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Journal of Modern Physics

Non-Classical Formulation of Photon Energy for the Degenerate Parametric Oscillator

Solomon Getahun

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We have analyzed photon statistics and quadrature squeezing of the signal mode produced by one-mode subharmonic generator. It is found that the mean photon energy of the signal mode is twice of a twin signal light beam. And the energy fluctuations of the two signal light beams are four times that of one of the signal light beams. We have also shown that the photon energy quadrature squeezing of the output signal mode is exactly equal to that of the cavity signal mode. In light of this, the global quadrature squeezing of the signal mode is independent of the mean photon energy. On the basis of the above results, the quantum analysis of a one-mode sub-harmonic generating system should somehow be modified.

DOI
10.4236/jmp.2014.515149

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We have analyzed photon statistics and quadrature squeezing of the signal mode produced by one-mode subharmonic generator. It is found that the mean photon energy of the signal mode is twice of a twin signal light beam. And the energy fluctuations of the two signal light beams are four times that of one of the signal light beams. We have also shown that the photon energy quadrature squeezing of the output signal mode is exactly equal to that of the cavity signal mode. In light of this, the global quadrature squeezing of the signal mode is independent of the mean photon energy. On the basis of the above results, the quantum analysis of a one-mode sub-harmonic generating system should somehow be modified.
We have established that the mean photon number obtained employing the conventional Hamiltonian for the twin light beams with the same frequency, produced by a subharmonic generator, is half that of the twin light beams with different frequencies. In view of this, we have found it to be quite appropriate to describe the process of subharmonic generation by the same Hamiltonian regardless of whether the twin light beams have the same or different frequencies. Applying this Hamiltonian, we have calculated the photon statistics and quadrature squeezing for the signal-signal and the signal-idler modes. Obviously, this time the mean photon number of the signal-signal modes is exactly the same as that of the signal-idler modes. In addition, we have found that the maximum global quadrature squeezing of the signal-signal or the signal-idler modes is 50%\%% below the vacuum-state level and the maximum local quadrature squeezing of the signal-signal modes is 74.9%\%% below the same level.
We have analyzed the statistical and squeezing properties of the signal mode applying the solution of c-number Langivin equations for the combination of the twin signal light beams. We have found that the mean photon number to be twofold of that of a twin signal light beam. And a large part of the mean photon number is confined in a relatively small frequency interval. In addition, we have shown that the local quadrature squeezing of the signal mode is in general greater than the global quadrature squeezing and approaches to the global quadrature squeezing as increases. Moreover, the one-mode subharmonic light beams have a maximum amplified squeezing of 75% below the vacuum state level and occurs in frequency interval.
In this work the statistical and squeezing properties of light-driven by sub-harmonic generation with two-mode coherent light are studied. With interaction Hamiltonian of both two-mode coherent and sub harmonic generation, we have driven master equation of system under consideration. From the master equation, the solution of the C-number Langevin equation is derived. It helps us to solve quadrature variance, quadrature squeezing, mean, and variance of photon number for light produced by sub-harmonic generation with the two-mode coherent light state. And the result shows that; the squeezing occurs in plus quadrature with the maximum squeezing of 87%. The photon statistics of the system under consideration is subpoissonian in which both mean & variance are increasing as kappa increase.
Abstract The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a singleport mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50 % maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50 % entangled.
In this paper, we have studied the statistical and squeezing properties of the light produced by superposed light beams generating by a pair of degenerate parametric oscillator whose cavity mode is driven by a coherent light and is coupled to a vacuum reservoir via a single port mirror. We obtain c-number Langevin equation associated with the normal ordering using the pertinent master equation. Employing the solution of the c-number Langevin equation and the density operator, we have determined the mean and the variance photon number, quadrature variances and squeezing spectrum of the superposed light beams.
We theoretically investigate the quantum statistical properties of a two-mode cavity light generated by a ∨ -type three-level atom interacting with nondegenerate subharmonic light and coupled to a two-mode squeezed vacuum reservoir. Using the master equation, we obtain steady-state expectation values for the atomic and cavity-mode operators. Based on these results, we analyze the global and local photon number variances, intensity fluctuation spectrum, joint photon number distribution, and photon count statistics. Our results reveal that squeezing parameter and subharmonic generation significantly enhance intensity fluctuations, as well as the mean and variance of photon counts, whereas atom-field coupling and cavity decay suppress them. The system exhibits super-Poissonian photon statistics, indicating that photon number fluctuations exceed the mean photon number. Furthermore, the photon count variance, which incorporates intracavity transmission and input noise, increases with detector efficiency. These results provide a comprehensive picture of photon statistics in atom-photon systems and guide the design of advanced quantum optical devices.