupled laser map with cavity loss via a one-dimensional laser map, where complex phenomena in the newly developed mathematical model, dynamical properties with coupling delay, and thermal fluctuation of the lasing system are discussed numerically and analytically. It is deduced that the intensity of the laser beam can be controlled and stabilized for a long time, and large values of the effective gain coefficient can be reached when thermal noise exists in the optical cavity and when a nonlinear feedback loop is provided with coupling delay. Utilizing noise and coupling delay as a nonlinear feedback loop to the coupled laser map, we observed non-autonomous behaviour at different growth rate values. In contrast, symmetrical and phase-entrained synchronized mirror imaged orthogonal strange attractors and fractals were seen at the same growth rate values. At specific values of the controlling parameters, the peculiar attractors experience cyclic collisions with their basin boundaries, which break symmetry and synchronization and cause irregular behaviour.