Quantum two-photon laser in Kerr-like medium / Faisal Hamood Ahmed Mathkoor - Faisal Hamood , Ahmed Mathkoor (2020)
In this thesis, we studied the Kerr nonlinearity effects on nonclassicality and statistics of the laser field besides the effects of detuning, injection rate, and intensity-dependent coupling (IDC). We developed a quantum theory of light generated from a two-photon laser (TPL) with nonlinear Kerr-like medium in a laser dissipative cavity. The full quantum mechanical approach with the density matrix of the particle-field system is used to derive the TPL master equation based on Scully-Lamb’s quantum theory of laser. Various dynamical operators of interest for the cavity field are calculated analytically and computed numerically. The sophisticated computational program was developed to obtain the numerical solution for the nonlinear density matrix equation where the exact solution is not possible. We obtained an approximate soluble form of the photon number distribution equation using reasonable assumptions. The assumptions are justified by making a comparison with the exact numerical results that show a good agreement for small fluctuations in the field. We studied the dynamics and effects of injection rate, two-photon detuning, the Kerr parameters, and IDC on mean photon number, entanglement criterion, second-order correlation functions 6¹2º , Mandel-& parameter, and photon number distribution. In the absence of IDC, we found that the field behaves nonclassically for a wide range of the selected parameters. The results show that the injection rate and detuning decrease the inter-mode correlation and change the field statistics from sub-Poissonian to super- Poissonian. However, the Kerr parameters change the field statistics from super-Poissonian to sub-Poissonian. This means that the Kerr parameters reduce the fluctuations in the mean photon number below the Poissonian classical limit, which is for photon number squeezed light. Moreover, Kerr parameters transform the detuning to become intensity-dependent and shift the field frequency through the effective detuning. In the presence of IDC, we found the effects of Kerr parameters and detuning are greatly suppressed, but the effects of the injection rate are enhanced. The nonlinearity of the Kerr effect results in a dramatic decrease in the mean photon number. However, the IDC rises mean photon numbers substantially. The generated photons have nonclassical properties that would last for a long time. Interestingly, statistics of the field are reversed and become super-Poissonian under the effects of Kerr parameters and sub-Poissonian under the injection rate, which is the opposite of the previous case of no IDC. The results show competition between the Kerr effect and both the two-photon detuning and the IDC with dominance in favor of the later. These competitions become important if we can exploit and control them to produce desirable nonclassical photons with acceptable photon number and photon number fluctuations that would be useful in certain applications in quantum metrology and quantum information.