Bloch equations, optical

Equation (A1.6.64) describes the relaxation to equilibrium of a two-level system in tenns of a vector equation. It is the analogue of tire Bloch equation, originally developed for magnetic resonance, in the optical regime and hence is called the optical Bloch equation. 

Theoretical level populations. Sinee there are population variations on time seale shorter than some level lifetimes, a complete description of the excitation has been modeled solving optical Bloch equations Beacon model, Bellenger, 2002) at CEA. The model has been compared with a laboratory experiment set up at CEA/Saclay (Eig. 21). The reasonable discrepancy when both beams at 589 and 569 nm are phase modulated is very likely to spectral jitter, which is not modeled velocity classes of Na atoms excited at the intermediate level cannot be excited to the uppermost level because the spectral profile of the 569 nm beam does not match the peaks of that of the 589 nm beam. 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

The observations of vibrational coherence in optically initiated reactions described above clearly show that the standard assumption of condensed-phase rate theories—that there is a clear time scale separation between vibrational dephasing and the nonadiabatic transition—is clearly violated in these cases. The observation of vibrational beats has generally been taken to imply that vibrational energy relaxation is slow. This viewpoint is based on the optical Bloch equations applied to two-level systems. In this model, the total dephasing rate is given by... 

If the system is in the presence of a radiation field, then Hs in Eq. (5.12) is augmented by the dipole-electric field interaction HUR [Eq. (2.10)]. The result is the so-called optical Bloch equations. Note that this approach focuses explicitly on decoherence in the energy representation. 

The simplest optical Bloch equations result from a system comprised of two eigenstates j), E2) of the molecule Hamiltonian HM that experience the electric field-dipole interaction... 

In recent studies [82, 83] it has been demonstrated that the deterministic two-level optical Bloch equation approach captures the essential features of SMS in condensed phases, which further justifies our assumptions. 

The physical interpretation of the optical Bloch equation in the absence of time-dependent fluctuations is well known [62, 73]. Now that the stochastic fluctuations are included in our theory we briefly discuss the additional assumptions needed for standard interpretation to hold. The time-dependent power absorbed by the SM due to work of the driving field is. 

At this point we have arrived at the connection between the correlation function and the density matrix elements described in Section 1.2.2.3, because the conditional probability is just proportional to the matrix element (J22 x) corresponding to the transient solution of the optical Bloch equations for our model three-level system in Fig. 6. Then it follows,... 

Indeed, it can be shown that the "two sites" vibrational optical Bloch equations lead to an expression of l(tjo) analogous to the above one (formula 17). The validity and limitations of those equations have been recently... 

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