Abstract This research aims to study the squeezingand entanglement features of light in three-level atomsunder an open cavity with coherent light excitation.Using an approximation scheme for large timescales,we obtained the steady-state solutions of the evolutionequations for the atomic operators’ expectation valuesand the quantum Langevin equation for the cavity modeoperators. We employed these steady-state solutions todepict the squeezing characteristics, magnification ofentanglement, and normalized second-order correlationof the cavity radiation.The results of our researchshow that the light produced by the three-level lasergets squeezed, mainly in the minus quadrature. Themaximum quadrature squeezing for the light in thetwo-mode cavity is obtained as 37.9% at hni th = 0,and 37.5% at hni th = 0.02, and 37.2% at hni th = 0.03below the vacuum-state level. We demonstrated thatthe average and the variance of the number of photonsdecrease under the influence of spontaneous emission.Moreover, we determined that both the average andthe variance of the photon number are amplified bythe thermal reservoir effect. Additionally, we foundthat quadrature squeezing is enhanced by spontaneousemission, and some entanglement is created. In two-mode light, squeezing and entanglement are directlyrelated, such that an increase in squeezing producesmore entanglement and vice versa.
Abstract This research aims to study the squeezingand entanglement features of light in three-level atomsunder an open cavity with coherent light excitation.Using an approximation scheme for large timescales,we obtained the steady-state solutions of the evolutionequations for the atomic operators’ expectation valuesand the quantum Langevin equation for the cavity modeoperators. We employed these steady-state solutions todepict the squeezing characteristics, magnification ofentanglement, and normalized second-order correlationof the cavity radiation.The results of our researchshow that the light produced by the three-level lasergets squeezed, mainly in the minus quadrature. Themaximum quadrature squeezing for the light in thetwo-mode cavity is obtained as 37.9% at hni th = 0,and 37.5% at hni th = 0.02, and 37.2% at hni th = 0.03below the vacuum-state level. We demonstrated thatthe average and the variance of the number of photonsdecrease under the influence of spontaneous emission.Moreover, we determined that both the average andthe variance of the photon number are amplified bythe thermal reservoir effect. Additionally, we foundthat quadrature squeezing is enhanced by spontaneousemission, and some entanglement is created. In two-mode light, squeezing and entanglement are directlyrelated, such that an increase in squeezing producesmore entanglement and vice versa.
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.
The analysis of quantum properties of the cavity light produced by a coherently driven nondegenerate three-level laser possessing an open cavity and coupled to a two-mode vacuum reservoir is presented. The normal ordering of noise operators associated with the vacuum reservoir is considered. 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, the squeezing properties, entanglement amplification, and the normalized second-order correlation function of the cavity radiation are described. The three-level laser generates squeezed light under certain conditions, with maximum intracavity squeezing being 50% below the vacuum-state level. Moreover, it is found that the presence of spontaneous emission increases the quadrature squeezing and entanglement and decreses the mean photon number of the two-mode cavity radiation.
We analyze the quantum properties of the light generated by a three-level laser with an open cavity and coupled to a two-mode squeezed vacuum reservoir via a single-port mirror. The three-level laser consists of three-level atoms available in an open cavity and pumped from the bottom to the top level by means of electron bombardment. Applying the large-time approximation scheme, we have obtained the steady-state solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators. Using the resulting steady-state solutions, we have calculated the mean photon number, the variance of the photon number, and the quadrature variance for the two-mode cavity light. We have seen that the light generated by the three-level laser is in a squeezed state and the squeezing occurs in the plus quadrature. It so turns out that the maximum quadrature squeezing of the two-mode cavity light is 45:68% for M0 = 0:59 and N0 = 0:27 below the vacuum-state level. In addition, we have shown that the effect of the squeezed parameter is to increase the mean and variance of the photon number.
In this paper, we investigated the steady-state analysis of the squeezing and statistical properties of the light generated by N two-level atoms available in a closed cavity pumped by a coherent light with the cavity coupled to a singele mode vacuum reservoir. Here we consider the noise operators associated with the vacuum reservoir in normal order. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langavin equations for the cavity mode operators, we obtain the mean photon number, the photon number variance, and the quadrature squeezing. The three-level laser generates squeezed light under certain conditions, with maximum global squeezing being 43%. Moreover, we found that the maximum local quadrature squeezing is 80:2% (and occurs at λ = 0:08). Furthermore, our results have shown that the local quadrature squeezing, unlike the local mean of the phonon number and photon number variance does not increase as the value of λ increases. It is also found that, unlike the mean photon number, the variance of the photon number, and the quadrature variance, the quadrature squeezing does not depend on the number of atoms. This implies that the quadrature squeezing of the two-mode cavity light is independent of the number of photons.
The squeezing, entanglement, and statistical properties of light produced by lambda-type three-level laser coupled to squeezed vacuum reservoir have been studied. We have determined the quadrature variances mean as well as variance photon number photon for cavity modes with the aid of the solutions of c-number Langevin equations associated with the normal order. The results show that the light produced by the system under consideration in squeezed state. The squeezed vacuum reservoir enhances both the quadrature squeezing and mean photon numbers. In addition, the mean photon number of mode b is greater than that of a if more atoms injected with state |a>. We have calculated the quadrature variances of the cavity modes, the result shows that the light produced by the system under consideration is in squeezed state and the squeezing occurs in the minus quadrature. The result also shows that the effect of the squeezed vacuum reservoir is not only enhancing the degree of squeezing for the light modes but also to generate the photons for the system under consideration. The system produce entangled two mode light that increase with η and linear gain coefficient but decrease with squeezing parameters. The correlation function of the two modes decreases as η, the linear gain coefficient and increase with squeezing parameter.
Abstract This study investigates a three-level laser system featuring a cascade-configured atom interacting with squeezed vacuum radiation within a lossy cavity, where the cavity modes are linked to a vacuum reservoir. By employing steady-state solutions derived from the expectation values of atomic operators and quantum Langevin equations for the cavity mode operators, we have calculated key quantum optical properties, including the mean photon number, normalized second-order correlation functions, and quadrature variances for cavity modes a 1 , a 2 , and their combined two-mode light. The findings reveal that the mean photon number of the two-mode light equals the sum of the individual mode photon numbers. Additionally, the influence of spontaneous and stimulated emissions, along with the squeeze parameter, is shown to enhance the mean photon numbers of the cavity modes. The results further suggest that the cavity modes exhibit thermal light characteristics, with the mean photon number of mode a 1 exceeding that of mode a 2 , as depicted in the analyzed graphs and equations.