The modification of the relaxation dynamics of a quantum system interacting with a strong laser field are investigated by modelling the frequency modulation by a dichotomic Markov process. For this model various physical quantities such as mean polarization, inversion, the spectrum of spontaneous emission and absorption from a probe beam are calculated exactly for all values of the laser field strength and the correlation time of the modulation. Numerical results for the spectra for a wide range of parameters are given. The long correlation time of the modulation leads to considerable narrowing of the spectra, the width of which is governed by the correlation time itself, and also to the further splitting of the spectral peaks at moderate strengths.
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.
We have developed an effective mathematical model to calculate the coherent population trapping (CPT) resonance in periodically modulated light, when the modulation frequency
f varies near the fractional part of hyperfine splitting in the ground state
Δhfs/N (where
N=1,2,...). In such polychromatic field, only two frequency components that are most resonant with atomic optical transitions are taken into account accurately, while all other off-resonant components are taken into account using the second-order perturbation theory in the field. Within the presented concept, equation for atomic density matrix is obtained, in which the contribution of all off-resonant components is reduced to the appearance of two new operators (non-diagonal, in general case): the shift operator and relaxation operators. In the case of three-level
Λ-system, the adequacy of presented effective model was verified by numerical calculations of various dependencies, in which we did not find visual differences from the exact calculations. In addition to a significant mathematical simplification, our model provides a clear physical picture of various features of CPT spectroscopy in a periodically modulated laser field, including effects that have not been discussed in the scientific literature before. In particular, we show that the widespread viewpoint that the CPT resonance shift is determined by usual ac Stark shifts of the lower levels is, in general, fundamentally incorrect, since the contribution to the light shift due to beats at the frequency
Δhfs between different off-resonant frequency components can be comparable (or even dominate) with the standard ac Stark shift. Therefore, even if we have detailed information on the modulated field spectrum (e.g. using a spectrum analyzer), this is, in general, absolutely insufficient to determine the light shift of CPT resonance.
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 .
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.