A model for the master equation of multiphoton processes with radiative damping of the atomic levels is proposed and a matrix method employed to solve exactly the rate equations for the matrix elements of the reduced density operator in the Fock representation. This model has been applied to the study of the low-noise properties of squeezed light in an all-optical transmission link formed from alternating sections of linear and nonlinear attenuating fibre and optical amplifiers. When the attenuators present radiative damping of the atomic levels (the lower atomic state is not the ground state) the signal-to-noise ratio is enhanced with respect to the case in which the lower atomic level is the ground state. The enhancement is improved when the input light is squeezed. The statistical properties of linear and two-photon amplification with an absorption process which exhibits radiative damping have also been analysed for coherent and squeezed inputs. The second-order fluctuations are reduced when radiative damping in the absorption process is considered except in the case of two-photon absorption for small values of the saturation parameter sa . When the value of this parameter is increased the behaviour of the fluctuations changes and the noise is reduced. These results could be of interest in all-optical transmission links and are improved when the input light is squeezed.
A model for the master equation of multiphoton processes with radiative damping of the atomic levels is proposed and a matrix method employed to solve exactly the rate equations for the matrix elements of the reduced density operator in the Fock representation. This model has been applied to the study of the low-noise properties of squeezed light in an all-optical transmission link formed from alternating sections of linear and nonlinear attenuating fibre and optical amplifiers. When the attenuators present radiative damping of the atomic levels (the lower atomic state is not the ground state) the signal-to-noise ratio is enhanced with respect to the case in which the lower atomic level is the ground state. The enhancement is improved when the input light is squeezed. The statistical properties of linear and two-photon amplification with an absorption process which exhibits radiative damping have also been analysed for coherent and squeezed inputs. The second-order fluctuations are reduced when radiative damping in the absorption process is considered except in the case of two-photon absorption for small values of the saturation parameter sa . When the value of this parameter is increased the behaviour of the fluctuations changes and the noise is reduced. These results could be of interest in all-optical transmission links and are improved when the input light is squeezed.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.
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.
The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.
The statistical and fluctuational properties of an electromagnetic field in a nonideal cavity are studied with the help of the collective two-atom Jaynes-Cummings model taking into account losses of photons and spontaneous radiation of atoms into bath modes. For the coherent state of the field and excited initial state of atoms, the general analytical expressions for the second-order field correlation function, the second-order squeezing parameters, and the squared field amplitude are obtained by solving the master equation for the density matrix. The statistics and the degree of squeezing of the cavity field mode are studied as functions of the initial field intensity and of the coefficients of the energy dissipation of the system. It is shown that, for the two-atom dissipative model, compared to the single-atom model, the type of field statistics can be changed and the maximal degree of short-term squeezing can be increased.
The present report deals with the condition under which an ensemble of atoms goes over into a regime of collective two-photon nutation, and with the behavior of Rabi frequency as function of external light. To simplify this problem, we consider a system of Λ-type atoms that enters into two-photon resonance with an external squeezed electromagnetic field relative to the forbidden transition ∣1> ∣2> , where ∣1> and ∣2> are ground and first exited states [1,2] The situation is examining, when the values of quantum fluctuations of electromagnetic field intensity have the same value as the mean value of electromagnetic field intensity. This is one of main difference between the our paper and [2]. The proposed mathematical model permits to take into account all the two-photon diagrams. These diagrams describe not only resonance two-photon transitions but two-photon scattering processes between ∣1> and ∣2> levels too. Using mathematical method which is proposed in [1,2] it is obtained the master equation for the atom subsystem. Two stationary solutions for the case when Rabi frequency is larger than the inverse value of the collective two-photon decay time and the case when external light is coherent are examined. It is showing that the absorption rate of an phase squeezed field is larger than the absorption rate of an amplitude squeezed light. We also obtained the behavior of inversion between the levels ∣1> and ∣2>, when the collective of atoms enters into two-photon resonance with external field.
A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.