With the aid of the solutions of the Quantum Langevin equations, we have calculated the Q-functions for the two-mode coherent and subharmonic cavity light beams. We have then determined the Q-function for the superposed two-mode coherent and subharmonic cavity light beams. With the help of the pertinent Q-functions for cavity light beams, we determined the photon statistics, quadrature statistics, and entanglement. we have obtained that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state and the squeezing occurs in the plus quadrature. Besides, our analysis shows that at steady state and at threshold, the superposed two-mode coherent and subharmonic light beams have a maximum squeezing of $25\%$ below the two-mode vacuum-state level. We have also clearly shown that the superposed two-mode light beam is entangled at steady-state and threshold and the entanglement turned out to be observed in the highly correlated squeezed photons with $75\%$ degree of entanglement.
With the aid of the solutions of the Quantum Langevin equations, we have calculated the Q-functions for the two-mode coherent and subharmonic cavity light beams. We have then determined the Q-function for the superposed two-mode coherent and subharmonic cavity light beams. With the help of the pertinent Q-functions for cavity light beams, we determined the photon statistics, quadrature statistics, and entanglement. we have obtained that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state and the squeezing occurs in the plus quadrature. Besides, our analysis shows that at steady state and at threshold, the superposed two-mode coherent and subharmonic light beams have a maximum squeezing of 25% below the two-mode vacuum-state level. We have also clearly shown that the superposed two-mode light beam is entangled at steady-state and threshold and the entanglement turned out to be observed in the highly correlated squeezed photons with 75% degree of entanglement.
We examined a two-mode coherent and subharmonic light beam within a cavity that is coupled to a two-mode vacuum reservoir through a single port mirror. Utilizing the solutions of the quantum Langevin equations, we developed Q-functions for the two-mode coherent and subharmonic cavity light beams. Subsequently, we calculated the Q-function for the superposed two-mode light beams in question. By leveraging the relevant Q-functions for the superposed cavity light beams, we investigated the quadrature statistics and entanglement. To conduct our analysis, we focused on a quantum system characterized by Gaussian operators with a zero mean. We have identified that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state, with the squeezing occurring in the plus quadrature. Moreover, our analysis revealed that at steady state and at threshold, the superposed two-mode coherent and subharmonic light beams exhibit a maximum squeezing of 25% below the two-mode vacuum-state level. We have also clearly illustrated, using continuous variable entanglement criteria, that the superposed two-mode cavity light beams are entangled at both steady-state and threshold, with the entanglement being manifested in the highly correlated squeezed photons, which show a 75% degree of entanglement. Our analysis, applying Cauchy-Schewarz, Hillary-Zubiary, and Logarithmic Negativity entanglement criteria, further confirmed that the superposed cavity light beams in question are entangled. The Logarithmic Negativity criteria validated the entanglement of the superposed light, indicating a 50% degree of entanglement.
Abstract The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a singleport mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50 % maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50 % entangled.
In this article, we have analyzed the squeezing and statistical properties of the light generated by the superposition of second harmonic light and degenerate three level squeezed laser beams. We have found that the mean photon number of the superposed light beams to be the sum of the mean photon number of that of the constituent light beams. However, the photon number variance of the superposed light beams does not happen to be the sum of the photon number variances of the separate light beams. On the other hand, the quadrature variance of the superposed light beams is the sum of the individual light beams. Furthermore, we have observed that the degree of squeezing for the superposed light beams is the average of the segregate light beams and the degree of squeezing is approximately 53.95% below the coherent state level. Even though, we have verified that the superposition of subharmonic and second harmonic light with injected degenerate three-level laser beams he haves squeezing, we do not show continuous variable entanglement. But, the absence of the laser beam in the superposition state give rise entangled photons.
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.
In this work the statistical and squeezing properties of light-driven by sub-harmonic generation with two-mode coherent light are studied. With interaction Hamiltonian of both two-mode coherent and sub harmonic generation, we have driven master equation of system under consideration. From the master equation, the solution of the C-number Langevin equation is derived. It helps us to solve quadrature variance, quadrature squeezing, mean, and variance of photon number for light produced by sub-harmonic generation with the two-mode coherent light state. And the result shows that; the squeezing occurs in plus quadrature with the maximum squeezing of 87%. The photon statistics of the system under consideration is subpoissonian in which both mean & variance are increasing as kappa increase.
The squeezing, and statistical properties of a superposed light beam produced by a lambda type three-level lasers configuration have been studied. We have determined the quadrature variances mean as well as variance photon number for cavity modes with the aid of the solutions of c-number Langevin equations associated with the normal order. We have carried out our analysis a light in a squeezing state can be produced by the system under consideration under the condition that the cavity decay constant is larger than the linear gain coefficient and the squeezing occurs in the minus-quadrature. Furthermore, we also obtain with the aid of the Q-functions and the density operator the superposition beam, and superposed light beams are determined in quadrature variance and mean photon number. The result shows that the mean photon number and the quadrature variance of the superposed light beam are the sum of the mean photon number and the quadrature variance of the constituent light beams.