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Physical Review A

Enhanced index and negative dispersion without absorption in driven cascade media

Xiangming Hu, Jun Xu

Published Apr 15, 2004• 14 citations
Publisher

Abstract

In this paper we investigate the dispersive and absorptive properties of a system of three-level cascade atoms driven by a strong coherent field. Three characteristic features are found. First, for the same set of atom-light interaction parameters, the indices of refraction are large at three different frequencies where the absorption vanishes. These three frequencies are determined by the resonance transition frequencies between dressed states produced by the strong driving field. Second, negative dispersion without absorption, which leads to superluminal light propagation, is achievable in the central resonance structure of the dispersion spectrum. Third, the whole absorption spectrum displays, in general, three pairs of absorption peaks and three pairs of gain (negative absorption) peaks. The minimal spacing between dressed states determines whether the outer adjacent gain peaks are separated from each other.

DOI
10.1103/physreva.69.043812

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•Dec 1, 2011•0 citations
In this paper we investigate the dispersive and absorptive properties of a system of three-level cascade atoms driven by a strong coherent field. Three characteristic features are found. First, for the same set of atom-light interaction parameters, the indices of refraction are large at three different frequencies where the absorption vanishes. These three frequencies are determined by the resonance transition frequencies between dressed states produced by the strong driving field. Second, negative dispersion without absorption, which leads to superluminal light propagation, is achievable in the central resonance structure of the dispersion spectrum. Third, the whole absorption spectrum displays, in general, three pairs of absorption peaks and three pairs of gain (negative absorption) peaks. The minimal spacing between dressed states determines whether the outer adjacent gain peaks are separated from each other.
We study the absorption and dispersion in the near-degenerate closed three-level V system, in which a single coherent driving field is tuned resonant with the average frequency of two dipole-allowed transitions. Firstly, the switching from positive to negative dispersion can be achieved simply by increasing the driving field intensity. This is the same as in the driven Λ system. Secondly, the common feature originates from the fact that both V and Λ systems have the same transitions in terms of atomic dressed states under given conditions. These dressed transitions interfere destructively in the central spectrum while the sideband resonance transitions determine the possible appearance of two pairs of absorption doublet lines and two pairs of gain doublet lines in the sideband spectrum. Thirdly, there are two minor differences between these two systems. For large driving field intensity, a narrow steep structure is always present in the central negative dispersion spectrum in the V system but it disappears in the Λ system. The driving field intensity for the appearance of the outer sideband absorption or gain peaks is larger in the V system than in the Λ system.
In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.
The possibility of obtaining strong negative dispersion without absorption in the central resonance structure of the spectrum of a bichromatically driven two-level system is investigated. A nonlinear analysis is performed using the technique of continued fractions with respect to the dressedstate basis of a strong pumping laser. We discuss the transition between the two regimes of the monochromatic driving case with a weak probing laser and of nearly equally strong lasers in terms of the contributions from coherences and populations of these dressed states. In contrast with the strong dependence of the Rabi side bands on probe field intensity, we find a remarkable stability of the negative dispersion in the central resonance structure.
The absorption spectra of a pair of two-level atoms driven on resonance by a coherent laser field are considered analytically including the dipole-dipole interaction between the atoms. Analytical formulae for the absorption spectra are derived for four regions of the dipole-dipole interaction Omega 12 : Omega >> gamma >> mod Omega 12 mod , Omega >> mod Omega 12 mod >> gamma Omega approximately= mod Omega 12 mod >> gamma , mod Omega 12 mod >> gamma >> Omega (2 gamma being Einstein's coefficient A, and Omega the Rabi frequency). The formulae, containing both absorption-like and dispersion-like terms, reveal explicitly the resonant structure of the absorption spectra. At great intensities of the driving field the absorption is negative in a certain range of frequencies. The dipole-dipole interaction between the atoms is shown to modify considerably the form of this absorption spectrum. For sufficiently strong dipole-dipole interaction it exhibits dispersion-like behaviour in the vicinity of 2 Omega with a new region of negative absorption. The spectrum is asymmetric, albeit slightly. For strong dipole-dipole interaction and a weak driving field the spectrum consists of one absorption-like peak, located at omega - omega 0 = Omega 12 .
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.
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.