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Physical Review A

Absorption spectra of a system of atoms under cooperative conditions

Akundi Suguna, G. S. Agarwal

Published Nov 1, 1979• 10 citations
Publisher

Abstract

The problem of the energy absorption from a weak probe field by a system of atoms driven by a coherent laser field is considered with special reference to the collective behavior of the atomic system. The changes in the nature of the absorption spectra as the intensity of the coherent laser field is changed are examined explicitly for a system of two atoms. Cooperative effects are shown to be important for weak laser fields. For strong fields, it is shown that the absorption spectra under cooperative conditions differ from those without cooperative conditions only by a scale factor.

DOI
10.1103/physreva.20.2022

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The problem of the energy absorption from a weak probe field by a system of atoms driven by a coherent laser field is considered with special reference to the collective behavior of the atomic system. The changes in the nature of the absorption spectra as the intensity of the coherent laser field is changed are examined explicitly for a system of two atoms. Cooperative effects are shown to be important for weak laser fields. For strong fields, it is shown that the absorption spectra under cooperative conditions differ from those without cooperative conditions only by a scale factor.
We examine the absorption of a weak probe beam by a laser driven V-type atom with a pair of closely lying excited levels, where both the driving and probe lasers interact simultaneously with the two transitions. The effects of quantum interference among decay channels on the absorption spectra are also investigated. We introduce dipole moments in the dressed-state representation and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. In the degenerate case, features similar to that of a driven two-level atomic system are found due to some dark transitions in the spontaneous emission and the fact that the probe beam only detects certain transitions. In the nondegenerate case, the absorption spectrum is strongly influenced by the degree of quantum interference, resulting in different line shapes for emission peaks, absorption peaks, and dispersionlike profiles. The effect of probe polarization on the absorption spectrum is also investigated.
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 .
The absorption spectrum of a weak probe radiation by a two-level atom strongly driven by an intense radiation field is examined. Using a Green's function method developed for calculations of general multiphoton processes, the author obtains some earlier results in which the spectrum has regions (in the probe frequency domain) of amplification and regions of attenuation. Such a spectrum is shown explicitly to be due to a coherent interference effect arising from the interaction of the atom with the vacuum field. Furthermore, an equation that relates the area under the amplification part of the spectrum to that under the attenuation part is obtained. This indicates that amplification cannot occur if a very-wide-band probe beam is used instead of a narrow-band one. At high driving intensities the absorption spectrum is shown explicitly to be inversely proportional to the Rabi frequency and has a dispersion-like behaviour near the Rabi sidebands at driving resonance.
The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.
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.