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Advances in physics theories and applications

Quantum Analysis of Degenerate Three-Level Laser

Habtamu Dagnaw Mekonnen

Published Jan 1, 2018• 1 citation
OpenAlex

Abstract

We have studied the squeezing and statistical properties of the light produced by degenerate three level lasers. In order to carry out the analysis, we have obtained the c-number Langevin equations associated with the normal order using the pertinent master equations. Applying the Q-functions for degenerate three-level laser, we have determined the mean and variance of the photon number as well as the photon number distribution for degenerate three-level laser. It has been found that the mean photon number and quadrature squeezing increase with linear gain coefficient. Keywords: Degenerate, Laser light, Squeezing, Quantum Noise, Photon

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We have studied the squeezing and statistical properties of the light produced by degenerate three level lasers. In order to carry out the analysis, we have obtained the c-number Langevin equations associated with the normal order using the pertinent master equations. Applying the Q-functions for degenerate three-level laser, we have determined the mean and variance of the photon number as well as the photon number distribution for degenerate three-level laser. It has been found that the mean photon number and quadrature squeezing increase with linear gain coefficient. Keywords: Degenerate, Laser light, Squeezing, Quantum Noise, Photon
We study the squeezing properties of the light generated by nondegenerate three-level laser in which the three-level atoms are in cascade configuration with degenerate parametric oscillator. We obtain the c-number Langevin equations associated with the normal ordering using the pertinent master equation. Making use of the solutions of the c-number Langevin equations, we calculate the quadrature variances. The results show that the two-mode light produced by the system under consideration is in squeezed state and the squeezing occurs in the minus quadrature. The degree of squeezing increase with the linear gain coefficient and almost perfect squeezing can be obtained for large values of the linear gain coefficient and the atoms initially prepared in lower level slightly greater than in the upper level. Moreover, the presence of nonlinear crystal increases the degree of squeezing for single mode and two-mode lights.
We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting 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 Langevin equation for the cavity mode operator, the mean photon number and the quadrature squeezing of the cavity light are calculated. And a large part of the mean photon number is confined in a relatively small frequency interval. Furthermore, we also obtain the antinormally ordered characteristic function defined in the Heisenberg picture. With the aid of the resulting characteristic function, we determine the Q function which is then used to calculate the photon number distribution.
Employing the master equation for a three-level laser driven by coherent light and coupled to a squeezed vacuum reservoir, we obtain stochastic differential equations associated with the normal ordering. Using the solutions of the stochastic differential equations, we calculate the quadrature variance, the squeezing spectrum, the mean photon number, and the variance of the photon number. It turns out that the degree of squeezing increases with the linear gain coefficient or the squeeze parameter. It is also found that the driving coherent light decreases the mean photon number.
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.
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.
We study the statistical and squeezing properties of the cavity light produced by a degenerate three-level laser with the use of the solution of the pertinent quantum Langevin equation. Moreover, applying the density operator to the cavity radiation superposition, we investigated the quantum properties of the superposed cavity light beams generated by a pair of degenerate three-level lasers. Superposing the cavity radiation increases the mean and the variance of the photon number without affecting the quadrature squeezing. It is observed that the degree of squeezing of the separate cavity radiation, as well as the superposed cavity radiation, increases with the rate at which the atoms are injected into the cavity. We have also shown that the mean photon number of the superposed cavity radiation is the sum of the mean photon numbers of the individual cavity radiation. However, the variance of the photon number of the superposed cavity radiation turns out to be four times that of the component cavity radiation.