Adiabatic population probability, nonadiabatic

Figure 3. Time-dependent simulations of the nonadiabatic photoisomerization dynamics exhibited by Model III, comparing results of the mean-field-trajectory method (dashed lines), the surface-hopping approach (thin lines), and exact quanmm calculations (full lines). Shown are the population probabilities of the initially prepared (a) adiabatic and (b) diabatic electronic state, respectively, as well as (c) the probability Pdsit) that the sytem remains in the initially prepared cis conformation.

Let us first consider the population probability of the initially excited adiabatic state of Model 1 depicted in Fig. 17. Within the first 20 fs, the quantum-mechanical result is seen to decay almost completely to zero. The result of the QCL calculation matches the quantum data only for about 10 fs and is then found to oscillate around the quantum result. A closer analysis of the calculation shows that this flaw of the QCL method is mainly caused by large momentum shifts associated with the divergence of the nonadiabatic couplings F = We therefore chose to resort to a simpler approximation... 

The population probabilities Pn t) defined in Eqs. (8)-(13) should not be confused with the population probabilities which have been considered in the extensive earlier literature on radiationless transitions in polyatomic molecules, see Refs. 28 and 29 for reviews. There the population of a single bright (i.e. optically accessible from the electronic ground state) zero-order Born-Oppenheimer (BO) level is considered. Here, in contrast, we define the electronic population as the sum of all vibrational level populations within a given (diabatic or adiabatic) electronic state. These different definitions are adapted to different regimes of time scales of the system dynamics. If nonadiabatic interactions are relatively weak, and radiationless transitions relatively slow, the concept of zero-order BO levels is useful the populations of these levels can be prepared and probed using suitable laser pulses (typically of nanosecond duration). If the nonadiabatic transitions occur on femtosecond time scales, the preparation of individual zero-order BO levels is no longer possible. The total population of an electronic state then becomes the appropriate concept for the interpretation of time-resolved experiments. ° ... 

Let us briefly discuss the characteristics of the nonadiabatic dynamics exhibited by this model. Assuming an initial preparation of the S2 state by an ideally short laser pulse. Fig. 1 displays in thick lines the first 500 fs of the quantum-mechanical time evolution of the system. The population probability of the diabatic state shown in panel (b) exhibits an initial decay on a timescale of w 20 fs, followed by quasi-periodic recurrences of the population, which are damped on a timescale of a few hundred femtoseconds. Beyond 500 fs (not shown) the S2 population probability becomes quasi-stationary, fluctuating statistically around its asymptotic value of 0.3. The time-dependent population of the adiabatic S2 state, displayed in panel (a), is seen to decay even faster than the diabatic population — essentially within a single vibrational period — and to attain an asymptotic value of 0.05. The finite asymptotic value of is a consequence of the restricted phase space of the three-mode model. The population Pf is expected to decay to zero for systems with many degrees of freedom. 

A magnetic field ramp over the avoided crossing can be used for state transfer. When the magnetic field is ramped slowly, the population follows the adiabatic states. This is called an adiabatic ramp. If the change in magnetic field is very fast, the molecules do not experience the coupling between the diabatic states, and therefore remain in their initial state. This is a nonadiabatic ramp. The well-known Landau-Zener model describes the final population in both molecular states after the ramp. The probability of adiabatic transfer is given by... 

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