Pulsed Incoherent Interference Control

Assuming that a(/) is available, either via the adiabatic approximation or via an exact numerical computation, the probabilities to observe [ ,) and E2) as a function of time are given by 

Ktatement of the adiabatic condition [Eq. (9.40)] shows that the breakdown of the diabatic approximation is due to the near divergence of the complex mixing angle a pc Eq. (11.12) at small Ai, the complex nature of which is a result of the presence of final continuum. 

Note that the approach introduced below relies exclusively on the computatir nbfi material matrix elements, as in the wealc-field domain. As a result, one need Ms compute these matrix elements once in order to obtain dissociation rates anu ifohj abilities for a variety of pulse configurations and field strengths. i I %  

Here n = m, q where q = 1,2... denotes the product arrangement channel a denotes the remaining quantum numbers other than the energy. 

Substituting Eq. (11.23) into the time-dependent Schrodinger equation and the orthogonality of the basis functions results in a set of first-order diffei 

---

Having suggested that the STIRAP process can be thought of as a special case of an assisted adiabatic process, we now examine another special case of an assisted adiabatic process, namely the composite STIRAP protocol proposed by Torosov and Vitanov [77]. This protocol uses a sequence of an odd number of pairs of delayed pulses (Figure 3.24) with carefully selected phases (listed in Table 3.4) to cancel by destructive interference the nonadiabatic transitions that reduce the efficiency of STIRAP-generated population transfer. We note that this protocol resembles the pulsed incoherent interference control protocol proposed by Shapiro et al. [78]. Torosov and Vitanov show that, for the triad of states illustrated in Figure 3.24, the efficiency of population transfer can be driven arbitrarily close to unity, for example, a deviation from unity of order 10 for the case of resonant excitation with three pairs of pulses. 

M. Shapiro, Z. Chen, and P. Brumer. Simultaneous control of selectivity and yield of molecular dissociation pulsed incoherent interference control. Chem. Phys., 217(2) 325—340(1997). 

Control over the product branching ratio in the photodissociation of Na2 into Na(3s) + Na(3p), and Na(3s) + Na(3d) is demonstrated using a two-photon incoherent interference control scenario. Ordinary pulsed nanosecond lasers are used and the Na2 is at thermal equilibrium in a heat pipe. Results show a depletion in the Na(3d) product of at least 25% and a concomitant increase in the Na(3p) yield as the relative frequency of the two lasers is scanned. 

Equation (7.75) defines what is meant by a so-called coherent sum of quantum states. The diagonal terms resemble the incoherent sum in Eq. (7.74) the values of the populations cn 2 are, however, determined by the laser pulse. The off-diagonal terms are called interference terms these terms are the key to quantum control. They are time dependent and we use the term coherent dynamics for the motion associated with the coherent excitation of quantum states. A particular simple form of Eq. (7.75) is obtained in the special case of two states. Then... 

---