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Physica Scripta

Coherent and incoherent pumping of a three-level laser

Babak Parvin

Published Dec 19, 2023• 2 citations
Publisher

Abstract

Abstract This article investigates the quantum and semi-classical aspects of a three-level atom-cavity system within the context of cavity quantum electrodynamics. The study examines the behavior of the system through a quantum perspective and a semi-classical approximation. The steady-state master equation is solved in the atom-cavity basis, resulting in a closed set of equations describing the atom’s level occupancies and the cavity’s photon number. The accuracy of the semi-classical approximation is assessed by comparing it with quantum simulations. The research analyzes the system’s behavior near the laser threshold, highlighting the interplay between semi-classical and quantum behaviors. Additionally, the conversion of the three-level atom to a two-level atom is explored under specific conditions, enabling an investigation into the weak driving limit. Quantum simulation results are used to validate the proposed approximations. This work contributes to the understanding of atom-cavity interactions and provides insights into the transition from semi-classical to quantum behavior in such systems.

DOI
10.1088/1402-4896/ad173a

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Abstract This article investigates the quantum and semi-classical aspects of a three-level atom-cavity system within the context of cavity quantum electrodynamics. The study examines the behavior of the system through a quantum perspective and a semi-classical approximation. The steady-state master equation is solved in the atom-cavity basis, resulting in a closed set of equations describing the atom’s level occupancies and the cavity’s photon number. The accuracy of the semi-classical approximation is assessed by comparing it with quantum simulations. The research analyzes the system’s behavior near the laser threshold, highlighting the interplay between semi-classical and quantum behaviors. Additionally, the conversion of the three-level atom to a two-level atom is explored under specific conditions, enabling an investigation into the weak driving limit. Quantum simulation results are used to validate the proposed approximations. This work contributes to the understanding of atom-cavity interactions and provides insights into the transition from semi-classical to quantum behavior in such systems.
We propose a cavity quantum electrodynamic system consisting of a five-level atom coupled to a single mode of the cavity electromagnetic field. The study is focused on the regime of strong coupling between the cavity and atom. Pump laser fields and cavity fields connect the split energy levels of the atom. Instead of the well-known two-level Dicke model obtained by adiabatic elimination of the high-energy levels, we consider the pump lasers' detunings to the atomic transitions to be very small such that we can examine the influence of the higher-energy states. We have studied the effect of an external coherent drive and incoherent pumping on these higher-energy levels and observed the enhancement of intracavity photon numbers due to quantum coherence effects. The amplification of intracavity photons is achieved even without a population inversion. However, the effect of the coherent and incoherent drive is negligible for very large detunings when the higher-energy states are adiabatically eliminated. At zero and small detunings, the system reaches the steady state at an earlier instant of time for higher incoherent pumping. We find an almost agreeable steady-state behavior of the system's exact full quantum dynamics model and its semiclassical approximation. Our model tries to accurately simulate the open system by considering the cavity decay, spontaneous decay, and dephasing of the system.
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.
We consider a three-level cascade laser in which a coherently driven non-degenerate three-level atom available in a closed cavity coupled to a twomode vacuum reservoir.Applying the interaction Hamiltonian and Heisenberg equation of motion, we analyze the mean photon number, quadrature squeezing, and entanglement properties of the light produced by this quantum optical system inside the cavity.We find that the light generated by this system is in a two-mode squeezed state under certain conditions and the state of the system is weakly entangled at steady state due to the presence of the two-mode vacuum reservoir noise.
In this paper two different behaviors of a V-type three-level atom which is driven by a classical field in an optical cavity are shown. We show that the behavior of an atom depends on the values of the critical photon number. The system treatment for large enough values of the critical photon number is described by the semiclassical laser theory. In contrast, for small enough values of the critical photon number, the system shows new quantum properties. In the former case, it is shown that the system performs like a conventional laser and in the latter one, the system acts as an effective two-level model. The behaviors of the system are investigated both in the semiclassical approximation and full quantum theory. For comparing the results, computer simulations are implemented.
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.
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.