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.
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.
Abstract We have studied the photon statistics of a nondegenerate two-photon laser with a medium that has both self- and cross-Kerr interactions as well as intensity-dependent atom–field coupling in the Hamiltonian. The density matrix equation of the atoms and two-mode cavity fields was derived using the standard Scully–Lamb approach and numerically solved. Under certain conditions, the photon distribution function equation was derived and solved analytically. The first few moments of photon numbers were calculated in the region above the lasing threshold. Nonclassicality of the fields was investigated by means of the Mandel Q parameter, second-order correlation functions and the Cauchy–Schwarz inequality. The results are analyzed for a range of finite Kerr parameters. Intensity-dependent coupling suppresses the nonclassicality of the field. It pushes the statistics of the field towards super-Poissonian.The self- and cross-Kerr interactions have significant roles in the nonclassicality of the two-photon cavity field and its statistics. These results are interesting for the field of quantum nonlinear optics and useful in quantum communications.
We have studied the photon statistics of the non-degenerate two-photon laser composed of many noninteracting atoms with Kerr nonlinearity. Nonlinearity of the gain is accounted for by the Lamb–Scully approach. Under certain conditions, we obtain an approximate photon distribution function. In the region above lasing threshold, the first few moments of the photon numbers are calculated analytically, and the threshold condition for stable lasing that depends on the Kerr parameter and detuning are obtained. We analyze the properties of the cavity field through the Mandel Q parameter, second-order correlation functions, Cauchy–Schwarz inequality for a range of Kerr parameters, atomic injection rate, and cavity detuning. Nonclassicality of the field is found through sub-Poissonian statistics, particularly at a low injection rate and high Kerr coupling with negative detuning. These nonclassicality conditions correspond to low photon numbers and depend on the sign of the detuning. The violation of the Cauchy–Schwarz inequality also occurs at low photon numbers but over a wide range of parameters, especially at short transient times. Our results show that the two-photon laser with Kerr nonlinearity is a promising quantum nonlinear optical system for developing controllable nonclassical light sources.
In this paper, we follow the model presented in our previous work [J. Opt. Soc. Am. B30, 1109 (2013)], in which the interaction between a Λ-type three-level atom and a quantized two-mode radiation field in a cavity in the presence of nonlinearities was studied. After giving a brief review of the procedure for obtaining the state vector of the atom-field system, we investigated some further interesting and important physical features of the whole system state, which are of particular interest to the quantum optics field of research, i.e., the number-phase entropic uncertainty relation (based on the two-mode Pegg–Barnett formalism) and a few of the nonclassicality signs that consist of sub-Poissonian statistics, Cauchy–Schwartz inequality, and two types of squeezing phenomena. During our presentation, the effects of intensity-dependent coupling, deformed Kerr medium, and the detuning parameters on the depth and domain of each of the mentioned nonclassical criteria of the considered quantum system are described in detail. The results show that each of the mentioned nonclassicality aspects can be obtained by appropriately choosing the related parameters.
In this paper, the dynamics of a system consisting of a three-level atom, which interacts with a single-mode quantized field in a lossy cavity, is studied in the presence of the dependence of atom–field coupling and third-order nonlinear susceptibility on the intensity of light. The system contains a Λ -type atom coupled to a single-mode radiation field, with a degenerate multi-photon transition in the intensity-dependent regime. Also, the nonlinearity of the medium due to Kerr and intensity-dependent Kerr effects, and the detuning parameters are considered. Furthermore, to see the effects of dissipation such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom, a non-Hermitian Hamiltonian is introduced, which results in obtaining the state vector of the whole system by applying the time-dependent Schrödinger equation. Thereupon, the dynamics of entanglement, coherence, photon statistics, and quadrature squeezing are numerically investigated. In each case, the roles of the intensity-dependent nonlinearity function, Kerr and intensity-dependent Kerr nonlinearity, different sources of dissipation, and detuning parameters are discussed. The numerical results indicate that the nonclassicality can remarkably be revealed, and can appropriately be controlled via the above-mentioned effects. It can be found that the presence of dissipation not only does not weaken the physical properties but also can enhance and protect the nonclassicality of the system.
In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of the time-dependent Schrödinger equation that provides a comprehensive framework for analyzing the system's quantum properties. To characterize the nonclassical features of the radiation field, we examine photon number distribution, second-order correlation function 𝑔2(0), squeezing properties, and Mandel's 𝑄𝑀 parameter. These properties reveal significant insights into the quantum statistical behaviour of the field and its deviation from classicality under different interaction regimes. In addition, we quantify the atom-atom entanglement using linear entropy which captures the mixedness of the atomic subsystem and elucidates the interplay between atom-atom interactions. The results highlight the crucial role of nonlinear interactions and the Stark shift in shaping the quantum correlations and nonclassical phenomena of the system.
In this paper, we explore the atomic population inversion and entanglement dynamics of a quantum system consisting of three identical two-level atoms interacting with a single-mode cavity field. The cavity is surrounded by a Kerr medium exhibiting f-deformed Kerr nonlinearity, and we consider a degenerate multi-photon transition in the nonlinear regime. The study systematically analyzes the effects of intensity-dependent coupling, detuning, Kerr nonlinearity, f-deformed Kerr nonlinearity, and multi-photon transition on the nonclassical properties of the system. Our results show that the Kerr and f-deformed Kerr nonlinearities significantly influence the atomic inversion dynamics, leading to phenomena such as collapse and revival, with distinct behaviors observed under varying detuning parameters. Furthermore, entanglement dynamics between the atoms and cavity mode are enhanced under intensity-dependent coupling and nonlinearity. The detuning parameter generally reduces entanglement but has a less pronounced effect in the two-photon transition case, where entanglement is notably enhanced. The study provides valuable insights into controlling quantum correlations in multi-atom systems, with potential applications in quantum information processing, computing, and communication.