State Preparation During the Pulse

To explore the behavior of the system while the pulse is on, we express the integrals over f, in Eq. (2.7), as follows  

Positive oo gives the so-called rotating-wave (rw) contribution whereas negative co gives the counterrotating wave (crw) contribution. 

We can show, using contour integration, that when we insert Eq. (2.13) in Eq. 

To show this, write co — com, = Re fl hence, = eiRTcosB RTsm0. Since  

The first term in Eq. (2.13) does contribute to bm(t) since exp[i(co,B j — cu)t) is ci nonzero on the large semicircle in the upper plane. Substituting the first term of Eq, ) 

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