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Advances in physics theories and applications

The Mean and Variance of Photon Number for Twin Light Beams Generated by Parametric Oscillator

Assaye Gedifew Yismaw

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

A detailed photon statistics of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented. We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies. According to our study we have observed that the mean photon number of the cavity mode decreases with the cavity damping constant increase, which implies that the more photons are escaped from the cavity for the large damping constant and the mean photon number of residue pump mode increases with the amplitude of pump mode.

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A detailed quantum entanglement of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented.We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies.According to our study we have the quadrature variance decreases with the amplitude of pump mode and it approaches to the value of the quadrature variance of a two-mode vacuum state as cavity damping constant approaches to 1.In addition to this the degree of entanglement of the cavity modes for the system under consideration increase with the amplitude of the pump mode and decrease with the cavity damping constant, which implies that the degree of entanglement of twin light beams decreases as quadrature variances approaches to that of a two-mode vacuum state.

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Ukrainian Journal of Physics•Apr 7, 2021•2 citations
A detailed photon statistics of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented. We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies. According to our study we have observed that the mean photon number of the cavity mode decreases with the cavity damping constant increase, which implies that the more photons are escaped from the cavity for the large damping constant and the mean photon number of residue pump mode increases with the amplitude of pump mode.
A detailed quantum entanglement of twin light beams with the same and different frequencies produced by the process of parametric oscillation has been presented.We have described the process of the parametric oscillation with first-order Hamiltonian regardless of whether the twin light beams have the same or different frequencies.According to our study we have the quadrature variance decreases with the amplitude of pump mode and it approaches to the value of the quadrature variance of a two-mode vacuum state as cavity damping constant approaches to 1.In addition to this the degree of entanglement of the cavity modes for the system under consideration increase with the amplitude of the pump mode and decrease with the cavity damping constant, which implies that the degree of entanglement of twin light beams decreases as quadrature variances approaches to that of a two-mode vacuum state.
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.
In this paper, the authors investigate the coupling of the radiations generated by a non-degenerate three-level cascade laser and a parametric oscillator in a cavity coupled with a two-mode squeezed vacuum reservoir, using a 50 : 50 beam splitter. They analyze the quantum statistical properties of the light superposed via the standard beam splitter with phase shift ϕ . When the beams of light superpose in phase ( ϕ = 0 ) and operate above threshold, they demonstrate that the mean and variance of photon number increase initially and remain constant over time. They also show that these quantities significantly rise with the linear gain coefficient when more atoms are initially prepared in the top energy level, and, regardless of the initial atomic preparation, increase with the driving amplitude of the parametric oscillator. Furthermore, at steady state and above threshold, the authors reveal that the superposed radiation, despite exhibiting super-Poissonian statistics, displays non-classical photon number correlations due to strong cross-correlations between the cavity modes of the coupled systems.
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 present the results of an experiment in which we observed photon-number statistics of twin beams emerging from a nondegenerate optical parametric oscillator. We generated the photocurrent for recording by detecting the light and mixing it with a standard electrical oscillator. The measured photocurrent variances exhibited a quantum correlation of as much as -4.9 dB between signal and idler, whereas their photon number distributions were super-Poissonian. We also obtained the difference photon-number distribution.
The statistical and squeezing properties of the cavity light produced by a three-level laser are studied. In the laser, N three-level atoms in an open cavity are coupled with a two-mode vacuum reservoir and are pumped to the top level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have obtained the global and local photon statistics for single-mode cavity light beams and for two-mode cavity light. It is found that the global mean photon number and the global photon-number variance of the light emitted from the top are greater than those for the light emitted from intermediate level. The cavity lights emitted from the top and intermediate levels can be separately in a chaotic state under certain conditions. However, the two-mode cavity light is in a squeezed state under certain conditions. We have established that the maximum quadrature squeezing of the two-mode cavity light to be about 46% below the coherent-state level. The presence of the vacuum reservoir noise has the effect of increasing the photon-number variance and decreasing the quadrature squeezing of the cavity light but has no effect on the mean photon number. We have shown that the local mean photon number and photon number variance of the cavity light approach the global mean photon number and photon number variance of the cavity light as the frequency interval increases.