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Comprehensive research and reviews in engineering and technology

Three-level laser quantum optics system coupled to thermal reservoirs

Takele Somano

Published Dec 30, 2022• 0 citations
Publisher

Abstract

In this study, we investigate the quantum characteristics of a three-level system coupled to a two-mode thermal reservoir. We employ stochastic differential equations, which incorporate normal ordering, to describe the dynamics of the system. Our primary focus is on examining the squeezing and entanglement properties of the two-mode cavity light. The results of the study demonstrate a significant level of entanglement between the two cavity modes. Furthermore, there exists a direct correlation between the degree of entanglement and the degree of two-mode squeezing. This discovery emphasizes the potential for enhancing the non-classical properties of the system by utilizing nonlinear optical elements. The study provides valuable insights into the interplay between squeezing, entanglement, and thermal noise in a three-level system coupled to a two-mode thermal reservoir. The findings suggest that the introduction of nonlinear elements can enhance the squeezing and entanglement of the system, even in the presence of thermal noise.

DOI
10.57219/crret.2022.1.1.0021

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In this study, we investigate the quantum characteristics of a three-level system coupled to a two-mode thermal reservoir. We employ stochastic differential equations, which incorporate normal ordering, to describe the dynamics of the system. Our primary focus is on examining the squeezing and entanglement properties of the two-mode cavity light. The results of the study demonstrate a significant level of entanglement between the two cavity modes. Furthermore, there exists a direct correlation between the degree of entanglement and the degree of two-mode squeezing. This discovery emphasizes the potential for enhancing the non-classical properties of the system by utilizing nonlinear optical elements. The study provides valuable insights into the interplay between squeezing, entanglement, and thermal noise in a three-level system coupled to a two-mode thermal reservoir. The findings suggest that the introduction of nonlinear elements can enhance the squeezing and entanglement of the system, even in the presence of thermal noise.
In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. Particularly, the enhancement of squeezing and the amplification of photon entanglement of the two-mode cavity light are investigated. It is found that the two cavity modes are strongly entangled and the degree of entanglement is directly related to the two-mode squeezing. Despite the fact that the entanglement and squeezing decrease with the increment of the mean photon number of the thermal reservoir, strong amount of these nonclassical properties can be generated for a considerable amount of thermal noise with the help of the nonlinear crystal introduced into the laser cavity. Moreover, the squeezing and entanglement of the cavity radiation enhance with the rate of atomic injection.
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 and for thermal reservoir th = 0, the maximum intra cavity photon entanglement is found at steady state and at threshold to be 60%.
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.
We study a nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir, by employing the stochastic differential equations associated with the normal ordering. The amplification of the properties of squeezing and entanglement of the cavity light is investigated. We have found that there is an entanglement between the states of the light generated in the cavity, due to the strong correlation of the light emitted, when the atom decays from the top level to the bottom level via the intermediate one. We have also obtained that the two cavity modes are strongly entangled, and the degree of entanglement is directly related to the two-mode squeezing.
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.
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%.