The nonclassical behavior of the optical model has important applications in numerous quantum information fields. The suggested optical model in this study is based on a five-level atom (5LA) influenced by a two-mode quantized field (2MQF) inside a high-Q cavity that is filled with three types of nonlinear Kerr media. The nonlinear optical model has been solved analytically in which the components of this optical model are in perfect resonance. By considering the initial state of 5LA is in the upper state (excited state), whilst the initial state of 2MQF is in the coherent state. Some useful statistical measurements such as population inversion, Shannon entropy, second-order correlation, as well as Cauchy–Schwarz inequality that corresponds to P-functions are studied and discussed. The effects of the Kerr parameters on these statistical measurements are analyzed. All proposed statistical measurements confirm the existence of nonclassical behavior with time except for some small-time intervals.
The nonclassical behavior of the optical model has important applications in numerous quantum information fields. The suggested optical model in this study is based on a five-level atom (5LA) influenced by a two-mode quantized field (2MQF) inside a high-Q cavity that is filled with three types of nonlinear Kerr media. The nonlinear optical model has been solved analytically in which the components of this optical model are in perfect resonance. By considering the initial state of 5LA is in the upper state (excited state), whilst the initial state of 2MQF is in the coherent state. Some useful statistical measurements such as population inversion, Shannon entropy, second-order correlation, as well as Cauchy–Schwarz inequality that corresponds to P-functions are studied and discussed. The effects of the Kerr parameters on these statistical measurements are analyzed. All proposed statistical measurements confirm the existence of nonclassical behavior with time except for some small-time intervals.
In this paper, we present the interaction between a five-level [Formula: see text]-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level [Formula: see text]-type atom can be reduced to the three-level [Formula: see text]-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.
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.
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, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformed su(2) algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.
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.
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.