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.
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 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 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 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.
Abstract The dynamics of an effective two-level atom coupled to two-mode intensity-dependent quantized cavity fields via a ladder process in the presence of a Kerr medium has been investigated. Eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained using a unitary transformation method. The cavity field statistics and non-classical properties are investigated numerically through second-order correlation functions. The effect of detuning and the Kerr medium on the non-classical features of the atom-field state has been analyzed. We find that the presence of Kerr non-linearity enhances the non-classical correlation between the correlated beams at short time intervals and increases antibunching at short time intervals.
In this paper, we study the quantum interaction between a moving two-level atom and a single-mode quantized field in an optical cavity with degenerate multi-photon transition, in the presence of intensity-dependent coupling and thermal effect. We introduce the appropriate Hamiltonian of the system, and we adopt the initial condition of subsystems, in which the atom is prepared in an arbitrary superposition of ground and excited states, and the field is considered in a thermal state. Consequently, we determine the density matrix of the entire system at any given time. We further assess some of the most important quantum properties, such as quantum coherence, sub-Poissonian statistics, and phase-space nonclassicality by means of negativity of the Wigner quasiprobability distribution function. We then investigate the impact of intensity-dependent nonlinearity, thermal noise, atomic motion, and multi-photon transition on these quantum properties. The numerical results show that the nonclassicality criteria can be significantly influenced and controlled by the effects discussed above. Interestingly, increasing the mean thermal photon number, which highlights the thermal effect, can, in some cases, enhance the nonclassicality features of the system.