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Physica Scripta

Role of incoherent pumping scheme on gain without population inversion in four-level systems

Bibhas Kumar Dutta, P.K. Mahapatra

Published Jan 23, 2008• 14 citations

Abstract

We have studied gain without population inversion in two similar four-level systems by employing semiclassical density-matrix formalism. If the incoherent pumping process is not taken into account, both systems can be visualized as an ideal V-type system. Along with the application of strong pump and weak probe fields, an incoherent pump field is added to each of the systems in a different configuration. It has been shown that the different mechanisms of application of an incoherent pump to the system can appreciably change the population difference between the energy levels of the strongly driven transition and results in the evolution of inversionless gain either at the line center or at the sidebands on probe detuning. The effect of inhomogeneous broadening on the probe gain has also been studied.

DOI: 10.1088/0031-8949/77/02/025403

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We have studied gain without population inversion in two similar four-level systems by employing semiclassical density-matrix formalism. If the incoherent pumping process is not taken into account, both systems can be visualized as an ideal V-type system. Along with the application of strong pump and weak probe fields, an incoherent pump field is added to each of the systems in a different configuration. It has been shown that the different mechanisms of application of an incoherent pump to the system can appreciably change the population difference between the energy levels of the strongly driven transition and results in the evolution of inversionless gain either at the line center or at the sidebands on probe detuning. The effect of inhomogeneous broadening on the probe gain has also been studied.

A four-level system driven by two coherent fields is considered. the probe gain at a short wavelength can be achieved due to the quantum interference in the presence of an incoherent pump. The density matrix calculation provides the conditions for probe amplification from different origin, including gain without population inversion in any state basis, gain with population inversion in the dressed-state basis, and gain with population inversion in the bare-state basis. Also, by controlling Rabi frequency of the coupling field a totally changing from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.

A four-level system driven by two coherent fields is considered. It is shown that in the presence of an incoherent pump, the probe gain at a short wavelength can be achieved due to the quantum interference. Our density matrix calculation provides the conditions for probe amplification from different origins, including gain without population inversion on any state basis, gain with population inversion on the dressed-state basis and gain with population inversion on the bare-state basis. Also, by controlling the Rabi frequency of the coupling field a total change from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.

For a four-level atomic system with a doublet of closely spaced levels, we find that, owing to the coherence that results from the vacuum of the radiation field, population trapping at excited levels and probe gain with population inversion can be achieved with weak incoherent pumping. This gain is different from both the conventional lasing gain and gain without inversion in that there exists population inversion on probe transitions but the inversion is achieved by the vacuum-induced coherence.

In a three-level V-type atomic system without any external coherent driving, owing to the coherence that results from the vacuum of the radiation field, both the probe gain with and without population inversion can be achieved with very weak incoherent pumping. The gain is achieved in the absence of any external coherent driving field, so it is different from the gain without inversion in ordinary laser-driven schemes where a coherent driving field is necessary to create the coherence. The gain is also different from the conventional lasing gain because the population inversion is achieved via vacuum-induced coherence, which is dependent on the atomic coherence.