Quantum and Statistical Properties of a Non-degenerate Three-Level Laser Pumped by Electron Bombardment and Coupled to a Two-Mode Thermal Reservoir

Abstract

This study investigates the quantum and statistical properties of light generated by a non-degenerate three-level laser system, where atoms are continuously pumped to the top energy level through electron bombardment in an open cavity coupled to a two-mode thermal reservoir. By applying the large-time approximation, we derive steady-state solutions to the quantum Langevin equations for the cavity mode operators and the evolution equations for the expectation values of the atomic operators. Our findings demonstrate that the mean photon number, photon number variance, squeezing, entanglement, and normalized second-order correlation function of the two-mode cavity light in the steady state are significantly affected by the initial seeding of thermal light \(\langle n_{th} \rangle \) and the spontaneous emission rate. Specifically, we observe that the mean photon number in the cavity decreases with increasing \(\langle n_{th} \rangle \), suggesting that thermal effects contribute to photon loss or redistribution. In contrast, the absence of thermal light results in a higher mean photon number, indicating a more stable cavity light state. The photon number variance \((\Delta n)^2\) increases rapidly with the pumping rate \(r_a\), with thermal light having a low impact at higher rates. A higher spontaneous emission rate \(\gamma \) reduces fluctuations, lowering the variance’s saturation level. Quadrature squeezing is negatively impacted by both initial thermal light and spontaneous emission, with maximum squeezing values of 44% and 50% achieved for \(\langle n_{th} \rangle = 0.1\) and \(\langle n_{th} \rangle = 0\), respectively. Photon entanglement also diminishes as the spontaneous emission decay constant and initial thermal light increase, emphasizing the interplay between these factors and the degree of photon entanglement. Additionally, the second-order correlation function \(g^{(2)}(a,b)(0)\) consistently decreases with increasing \(r_a\), regardless of the presence of initial thermal light. These insights have significant implications for advancing quantum technologies, such as quantum communication where controlled squeezing and entanglement enhance secure communication channels and improve signal to noise ratios as well as quantum computing and quantum sensing.