Abstract On this paper, We investigate the generation and enhancement of bipartite entanglement in a three level cascade laser embedded in a Kerr nonlinear resonator and coupled to a squeezed vacuum reservoir. The system dynamics are modeled using a quantum master equation that incorporates atom-field interactions, Kerr nonlinearity, cavity damping, spontaneous emission, and squeezed vacuum effects. Applying the good cavity approximation, the atomic variables are adiabatically eliminated to derive effective cavity-field equations, which are transformed into c-number Langevin equations. Linearization around the steady state yields analytical expressions for second-order moments and the covariance matrix. Bipartite entanglement is quantified using the Duan inseparability criterion and logarithmic negativity. Our numerical results show that stronger Kerr nonlinearity and more squeezing greatly increase quantum correlations, while coherent pumping improves entanglement by boosting atomic coherence.However, higher cavity losses reduce entanglement due to photon loss.These findings highlight Kerr-enhanced cascade lasers with squeezed reservoirs as potential sources of entangled light for engineering bright, highly entangled CV optical sources for quantum key distribution, teleportation, and optical quantum networks.
Abstract On this paper, We investigate the generation and enhancement of bipartite entanglement in a three level cascade laser embedded in a Kerr nonlinear resonator and coupled to a squeezed vacuum reservoir. The system dynamics are modeled using a quantum master equation that incorporates atom-field interactions, Kerr nonlinearity, cavity damping, spontaneous emission, and squeezed vacuum effects. Applying the good cavity approximation, the atomic variables are adiabatically eliminated to derive effective cavity-field equations, which are transformed into c-number Langevin equations. Linearization around the steady state yields analytical expressions for second-order moments and the covariance matrix. Bipartite entanglement is quantified using the Duan inseparability criterion and logarithmic negativity. Our numerical results show that stronger Kerr nonlinearity and more squeezing greatly increase quantum correlations, while coherent pumping improves entanglement by boosting atomic coherence.However, higher cavity losses reduce entanglement due to photon loss.These findings highlight Kerr-enhanced cascade lasers with squeezed reservoirs as potential sources of entangled light for engineering bright, highly entangled CV optical sources for quantum key distribution, teleportation, and optical quantum networks.
Squeezing and entanglement of a two-mode cascade laser, produced by a three-level atom which is initially prepared by a coherent superposition of the top and bottom levels then injected into a cavity coupled to a two-mode squeezed vacuum reservoir is discussed. I obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. Making use of the solutions of the resulting differential equations, we determined the mean photon number for the cavity mode and their correlation, EPR variables, smallest eigenvalue of the symplectic matrix, intensity difference fluctuation, and photon number correlation. It is found that the squeezed vacuum reservoir increases the degree of the statistical and nonclassical features of light produced by the system. Furthermore, using the criteria developed by logarithm negativity and Hillery-Zubairy criteria, the quantum entanglement of the cavity mode is quantified. It is found that the degree of the entanglement for the system under consideration increases with the squeezing parameter of the squeezed vacuum reservoir.
We analyze the CV bipartite entanglement of the light generated by a coheretly pumped non degenerate three-level laser with a two-mode subharmonic generator coupled to a twomode vacuum reservoir via a single-port mirror, whose open cavity contains N non-degenerate three-level cascade atoms. We carry out our analysis by putting the noise operators associated with a vacuum reservoir in normal order. It is found that the photon-state of the system is strongly entangled at steady state where as the atom state of the system is not entangled. We have also shown that as the stimulated decay constant increases, the degree of entanglement increases. In addition, we have established that the photons in the laser cavity are highly correlated and the photon correlation and entanglement increases as the amplitude of the coherent light driving the pump mode increases. Moreover, we have realized that the presence of the subharmonic generator leads to an increase in the degree of entanglement and correlations.
In this paper, quantum entanglement of correlated two-mode light generated by a three-level laser coupled to a two-mode squeezed vacuum reservoir is thoroughly analyzed using different inseparability criteria, using the master equation, we obtain the stochastic dierential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the photon entanglement by considering different inseparability criteria. In particular, the criteria applied are Duan-Giedke-Cirac-Zoller (DGCZ) criterion, logarithmic negativity, Hillery-Zubairy, and Cauchy-Schwartz inequality and we found that the presence of the squeezing parameter leads to an increase in the degree of entanglement. Moreover, the linear gain coecient significantlyachieved the degree of entanglement for the cavity radiation.
Abstract Externally induced entanglement amplification in a coherently pumped Correlated Emission Laser (CEL) with parametric amplifier and coupled to a squeezed vacuum reservoir is presented. The combination of the master equation and stochastic differential equation is applied to investigate the entanglement of the correlated two photons generated by the quantum system. The resulting solutions of the correlation properties of noise forces associated with the normal ordering are used to find the mean photon number of the separate cavity modes and their correlation, EPR-pair variables, and smallest eigenvalue of the sympectic matrix. It is found that pumping atoms from the lower energy state to excited state results in a strong entanglement that remains in its maximum strength over a wide range of the strong classical pumping radiation. The introduction of the nonlinear crystal into the laser cavity, and coupling the system to the two-mode squeezed vacuum environment lead to a significant enhancement of entangled cavity light. The entanglement produced is quantified employing logarithmic negativity, Hillary Zubairy and Duan et al criteria. It has been observed that an intense light can be produced where the entanglement is strong. The amount of the entanglement produced is found to be 87% by both Duan et al and logarithmic negativity criteria.
Abstract We investigate the steady-state photon statistics and quantum properties of a cascade three-level atom coupled to a two-mode squeezed-vacuum reservoir. The mean photon number, photon-number correlations, second-order coherence, and quadrature fluctuations are examined as functions of the stimulated-emission decay constant and the squeezing parameter. The system exhibits two distinct regimes: a squeezing-dominated regime, governed by reservoir-induced correlations, and a cavity-dynamics-dominated regime, characterized by strong gain–loss competition. Enhanced squeezing increases photon generation, intermodal correlations, and intracavity energy through correlated photon-pair injection while reducing vacuum fluctuations. Conversely, stronger stimulated emission induces nonlinear amplification, asymmetric photon distributions, and sequential emission dynamics. A transition from super-Poissonian to sub-Poissonian statistics is observed, indicating the coexistence of photon antibunching and continuous-variable quantum correlations. Furthermore, atom–cavity interactions modify the generalized uncertainty bounds, revealing fundamental limitations on achievable squeezing imposed by higher-order noise processes. These findings demonstrate that engineered reservoirs and cascade atomic systems provide versatile control of nonclassical light for quantum communication, precision metrology, and continuousvariable quantum information processing.
In this paper we have studied the squeezing and entanglement properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have calculated the mean, variance of the photon number, the quadrature squeezing, entanglement amplification as well as the normalized second-order correlation function for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. In addition, we have found that the effect of the vacuum reservoir noise is to increase the photon-number variance and to decrease the quadrature squeezing of the cavity light. However, the vacuum reservoir noise does not have any effect on the mean photon number. Moreover, the maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for than that for for 0.01 < < 0.35 and is smaller for than that for for 0.35 < < 1. We have also noted that the squeezing and entanglement in the two-mode light are directly related. As a result, an increase in the degree of squeezing directly leads to an increase in the degree of entanglement and vice versa. This shows that, whenever there is squeezing in the two-mode light, there exists an entanglement in the system.