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Journal of the Optical Society of America B

Multiphoton-process-induced coherence effects in a dissipative quantum system

Indranil Bayal, Bibhas Kumar Dutta, Pradipta Panchadhyayee, P.K. Mahapatra

Published Sep 23, 2015• 4 citations
Publisher

Abstract

The work is aimed at modeling coherence effects in a dissipative quantum system under the semi-classical density matrix formalism. A number of multiphoton coherence effects have been shown to be feasible by controlling the incoherent pumping mechanism in a generic four-level model. The specialty of the model is in finding inversionless gain without any restrictions being imposed on the decay rates of the driven transitions. Many of the coherence effects, such as absorption cancellation, inversionless gain at the line center, and sidebands of an absorptive line shape accompanied by dispersive switching, are explained using the same model under different parametric conditions. Further, it is shown that modulation in the coherence effects can effectively be controlled by the two- and three-photon excitation mechanisms with the proper choice of the rates of incoherent pumping under a stimulated Raman process. Different conditions of population inversion are found for both coherent and incoherent control of stimulated Raman resonance. In addition to Raman gain, gain without inversion in any standard state basis is found to be achieved in our present model. The proposed scheme can have potential application in controlling the properties of an optical field on propagation through rare earth ion-doped fiber material or other solid-state, as well as atomic, media.

DOI
10.1364/josab.32.002178

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The work is aimed at modeling coherence effects in a dissipative quantum system under the semi-classical density matrix formalism. A number of multiphoton coherence effects have been shown to be feasible by controlling the incoherent pumping mechanism in a generic four-level model. The specialty of the model is in finding inversionless gain without any restrictions being imposed on the decay rates of the driven transitions. Many of the coherence effects, such as absorption cancellation, inversionless gain at the line center, and sidebands of an absorptive line shape accompanied by dispersive switching, are explained using the same model under different parametric conditions. Further, it is shown that modulation in the coherence effects can effectively be controlled by the two- and three-photon excitation mechanisms with the proper choice of the rates of incoherent pumping under a stimulated Raman process. Different conditions of population inversion are found for both coherent and incoherent control of stimulated Raman resonance. In addition to Raman gain, gain without inversion in any standard state basis is found to be achieved in our present model. The proposed scheme can have potential application in controlling the properties of an optical field on propagation through rare earth ion-doped fiber material or other solid-state, as well as atomic, media.
The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.
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 consider a four-level atomic system with a degenerate or quasidegenerate ground-state doublet and two excited states. One of the upper levels is coupled to the ground doublet by a coherent field of variable strength, which we refer to as the Raman field, whose role is to create atomic coherence between the driven atomic states. The other higher lying state is coupled to the ground states when laser action develops. This model includes an incoherent pump mechanism to create some population in the top lasing state. In appropriate conditions, for the incoherent pump rate and the Raman field strength, the absorption profile of the laser transition develops gain features. We discuss the physical origin of this gain which we find to be the consequence of a population inversion between dressed atomic states. It is interesting to compare the results of this analysis with a similar study of a three-level lambda system which was previously recognized to yield lasing without inversion.1 In this case the appearance of gain can be attributed to the induced atomic coherence.
We analyze the physical origin of the inversionless amplification in four-level atoms driven by a Raman field and identify the existence of two different mechanisms for the predicted gain. The first mechanism is connected with the appearance of a population inversion between the atomic states dressed by the coherent pump, while the second is linked to the buildup of coherence among these states. Proper selection of the relaxation parameters can make either the first or the second mechanism dominant over the other although usually both coexist.
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.
The resonant absorption, emission, and scattering of light are the fundamental optical processes that have been used both to probe matter and to manipulate light itself. In the last decade there has been essential progress in coherent control of both linear and nonlinear optical responses based on resonant excitation of atomic coherence in multilevel quantum systems. Some interesting and useful phenomena, resulting from coherent control of absorption and the group index, such as electromagnetically induced transparency, lasing without inversion, and ultra-slow group velocity of light have been widely studied. This work is focused on coherent control of refractive index and resonant fluorescence in multilevel medium. \n \nWe suggest two promising schemes for resonant enhancement of the refractive index with eliminated absorption and propose their implementation in transition element doped crystals with excited state absorption and in a cell of Rb atoms at natural abundance. We show how to use one of these schemes for spatial variation of the refractive index via its periodic resonant increase/decrease, remarkably keeping at the same time zero absorption/gain. It opens the way to production of transparent photonic structures (such as distributed Bragg reflectors, holey fibers, or photonic crystals) in a homogeneous resonant atomic media such as dielectrics with homogeneously distributed impurities, atomic, or molecular gases. These optically produced photonic structures could easily be controlled (including switching on/off, changing amplitude and period of modulation) and would be highly selective in frequency, naturally limited by the width of the optical resonance. \n \nWe also derive the optical fluorescence spectra of a three-level medium driven by two coherent fields at the adjacent transitions in a general case when all three transitions are allowed. We show that coherent driving can efficiently control the distribution of intensities between the fluorescent channels. In particular, the total intensity of fluorescence at the transition which is not driven by the optical fields may essentially exceed the fluorescence intensity at the driven transitions under the condition of two-photon resonance. This counter-intuitive effect is due to depletion of the intermediate state via atomic interference.