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Journal of Physics & Optics Sciences

Quantum Entanglement and its Quantification in a Two-Mode Cascade Laser

Ebisa Mosisa Kanea

Published Jul 31, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.47363/jpsos/2021(3)152

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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 nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir are throughly analyzed with the use of the pertinent master equation and stochastic differential equations associated with the normal ordering. 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. Moreover, the squeezing and entanglement of the cavity radiation enhance with the rate of atomic injection.
We analyze a nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir employing the stochastic differential equations associated with the normal ordering. We study the squeezing properties and entanglement amplification of the cavity radiation. We also calculate the correlation of the photon numbers and the fluctuations of the intensity difference. It turns out that the generated light exhibits a two-mode squeezing and entanglement when initially there are more atoms in the lower level. Moreover, a strong correlation between photon numbers along with a significant fluctuation in the intensity difference is found.
A detailed comparison among the exhibited nature of entanglement of the cavity radiation of the nondegenerate three-level cascade laser when different inseparability criteria are employed is presented. Although the achievable degree of entanglement is generally found to vary with the applied inseparability criteria, there are cases for which more than two of the applied criteria lead to a significant degree of entanglement for certain parameters. Particularly, the procedures following from the criterion of Duan–Geidke–Cirac–Zoller and logarithmic negativity predict a similar pattern of entanglement except when the atoms are initially prepared in a maximum atomic coherent superposition. In the same manner, in relation to the absence of interatomic interaction, the Hillery–Zubairy and Cauchy–Schwarz inequalities virtually lead to a similar degree of entanglement. Since an appreciably large degree of entanglement is shown to be realizable using various criteria, there is no doubt that this quantum system can be utilized as a viable source of entangled light.
We have studied the squeezing and entanglement properties of the light induced by a three-level laser coupled to the squeezed vacuum reservoir. Applying the pertinent master equation, we have obtained the evolution equations for the cavity mode variables. Using the solutions of the resulting equations, the squeezing properties, entanglement amplification, and the normalized second-order correlation function of the cavity radiation are described. We have seen that the light generated by a three-level laser is in a squeezed state, and the squeezing occurs in the plus quadrature. In addition, we have also established that the effect of the squeezed parameter increases the mean and variance of the photon number. It is found 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.