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arXiv:2301.06214 · Physical Review A

Quantum-jump analysis of frequency up-conversion amplification without inversion in a four-level scheme

J. L. Rubio, J. Mompart, V. Ahufinger

Published Jan 10, 2023• 2 citations
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Abstract

In this work, we use the quantum-jump approach to study light-matter interactions in a four-level scheme giving rise to frequency up-conversion amplification without inversion (AWI). The results obtained apply to the case of neutral Hg vapor where the AWI of a probe field in the UV regime was recently reported, opening the way for lasing without inversion in this range of frequencies. We show that, in this scheme, the key element to obtain maximum amplification is the fulfillment of the three-photon resonance condition, which favors coherent evolution periods associated with the probe field gain. We also investigate the parameter values to optimize amplification. The present study extends the theoretical understanding of the underlying mechanisms involved in AWI.

DOI
10.1103/physreva.107.013707

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In this work, we use the quantum-jump approach to study light-matter interactions in a four-level scheme giving rise to frequency up-conversion amplification without inversion (AWI). The results obtained apply to the case of neutral Hg vapor where the AWI of a probe field in the UV regime was recently reported, opening the way for lasing without inversion in this range of frequencies. We show that, in this scheme, the key element to obtain maximum amplification is the fulfillment of the three-photon resonance condition, which favors coherent evolution periods associated with the probe field gain. We also investigate the parameter values to optimize amplification. The present study extends the theoretical understanding of the underlying mechanisms involved in AWI.
We review amplification and lasing without inversion (AWI and LWI) in homogeneously broadened closed three-level systems in the framework of both density-matrix and quantum- jump formalisms. With the density-matrix formalism: (1) we study the nature of quantum interference in these systems; (2) determine analytically the conditions for AWI and locate the position of maxima and minima in the probe absorption spectrum; and (3) study various regimes of lasing, namely, continuous wave, self-pulsing and giant pulse lasing. Within the quantum-jump formalism we calculate the relative probabilities of the various physical processes responsible for probe field amplification and absorption.
We show that amplification without inversion (AWI) can be realized with two coherent driving lasers in a four-level atom. With the help of quantum-jump theory, two transition processes are found to contribute to the absorption or gain behaviour. It is explicitly shown that an asymmetry between the three-photon stimulated emission and the single-photon absorption process leads to AWI. Furthermore, it is demonstrated that AWI can occur in this model with or without quantum interference. The origin of AWI without interference is explained by introducing weights for dressed-state transitions. The asymmetry between the weights for a dressed-state transition in absorption and its counterpart in emission leads to the possibility of AWI.
We review amplification and lasing without inversion (AWI and LWI) in homogeneously broadened closed three-level systems in the framework of both density-matrix and quantum- jump formalisms. With the density-matrix formalism: (1) we study the nature of quantum interference in these systems; (2) determine analytically the conditions for AWI and locate the position of maxima and minima in the probe absorption spectrum; and (3) study various regimes of lasing, namely, continuous wave, self-pulsing and giant pulse lasing. Within the quantum-jump formalism we calculate the relative probabilities of the various physical processes responsible for probe field amplification and absorption.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Amplification without inversion (AWI) in a resonant V-type system is studied using a dressed basis which reduces the coherent interaction of both involved optical transitions to that of a single two-level system. The transient AWI recently reported through a numerical analysis of the density matrix equations of the V-system in the bare atom basis (Zhu Y 1996 Phys. Rev . A 53 2742) is damped Rabi nutation with transient population inversion in this dressed basis. Although the transient AWI in the bare state basis occurs both with and without an incoherent pump field, the integrated probe gain is positive only in the first case.
We study propagation effects on lasing without population inversion in a Doppler-broadened V -type three-level system. In particular, we focus our analysis on frequency up-conversion lasing without inversion in atomic rubidium. In an atomic beam configuration, we show that it is possible to increase notably the probe gain per single pass through the active medium by detuning driving and probe fields out of one-photon resonance but maintaining the two-photon resonance condition. In a vapour cell configuration, we show that due to propagation effects the probe gain per single pass depends strongly on the driving field intensity at the entrance of the active medium. In fact, for appropriate parameter values, it is possible to reach values of the probe gain per single pass of around 40%. For this last case, we have considered the feedback of a ring laser cavity.
Two essentially different mechanisms are known for inversionless amplification. The first is based on coherent population trapping, while the second is connected with the existence of quantum interference effects among dressed states of the coupled atom-field system. Previous investigations of four-level atoms with Raman pumping have emphasized the existence of noninversion lasing by way of the first mechanisms and have interpreted the gain as a result of a population inversion between dressed states. In this case the quantum interference generally hinders the amplification process. By extending this analysis to a broader range of parameters we find that the second mechanism can also become effective. The purpose of this presentation is to show that four-level atoms with a Raman pump can generally support both amplification mechanisms and to define the conditions under which either process may dominate.