Tn this paper, the optical Bloeh equation with relaxation terms in saturated spe-ctroseopy is solved directly by using the perturbation theory. The reenrren formulas are given, approximate results of any order can be obtained from them. The first and second order solutions are derived and explained.
A solution is presented for the damped optical Bloch equations under the excitation of a smooth pulse by first deriving three independent third-order equations of the Bloch vector components. Each equation is reduced to quadratures by assuming that the logarithmic time derivative of the field amplitude is small compared to the Rabi frequency. This results in an approximate summation of the infinite-order time-dependent perturbation in the field amplitude. The relaxation-dependent induced damping of the population inversion is calculated. Also calculated are additional relaxation-dependent contributions to the intensity-dependent refractive index. The time-integrated intensity contribution tends to cause line asymmetry, which becomes, at later times, linear in ${\ensuremath{\gamma}}_{2}$ when ${\ensuremath{\gamma}}_{2}\ensuremath{\gg}{\ensuremath{\gamma}}_{1}$ and zero when $2{\ensuremath{\gamma}}_{2}={\ensuremath{\gamma}}_{1}$, where ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are the atomic energy and phase-changing relaxations, respectively. The dependence of the spectral broadening on pulse length, pressure, and length of the sample is discussed.
In this paper, the general optical Bloch equation describing interaction between intensive fields and two level system is obtained without using rotating wave approximation. The first-order solution of this equation is obtained by iterative method and analytic formulas of transition probability as a function of time, perturbation frequency and strength are presented. These results are in agreement with those obtained by an iterative step-wise power series and numerical integration solution for the time dependent Schr(?)dinger equation. And these simplified and clear mathmatical formulas facilitate the application of physics.
In a recent experiment [ DevoeR. G.BrewerR. G., Phys. Rev. Lett.50, 1269 ( 1983)], it was found that the optical Bloch equations could not satisfactorily explain the signal that was observed for free-induction decay in the impurity ion cyrstal Pr3+:LaF3. Several theories have been proposed to explain this failure of the Bloch equations. In this paper, the general validity conditions for the optical Bloch equations are examined within the limits of a Markovian relaxation model. The specific problem to be considered is the interaction of an optical field with two-level atoms. The atoms undergo relaxation as a result of coupling to a perturber bath that, itself, is negligibly affected by the relaxation process. First, a simple decay-parameter model is assumed for the relaxation of atomic density-matrix elements. Such a model is found to lead to a set of generalized Bloch equations of which the conventional Bloch equations form a subset. Subsequently, more-realistic models for relaxation in both vapors and solids are considered within the limits of the impact approximation (i.e., the duration of a fluctuation can be viewed as instantaneous with respect to all relevant time scales in the problem). It is found that, even in the impact (Markovian) approximation, the generalized Bloch equations cannot be expected to provide an adequate description of relaxation, owing to effects in which a fluctuation-induced change in the atomic transition frequency persists between fluctuations. In vapors this frequency shift is produced by velocity-changing collisions that change the atomic resonance frequency (as seen in the laboratory frame), whereas in solids it is produced by local-field fluctuations. The limiting conditions under which one can expect both the generalized and the conventional Bloch equations to retain their validity are explored.
The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.