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Scientific Reports

Quantum dynamics and squeezing in a noiseless cavity mode driven by a coherent three-level atom

Beshir Awol, Bawoke Mekuye, Mihretu Tamina

Published Dec 12, 2025• 0 citations
Publisher

Abstract

We investigate a cavity mode that interacts with a three-level atom in an open cavity that is coupled to a vacuum reservoir and is driven by coherent light. In our analysis, the interaction of the three-level atom with the external vacuum reservoir is taken into account and the noise operators of the vacuum reservoir are placed in normal order. While the spontaneous emission rate fluctuates as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], the cavity damping constant and stimulated emission decay constant, both set to 0.8, govern the system dynamics. Both the plus and negative components of the cavity light display quadrature squeezing. For coherent driving strengths [Formula: see text] and [Formula: see text] at [Formula: see text], and [Formula: see text] at [Formula: see text], the plus quadrature exhibits [Formula: see text] squeezing below the vacuum level, indicating that increasing the coherent drive can compensate for the decoherence introduced by spontaneous emission. Moreover, for [Formula: see text], the minus quadrature achieves [Formula: see text] squeezing. At high driving strengths, the squeezing in both quadratures becomes independent of spontaneous emission. In the absence of spontaneous emission, the mean photon number increases, and the photon number distribution shows a higher probability for even photon numbers than for odd ones, with the overall distribution decreasing as the photon number increases.

DOI
10.1038/s41598-025-31100-3

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We investigate a cavity mode that interacts with a three-level atom in an open cavity that is coupled to a vacuum reservoir and is driven by coherent light. In our analysis, the interaction of the three-level atom with the external vacuum reservoir is taken into account and the noise operators of the vacuum reservoir are placed in normal order. While the spontaneous emission rate fluctuates as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], the cavity damping constant and stimulated emission decay constant, both set to 0.8, govern the system dynamics. Both the plus and negative components of the cavity light display quadrature squeezing. For coherent driving strengths [Formula: see text] and [Formula: see text] at [Formula: see text], and [Formula: see text] at [Formula: see text], the plus quadrature exhibits [Formula: see text] squeezing below the vacuum level, indicating that increasing the coherent drive can compensate for the decoherence introduced by spontaneous emission. Moreover, for [Formula: see text], the minus quadrature achieves [Formula: see text] squeezing. At high driving strengths, the squeezing in both quadratures becomes independent of spontaneous emission. In the absence of spontaneous emission, the mean photon number increases, and the photon number distribution shows a higher probability for even photon numbers than for odd ones, with the overall distribution decreasing as the photon number increases.
We have considered a cavity mode driven by coherent light and interacting with a three-level atom available in an open cavity coupled to a vacuum reservoir. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. We have also considered the interaction of the three-level atom with the vacuum reservoir outside the cavity. It is found that the squeezing occurs in both the plus and the minus quadratures and the maximum quadrature squeezing happens to be 52.08% and 33.32% below the vacuum state level, respectively. We have established that the uncertainty relation holds perfectly for this case as well. In addition, we have found that the squeezing in a pair of superposed cavity modes occurs in the plus and minus quadratures and have the same value. The amount of squeezing in each quadrature turns out to be half of the sum of the squeezing in the plus and minus quadratures of each cavity mode. Furthermore, we have observed that the presence of spontaneous emission decreases the mean photon number of the cavity mode but does not affect the maximum quadrature squeezing.
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.
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.
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.
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.
A three-level laser with an open cavity and a two-mode vacuum reservoir is explored for its quantum properties. Our investigation begins with a normalized order of the noise operators associated with the vacuum reservoir. The master equation and linear operators' equations of motion are used to determine the equations of evolution of the atomic operators' expectation values. The equation of motion answers are then used to calculate the mean photon number, photon number variance, and quadrature variance for single–mode cavity light and two–mode cavity light. As a result, for γ=0, the quadrature variance of light mode a is greater than the mean photon number for two-mode cavity light. As a result, for the two-mode cavity light, the maximum quadrature squeezing is 43.42 percent.