Pump-Dump Control Few-Level Excitation

Consider then a system irradiated by two pulses, termed the pump-and-dump pulse. These pulses are assumed to be temporally separated by a time delay Ad. The analysis below shows that under these circumstances control over the photodissocia-tion yields is obtained by vaiying the central frequency of the pump pulse and the tune delay between the two pulses. 

Consider a molecule, initially (t = 0) hi an eigenstate i i) of the molecular Hamiltonian HM that is subjected to two transform-limited light pulses. The electric.  

For convenience we use Gaussian pulses that peak at t = tx and td, respectively. In particular, the excitation pulse is of the form 

4 The analogous quantities for the dissociation laser, Ed(z), ed(o ), and ed(a ) are defined similarly, with the parameters td and cod replacing tx and mx, and so forth. %The pump pulse Ex(t) induces a transition to a linear combination of the eigenstates p of the excited electronic state. The pump pulse may be chosen to encompass any. timber of states. Here we choose the pump pulse sufficiently narrow in frequency to incite only two of these states, E2) and IE3). The dump pulse Erf(r) dissociates the Sfjnolecuie by further exciting it to the continuous part of the spectrum. Both fields are chosen sufficiently weak for perturbation theory to be valid. 

After the action and subsequent decay of the Ef/(x) pulse, the system wave function is  

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