The quantum features and quantum statistical properties of a cavity-mode radiation emitted from the coherently prepared degenerate three-level laser have been investigated, by using the standard quantum electrodynamics approach and accounting for the light-matter interaction. We considered the vacuum reservoir, squeezed vacuum reservoir, and thermal reservoir to see the effect of reservoir input fields on the statistical and squeezing nature on the cavity radiation. It is found that the squeezed vacuum reservoir has enhancement effect on the squeezing property, as well as the brightness of the cavity radiation compared to those of the vacuum and thermal reservoirs. It is also observed that the radiation emitted from the cavity is in the squeezed state with super-Poissonian photon statistics regardless of the reservoir nature.
The quantum features and quantum statistical properties of a cavity-mode radiation emitted from the coherently prepared degenerate three-level laser have been investigated, by using the standard quantum electrodynamics approach and accounting for the light-matter interaction. We considered the vacuum reservoir, squeezed vacuum reservoir, and thermal reservoir to see the effect of reservoir input fields on the statistical and squeezing nature on the cavity radiation. It is found that the squeezed vacuum reservoir has enhancement effect on the squeezing property, as well as the brightness of the cavity radiation compared to those of the vacuum and thermal reservoirs. It is also observed that the radiation emitted from the cavity is in the squeezed state with super-Poissonian photon statistics regardless of the reservoir nature.
Abstract We investigate the quantum statistical and squeezing properties of radiation generated by a coherently driven three-level laser system coupled to a squeezed vacuum reservoir. The analysis is carried out using c-number Langevin equations for normally ordered operator moments, allowing a transparent description of the interplay among atomic coherence, coherent driving, and reservoir-induced correlations. We show that significant quadrature squeezing can be achieved under appropriate conditions, with the degree of squeezing strongly influenced by the linear gain coefficient of the squeezed-vacuum reservoir, the strength of the coherent driving, and the initial atomic preparation. In particular, we find that maximal initial atomic coherence alone does not lead to squeezing in the absence of coherent driving, highlighting the essential role of phase-sensitive amplification. The results further reveal a shift of optimal squeezing toward lower values of the atomic coherence parameter and higher values of the driving strength as the gain and reservoir squeezing increase. In addition, we demonstrate the coexistence of strong quadrature squeezing with super-Poissonian photon statistics, reflecting the distinct roles of phase-sensitive and intensity fluctuations. The squeezing spectrum is also analyzed to provide frequency-resolved insight into noise suppression, directly relevant to homodyne-detection measurements. These findings clarify the trade-off between coherent excitation, which enhances phase-sensitive correlations, and photon population growth, which tends to increase intensity fluctuations, and they highlight parameter regimes where strong nonclassical effects can be realized under parameter regimes consistent with experimentally demonstrated cavity-QED and squeezed-light implementations.
Abstract This study investigates a three-level laser system featuring a cascade-configured atom interacting with squeezed vacuum radiation within a lossy cavity, where the cavity modes are linked to a vacuum reservoir. By employing steady-state solutions derived from the expectation values of atomic operators and quantum Langevin equations for the cavity mode operators, we have calculated key quantum optical properties, including the mean photon number, normalized second-order correlation functions, and quadrature variances for cavity modes a 1 , a 2 , and their combined two-mode light. The findings reveal that the mean photon number of the two-mode light equals the sum of the individual mode photon numbers. Additionally, the influence of spontaneous and stimulated emissions, along with the squeeze parameter, is shown to enhance the mean photon numbers of the cavity modes. The results further suggest that the cavity modes exhibit thermal light characteristics, with the mean photon number of mode a 1 exceeding that of mode a 2 , as depicted in the analyzed graphs and equations.
Squeezing and entanglement of a two-mode cascade laser, produced by a three-level atom which is initially prepared by a coherent superposition of the top and bottom levels then injected into a cavity coupled to a two-mode squeezed vacuum reservoir is discussed. I obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. Making use of the solutions of the resulting differential equations, we determined the mean photon number for the cavity mode and their correlation, EPR variables, smallest eigenvalue of the symplectic matrix, intensity difference fluctuation, and photon number correlation. It is found that the squeezed vacuum reservoir increases the degree of the statistical and nonclassical features of light produced by the system. Furthermore, using the criteria developed by logarithm negativity and Hillery-Zubairy criteria, the quantum entanglement of the cavity mode is quantified. It is found that the degree of the entanglement for the system under consideration increases with the squeezing parameter of the squeezed vacuum reservoir.
Abstract We investigate the steady-state photon statistics and quantum properties of a cascade three-level atom coupled to a two-mode squeezed-vacuum reservoir. The mean photon number, photon-number correlations, second-order coherence, and quadrature fluctuations are examined as functions of the stimulated-emission decay constant and the squeezing parameter. The system exhibits two distinct regimes: a squeezing-dominated regime, governed by reservoir-induced correlations, and a cavity-dynamics-dominated regime, characterized by strong gain–loss competition. Enhanced squeezing increases photon generation, intermodal correlations, and intracavity energy through correlated photon-pair injection while reducing vacuum fluctuations. Conversely, stronger stimulated emission induces nonlinear amplification, asymmetric photon distributions, and sequential emission dynamics. A transition from super-Poissonian to sub-Poissonian statistics is observed, indicating the coexistence of photon antibunching and continuous-variable quantum correlations. Furthermore, atom–cavity interactions modify the generalized uncertainty bounds, revealing fundamental limitations on achievable squeezing imposed by higher-order noise processes. These findings demonstrate that engineered reservoirs and cascade atomic systems provide versatile control of nonclassical light for quantum communication, precision metrology, and continuousvariable quantum information processing.
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.
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezing of the cavity and output modes. It appears that almost perfect squeezing can be achieved at steady state and at threshold for a suitable choice of parameters.