Superposition Of Squeezed Laser Light Beams

In this research we have studied the squeezing and statistical properties of a pair of superposedrnoutput light beams generated by three-level lasers, with the injected atoms preparedrninitially in a coherent superposition of the top and bottom levels. In particular, applying therndensity operator for the superposed output laser light beams together with the Q functions,rnwe have calculated the global and local mean and variance of the photon number as well asrnthe quadrature squeezing. In addition, we have determined the mean and variance of thernphoton number sum and difference and the photon numbers correlation of a pair of superposedrntwo-mode output light beams.rnIt is found that both the mean photon number and quadrature variance of the superposedrnoutput laser light beams is the sum of the mean photon numbers and the quadrature variancesrnof the constituent output light beams. However, the variance of the photon number ofrnthe superposed output laser light beams is not the sum of the variances of the photon numbersrnof the component output laser light beams. Moreover, the global and local quadraturernsqueezing of a pair of superposed output laser light beams turned out to be the average ofrnthe global and local quadrature squeezing of the constituent output light beams. We havernalso noticed that the squeezing of the superposed output laser light beams is 61.5% belowrnthe vacuum state-level. On the other hand, we have seen that the local quadrature squeezingrnis greater than the global quadrature squeezing. It is found that the maximum local quadraturernsqueezing is 92.5% and occurs in the frequency = ±0.01. Furthermore, our resultsrnhave shown that the local quadrature squeezing, unlike the local mean of the phonon number,rnquadrature variance, and photon number variance does not increase as the value of rnincreases. In addition, our analysis indicates that the quadrature squeezing of the superpositionrnof squeezed laser light beam and a light beam in vacuum state turned out to be justrnhalf of the quadrature squeezing of the three-level laser output light beam. Finally, we wouldrnlike to mention that the photon numbers of a pair of superposed two-mode light beams arerncorrelated

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