First-order coherence, quantum interference

The first order term in A/p comes from the difference of the potential energy and the higher order terms should be included when AIP/UP is not small enough. The phases, which the freed electrons accumulate during their different quantum paths, are transferred to the harmonics through the coherent process of HHG and lead to the interferences (Fig. 4.1). 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

We observed the phase-dependent quantum interference in the double A system realized with cold Rb atoms coupled by four laser fields. The coherently coupled four-level double A-type system realized with the laser coupling scheme for the Rb Di transitions is shown in Fig. 8 and the simplified experimental set up is depicted in Fig. 4(b). An extended-cavity diode laser with a beam diameter 3 mm and output power 50 mW is used as the coupling laser. The driving electric current to the diode laser is modulated at 5=181 MHz with a modulation index -0.5, which produces two first-order frequency sidebands separated by 362 MHz. The two sidebands are tuned to the Rb Di F=3—>F =2 and F=3 F =3 transitions respectively and serve as the two coupling fields due to a tt phase difference between the two sidebands). Another... 

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