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Acta Physica Sinica

Full quantum theory of an optimally pumped three-level laser

Guo Guang-Can

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in a type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over the reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than a certain value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vacuum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.

Related papers

FULL QUANTUM THEORY OF OPTICALLY PUMPED THREE-LEVEL LASER

Guo Guang-Can, 中国科学技术大学物理系

The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in the type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than some value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vaecum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.

Acta Physica Sinica•Jan 1, 1984•0 citations

LANGEVINIAN THEORY OF TWO-PHOTON LASERS BY OPTICAL PUMPING

Xiangming Hu, Wang Dexin, 华中师范大学物理系,武汉,430070

In this paper, a two-photon laser by optical pumping, with two-photon losses, is studied by means of the Langevinian theory, the langevinian equation is obtained. Then the steady-state average photon number, the frequency pulling, the linewidth and the dynamical Stark effect are obtained. From the analysis of the gain, it is shown that, for the incoherent pumping, only the two-step process of single-and two-photon gives contribution. And for the coherent pumping, in addition, the one-step process of single and two-photon also contributes. And two processes are confined by the negative-feedback and saturation. The linewidth is independent of the steady state average photon number.

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Menisha Alemu

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Universal Journal of Physics and Application•Mar 1, 2020•8 citations
The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in a type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over the reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than a certain value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vacuum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.
The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in the type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than some value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vaecum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.
In this paper, a two-photon laser by optical pumping, with two-photon losses, is studied by means of the Langevinian theory, the langevinian equation is obtained. Then the steady-state average photon number, the frequency pulling, the linewidth and the dynamical Stark effect are obtained. From the analysis of the gain, it is shown that, for the incoherent pumping, only the two-step process of single-and two-photon gives contribution. And for the coherent pumping, in addition, the one-step process of single and two-photon also contributes. And two processes are confined by the negative-feedback and saturation. The linewidth is independent of the steady state average photon number.
In this paper we have studied the statistical and squeezing properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. We have considered the case in which the three-level atoms and the cavity modes interact with the two-mode vacuum reservoir. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, we have calculated the mean and variance of the photon number as well as the quadrature squeezing for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. In addition, we have found that the effect of the vacuum reservoir noise is to increase the photon-number variance and to decrease the quadrature squeezing of the cavity light. However, the vacuum reservoir noise does not have any effect on the mean photon number. Moreover, the maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be 37.5% below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for γ=0 than that for γ=0.4 for 0.01 < ra < 0.35 and is smaller for γ=0 than that for γ=0.4 for 0.35 < ra < 1.
The analysis of quantum properties of the cavity light produced by a coherently driven nondegenerate three-level laser possessing an open cavity and coupled to a two-mode vacuum reservoir is presented. The normal ordering of noise operators associated with the vacuum reservoir is considered. Applying the solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators, the squeezing properties, entanglement amplification, and the normalized second-order correlation function of the cavity radiation are described. The three-level laser generates squeezed light under certain conditions, with maximum intracavity squeezing being 50% below the vacuum-state level. Moreover, it is found that the presence of spontaneous emission increases the quadrature squeezing and entanglement and decreses the mean photon number of the two-mode cavity radiation.
In this paper we have studied the statistical and squeezing properties of the cavity light generated by a three-level laser. In this quantum optical system, N three-level atoms available in an open cavity, coupled to a two-mode vacuum reservoir, are pumped to the top level by means of electron bombardment at constant rate. We have considered the case in which the three-level atoms and the cavity modes interact with the two-mode vacuum reservoir. 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 equations for the cavity mode operators, we have calculated the mean and variance of the photon number as well as the quadrature squeezing for the cavity light. In addition, we have shown that the presence of the spontaneous emission process leads to a decrease in the mean and variance of the photon number. We have observed that the two-mode cavity light is in a squeezed state and the squeezing occurs in the minus quadrature. The maximum quadrature squeezing of the light generated by the laser, operating far below threshold, is found to be 50% below the vacuum-state level. We have also established that the mean photon number in the presence of spontaneous emission is less than the absence of spontaneous emission.