The aim of this work is to investigate the changing effects of the atom–cavity coupling constant on an atom–cavity system. A three-level atom in the Λ configuration with q-photon transition between levels 2 and 3 is confined in a single-mode Fabry–Pérot optical cavity. To solve the master equation of this system in the steady-state by using the appropriate physical quantities, the matrix continued fractions method for recurrence equations is applied. The behavior of physical observables including atom–field correlation, mean photon number, and second-order coherence function is discussed. The effect of altering the atom–cavity coupling constant for different transitions on these observables is fully considered. The results of calculations show that by increasing this coupling constant, the range of atom–cavity correlation becomes longer, the maximum value of the output mean photon number from the cavity remains almost constant, the broadening in the curves of the mean photon number increases and the lasing process is amplified in the system. Finally, the transformation of the three-level atom into a two-level one under several specific conditions in a four-photon transition case has been studied. The obtained results of the two-level atomic pattern are adequately confirmed by the simulations related to the three-level atom.
The aim of this work is to investigate the changing effects of the atom–cavity coupling constant on an atom–cavity system. A three-level atom in the Λ configuration with q-photon transition between levels 2 and 3 is confined in a single-mode Fabry–Pérot optical cavity. To solve the master equation of this system in the steady-state by using the appropriate physical quantities, the matrix continued fractions method for recurrence equations is applied. The behavior of physical observables including atom–field correlation, mean photon number, and second-order coherence function is discussed. The effect of altering the atom–cavity coupling constant for different transitions on these observables is fully considered. The results of calculations show that by increasing this coupling constant, the range of atom–cavity correlation becomes longer, the maximum value of the output mean photon number from the cavity remains almost constant, the broadening in the curves of the mean photon number increases and the lasing process is amplified in the system. Finally, the transformation of the three-level atom into a two-level one under several specific conditions in a four-photon transition case has been studied. The obtained results of the two-level atomic pattern are adequately confirmed by the simulations related to the three-level atom.
The mechanism of a four-level atom confined in a single-mode optical cavity with multiphoton transition is theoretically investigated in the steady-state. The behavior of the atom-cavity system is delineated by the master equation which in order to solve this equation, a set of expected values of a series of operators has been used. To numerically solve this set of coupled expectation values, the matrix continued fractions method is used. How the changes of the physical quantities including the atomic population inversion, mean photon number and second-order correlation function have been studied for any transition. Finally, the process of converting the four-level atom to a three-level one under several specific conditions is discussed for each transition.
A single atom is trapped in an optical cavity in the presence and absence of a nonlinear mirror corresponding to the nonlinear and linear regimes, respectively. The time evolutions of both systems are derived. The resultant equations are numerically solved by a fourth-order Runge–Kutta method. The effect of the nonlinear mirror over time evolution of the population inversion, the mean photon number and the second-order coherence function is investigated. It is shown that in the presence of the nonlinear effects, the time average of the population inversion is increased. As the time evolution proceeds, the mean photon number is decreased as well as the light exhibiting sub-Poissonian photon distributions. Under specific conditions and in a weak-driving limit, these systems can be well approximated by an effective two-level atom. The result of the calculations confirms the predictions of the two-level model.
We analyze the quantum properties of the light generated by a three-level laser with an open cavity and coupled to a two-mode squeezed vacuum reservoir via a single-port mirror. The three-level laser consists of three-level atoms available in an open cavity and pumped from the bottom to the top level by means of electron bombardment. Applying the large-time approximation scheme, we have obtained the steady-state solutions of the equations of evolution for the expectation values of the atomic operators and the quantum Langevin equations for the cavity mode operators. Using the resulting steady-state solutions, we have calculated the mean photon number, the variance of the photon number, and the quadrature variance for the two-mode cavity light. We have seen that the light generated by the three-level laser is in a squeezed state and the squeezing occurs in the plus quadrature. It so turns out that the maximum quadrature squeezing of the two-mode cavity light is 45:68% for M0 = 0:59 and N0 = 0:27 below the vacuum-state level. In addition, we have shown that the effect of the squeezed parameter is to increase the mean and variance of the photon number.
In this paper we have studied the squeezing and entanglement 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. 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, variance of the photon number, the quadrature squeezing, entanglement amplification as well as the normalized second-order correlation function 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 below the vacuum-state level. In addition, our result indicates that the quadrature squeezing is greater for than that for for 0.01 < < 0.35 and is smaller for than that for for 0.35 < < 1. We have also noted that the squeezing and entanglement in the two-mode light are directly related. As a result, an increase in the degree of squeezing directly leads to an increase in the degree of entanglement and vice versa. This shows that, whenever there is squeezing in the two-mode light, there exists an entanglement in the system.
We consider the system which is composed of a two-level atom and a two-mode cavity,and two modes are coupled in the cavity.The evolution of the state vector of the system is given.The squeezing,antibunching effect and the photon number statistical distribution of two-mode field are investigated.First,through calculating the fluctuations of two quadrature components of the field,we get that a-mode and b-mode of two-mode field do not both display squeezing.Second,by calculating second-order correlation function of two-mode field,the results show that a-mode and b-mode of two-mode field both display antibunching effects,and there is anti-correlation between the two modes.Third,by means of the numerical calculations,we plot evolution curves of Mandel Q function for different values of the coupling constants between two modes.Through comparing these curves,the influence of coupling constant between two modes on the photon number statistical distribution of the field is discussed.The evolution curves of Mandel Q function show that the two-mode cavity field displays sub-Poisson distribution.Moreover,the sub-Poisson distribution is weakened with increasing of the coupling constant between two modes.
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.