Quantum Analysis of Three-Level Cascade Laser with the Same and Different Frequencies Coupled to Vacuum Reservoir

Abstract

We obtained the equation of evolution of the expectation values of the cavity operators for a cascade three-level laser with the same and different frequencies by applying the pertinent masterequation. Applyingthesteadystatesolutionsoftheexpectationvalues,westudiedthe squeezing, photon statistics and entanglement of the cavity and output modes. The results obtained show that the light generated by this system is squeezed and entangled and, also the squeezing inside and outside the cavity is related with the entanglement. Furthermore, our calculation show that the mean photon number, the variance of the photon number, the degreeofsqueezingandentanglementofthecavityandoutputmodesincreaseforlargevalue of A, small value of η(if more atoms are initially prepared at the bottom level). Moreover, we found that as κ increase from 0 to 1, squeezing and entanglement of light inside the cavity is decreasewhereasincreaseatoutside.