Optimal Control in Perturbative Domain

In general, when perturbation theory applies, one can devise an elegant method] obtaining the optimal solution to problems such as those in photodissociation, f optimal fields derived in the perturbative domain [92, 126, 129-131] do noth by much from the fields derived via the more general brute-force opti methods. 

To examine a particular case, consider the pump—dump control discussed in Section 3.5 and Chapter 4. Here a sequence of two pulses first excite a molecule to a set of intermediate bound states with wave func and energy and then to dissociate these states. We denote the two (k = 1,2) by 

After the second pulse the probability Pq(E) of observing a given product channel q at energy E is given by 

Here the c,-, coefficients are the eigenstate coefficients resulting ifom excitation with the first pulse, defined in Eq. (2.15), and the 

The probability of observing a given q product channel irrespective of the energy is then 

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