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 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 influence of relaxation parameters, as well as temporal fluctuations in the laser field on the modulation rate and phaseshift of the fluorescence from a two-level atom excited by a weakly modulated source is studied in detail. It is shown that, for intense resonant laser fields, the resonance in the modulation rate occurs at the modulation frequency Omega =2 due to the dynamical Stark splitting and has a width equal to 1 / 2 (T 1 -1 +T 2 -1 ). When temporal fluctuations of the exciting laser field are taken into account, the phaseshift of the scattered light is found to be strongly dependent on the bandwidth of the exciting source, as well as the frequency of modulation; hence experimental results on the determination of the lifetime by the phaseshift method have to be interpreted carefully. Numerical results for the modulation rates and phaseshift at different field strengths and various values of T 1 -1 , T 2 -1 , Delta laser bandwidth and Doppler broadening are presented.
Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.
It is shown that, in general, the interaction between relaxing quantum systems and radiation is described by non-Markov transport equations for the density matrix ρ p and the relaxation matrix depends on the properties of the radiation. The usual Markov-type equations for ρ p are obtained from these equations if γτ c ≪1 and (∊ 2 +4 V 2 ) 1/2 τ c ≪1 (γ is the width of the investigated transition in a quantum system, rc is the correlation time of the perturbations causing relaxation, e is the frequency detuning, and V is the energy of the interaction between the system and the radiation field). When the second inequality is disobeyed, the relaxation process deviates strongly from the Markov type. In the case of small values of V , this results in a non-Lorentzian profile of the absorption lines characterized by a steep descent in the wings. In the range of high values of V , when 2 V τ c 1, the whole relaxation process becomes greatly modified: the dependence of the relaxation coefficients on V becomes strong and a coupling appears between the relaxations of the diagonal and the nondiagonal elements of the density matrix. This is manifested, in particular, in the saturation effect: the term describing saturation in the expression for the polarizability changes considerably and the expression for the line width loses the component due to the adiabatic (elastic) perturbation.
We have numerically calculated the excitation spectra arising from the 3rd order mixing of the frequencies ωa and ωb of two laser fields interacting with a three-level atom, where each laser field resonantly couples the ground state with each excited state of the atom, respectively. In the limit of high photon densities, the excitation spectra near the reduced frequency X = (ω−ωa + 2ωb)/γ0 ≈ 0 are considered as a function of the reduced Rabi frequencies ηa and ηb of the two laser fields, respectively and γ0 is the spontaneous emission probability. For ηa < ηb the spectra consist of a doublet peaked at [Formula: see text] and its intensity is constant. When ηa = ηb, the spectra are composed of five pairs of bands peaked at [Formula: see text], and [Formula: see text]. When ηa < ηb the computed spectra consist of five pairs of bands, where the intensities of the peaks at [Formula: see text] and [Formula: see text] are positive indicating absorption, those at [Formula: see text] are negative implying amplification, and the two pairs of peaks at [Formula: see text] have positive and negative components describing the mixed process of absorption–amplification. The intensities of these bands are found to vary as (ηa/ηb)2 for (ηa/ηb) > 1 and, therefore, the intensities of the bands are immensely enhanced as the value of the ratio (ηa/ηb) increases. The computed spectra for a wide selection of Rabi frequencies are graphically presented and compared with those derived by analytical methods.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x (3x2), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.