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Chinese Physics

Quantum interference effects on the probe amplification without and with inversion in a four-level system

Bing Zhang, Weihua Xu, Zhang Hui-Fang, Jin-Yue Gao

Published Sep 28, 2004• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/13/10/026

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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.
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.
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.
We propose a new four-level atomic model for achieving light amplification at a short wavelength, where direct incoherent pumping into the top level is avoided by the advantage of coherent pumping. In this model, the lower level of the probe transition is an excited state but not the usual ground state. By analytical as well as numerical calculations, we find that the probe gain, either with or without population inversion, which depends on the relation between spontaneous decay rates γ42 and γ21, can be achieved with proper parameters. We note that the Raman scattering gain always plays an important role in achieving the probe amplification.
Density-matrix calculations provide the steady-state conditions for probe amplification or lasing between atomic levels with an uninverted population, but additional insight into the underlying physics is given by a probability amplitude approach. In this paper we derive the gain coefficient from the Feynman diagrams for a probe-laser incident on a resonantly pumped, V-type system using time-dependent perturbation theory in a dressed basis. The connection is made to density-matrix calculations for this model, which have been used recently to describe experiments in Rb [A. S. Zibrov et al., Laser Phys. 5, 553 (1995); Phys. Rev. Lett. 75, 1499 (1995)]. In the density-matrix calculation the overall gain is possible because the pump-induced coherence of a strongly driven transition leads to probe amplification, despite the lack of inversion on the probe transition. In our amplitude approach we associate a specific physical process with each of the scattering channels for the probe and show how amplification without inversion can be achieved. The amplitude calculation reveals a distinction between stepwise and two-quantum processes. Interference is shown to result from the two-quantum processes, constructive for the amplification channels and destructive for the absorption. Terms appearing in the gain coefficient are traced to different sources in the amplitude and density-matrix approaches. The physical origin of each term is discussed and compared for both approaches. Terms that arise from coherences in the density-matrix approach are shown to correspond to noninterfering stepwise contributions in the amplitude approach. In deriving these results, we find that the Feynman rules that we construct for forming the probability amplitude for an arbitrary scattering process of the electromagnetic field from the coupled atom-strong pump system are consistent with Rayleigh-Schr\"odinger perturbation theory in the quantum dressed basis. In addition, the spontaneously emitted photons become entangled with the probe field, correlating the emission spectrum with specific scattering channels.
We propose a new four-level atomic model for achieving light amplification at a short wavelength,where direct incoherent pumping into the top level is avoided by the advantage of coherent pumping.In this model,the lower level of the probe transition is an excited state but not the usual ground state.By analytical as well as numerical calculations,we find that the probe gain,either with or without population inversion,which depends on the relation between spontaneous decay rates γ42 and γ21,can be achieved with proper parameters.we note that the Raman Scattering gain always plays an important role in achieving the rpobe amplification.
We propose a new scheme for achieving inversionless gain that depends on both an internal interference effect and external coherent fields. We have found that, owing to the quantum interference effect that originates from spontaneous emissions from two closely lying levels, large inversionless gains can be achieved under appropriate conditions. In particular, in addition to the amplitudes, the phases of the applied fields also affect inversionless gain remarkably. That is to say, we can use the relative phase between two intense fields to control probe gain without inversion.