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 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.
An analytic expression of the polarization induced by a polychromatic weak probe field in a two-level medium, driven by a strong polychromatic pumping field, is obtained. This expression allows one to obtain both the absorption and dispersion spectra at any frequency of a probe field. The numerically calculated graphs of the central-component probe-field absorption and dispersion spectra, depending on the pumping-field amplitude in the cases of the one-, two- three-, four-, and five-component pumping field, are presented. It is shown that when the probe-field detuning is close to the strong-field Rabi frequency, the absorption spectrum changes to the dispersionlike form, while the dispersion spectrum changes to the absorptionlike one.
A numerical method is introduced that solves the optical Bloch equations describing a two-level atom interacting with a strong polychromatic pump field with an equidistant spectrum and an arbitrarily intense monochromatic probe field. The method involves a transformation of the optical Bloch equations into a system of equations with time-independent coefficients at steady state via double harmonic expansion of the density-matrix elements, which is then solved by the method of matrix inversion. The solutions so obtained lead immediately to the determination of the polarization of the atomic medium and of the absorption and dispersion spectra. The method is applied to the case when the pump field is bichromatic and trichromatic, and the physical interpretation of the numerically computed spectra is given.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
The analytic solutions of equations, which describe the time behavior of density-matrix elements of a two-level medium driven by weak-probe tunable and strong fields, namely, scrE(t)=E(t)cos[\ensuremath{\omega}t+\ensuremath{\varphi}(t)]+\ensuremath{\varepsilon} cos[(\ensuremath{\omega}+\ensuremath{\delta})t], the amplitude E(t) and phase \ensuremath{\varphi}(t) of which are any arbitrary functions of time, are obtained. We obtain explicit expressions of the medium polarizability in two cases of the strong-field parameters modulation: first, E(t)=
E0cos(\ensuremath{\xi} cos\ensuremath{\Omega}t), where
E0, \ensuremath{\Omega}, and \ensuremath{\xi} are constants, and \ensuremath{\varphi}=0; and second, both the amplitude E(t) and the phase \ensuremath{\varphi}(t) are periodic functions of time, and E(t)=C\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, where C is an arbitrary constant. These cases of modulation are generalizations of cases that were considered earlier. The first case of modulation causes a shift of the well-known Rabi resonances in the weak-probe absorption and dispersion spectra by the factor
J0(\ensuremath{\xi}) (
J0 is the zero-order Bessel function of the first kind) in comparison with a nonmodulated exciting field. In the second case of the modulation, the Rabi resonances are present but the effect of such a modulation results in an attenuation of the amplitude-modulation effect. The values of the parameters
E0, \ensuremath{\Omega}, C, and \ensuremath{\xi} and the frequency ranges in which the weak-probe gain, caused by resonant Rayleigh scattering and by three-photon scattering, takes place are determined for these two cases of the modulation.