By Vladimir M. Akulin
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Additional resources for Coherent Dynamics of Complex Quantum Systems
In some cases more than two electronic terms may get involved in the dynamical process at moderate laser intensities. 16) where I denotes the number of absorbed quanta, and m enumerates the vibrational eigenstates in each of the electronic terms involved. Accommodation of the energy of an absorbed optical quantum by molecular vibrations is also an example of processes in multilevel systems. Consider a molecule initially in the ground vibrational state of the lowest electronic term which absorbs a quantum of radiation and makes a transition to an excited vibrational state of the higher electronic term.
Term. The photon, in its turn, creates another electron–hole pair by transporting an electron from another occupied one-electron level to a diﬀerent empty state. Therefore all excited states |S = |ne , le , me , nh , lh , mh interact among themselves via the ground electronic term and diﬀerent states of the electromagnetic ﬁeld. It yields a speciﬁc (factorized) structure of the inter(1) action Hamiltonian: each matrix element VS,S = TS × TS is a product of a quantity related to the starting state |S and the same quantity related to the ﬁnal state |S .
The simplest model of this ﬁeld is just a rectangular potential well shown in Fig. 15. For spherically symmetric clusters the angular momentum l of each of the electrons is conserved, and their angular motion can be taken into account by introducing the centrifugal force potential U (r) = (l)2 /2me r2 , acting on the motion in the radial direction r. 8 r/Rcl y(r) Fig. 15. Spherically symmetric potential of cluster electrons. (a) Rectangular well model of the work function and self-consistent local density potential.
Coherent Dynamics of Complex Quantum Systems by Vladimir M. Akulin