Externally induced entanglement amplification in a coherently pumped emission of laser with parametric amplifier and coupled to squeezed vacuum reservoir
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 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.
The quantum and statistical properties of light generated by an external classical field in a correlated emission laser with a parametric amplifier and coupled to a squeezed vacuum reservoir are investigated using the combination of the master and stochastic differential equations. First, the solutions of the cavity-mode variables and correlation properties of noise forces associated to the normal ordering are obtained. Next, applying the resulting solutions, the mean photon number of the separate cavity modes and their crosscorrelation, smallest eigenvalue of the symplectic matrix, mean photon number, intensity difference fluctuation, photon number variance, and intensity correlation are derived for the cavity-mode radiation. The entanglement produced is studied employing the logarithmic negativity criterion. It is found that pumping atoms from the lower energy state to excited state, introducing the nonlinear crystal into the cavity and coupling the system to a biased noise fluctuation, generate a bright and strong squeezing and entanglement with enhanced statistical properties although the atoms are initially in the ground state.
In this paper, the detailed inseparability criteria of entanglement quantification of correlated two-mode light generated by a three-level laser with a coherently driven parametric amplifier and coupled to a two-mode vacuum reservoir is thoroughly analyzed. Using the master equation, we obtain the stochastic differential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the squeezing and the photon entanglement by considering different inseparability criteria. The various criteria of entanglement used in this paper show that the light generated by the quantum optical system is entangled and the amount of entanglement is amplified by introducing the parametric amplifier into the laser cavity and manipulating the linear gain coefficient.
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.
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.
The quantum properties of a non-degenerate three-level laser with the parametric amplifier and coupled to a thermal reservoir are thoroughly analyzed with the use of the pertinent master equation and stochastic differential equations associated with the normal ordering. Applying solutions of resulting differential equations, quadrature variance, the mean and variance of photon number, the photon number correlation are calculated. However, the two-mode driving light has no effect on the squeezing properties of the cavity modes. Employing the same solutions, one can also obtain anti normally ordered characteristic function defined in the Heisenberg picture. For a linear gain coefficient of (A = 100), for a cavity damping constant of K= 0:8, μ = 0.16 and for thermal reservoir nth = 0, the maximum intra cavity photon entanglement is found at steady state and at threshold to be 70%.
The detailed analysis of the two-mode quadrature squeezing and statistical properties of light generated by a nondegenerate three-level laser which has a parametric amplifier and coupled with a thermal reservoir is executed. The combination of the master equation and the stochastic differential equation is presented to study the nonclassical features of the light generated by the quantum system. Moreover, with the aid the resulting solutions together with the correlation properties of noise operators, we calculated the quadrature squeezing, entanglement, and mean number of photon pairs of the cavity light. It is found that the external small-amplitude driving radiation induces a strong correlation between the top and bottom states of three-level atoms to produce a high degree of squeezing. Moreover, the presence of a parametric amplifier is found to enhance the degree of squeezing of the cavity light. We have also established that an increase in the mean thermal photon number appears to degrade the squeezing, but enhances the mean number of photon pairs of the cavity light.