By Sheng-Hsien Lin, Albert A Villaeys, Yuichi Fujimura

This quantity offers the hot development and viewpoint in multi-photon tactics and spectroscopy of atoms, ions, molecules and solids. the topics within the sequence hide the experimental and theoretical investigations within the interdisciplinary examine fields of typical technological know-how together with chemistry, physics, bioscience and fabric technology. This sequence is a pioneer within the evaluate of nonlinear interactions of photon and topic, and has made a necessary contribution to improvement and promoting of the comparable learn fields. In view of the swift development in multi-photon procedures and multi-photon spectroscopy, care has been taken to make sure that the evaluate articles inside the sequence are readable not just through lively researchers but additionally people who find themselves now not but specialists yet intend to go into the sector.

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Extra resources for Advances in Multi-Photon Processes and Spectroscopy (Volume 22)

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U. 99720. Reprinted from Ref. 60. For figure in full color, refer to Appendix (Page 224). September 4, 2014 8:18 Advances in Multi-Photon Processes and Spectroscopy 9in x 6in Theoretical Foundations for Exploring Quantum Optimal Control of Molecules b1825-ch01 page 49 49 perfect control at the end of the optimal laser pulse. Finally, the resultant optimal control, Fig. u. 4 × 1015 W/cm2 ). 11. Summary We have presented theoretical foundations for exploring quantum optimal control of non-adiabatic dynamics of molecules.

20) The non-adiabatic coupling γα(1)k (R) ∀ = k can be written as γα(1)k (R, (t)) = − =− φ (R, (t))|{∇α Hˆ el (R, (t))}|φk (R, (t)) E (R, (t)) − E k (R, (t)) φ ∗ (r; R, (t))[∇α Hˆ el (r, R, (t))]φk (r; R, (t))dr . 21) (3) The field-induced polarization non-adiabatic coupling τ k (R, (t)), ∀ k = , after taking the gradient ∇ of Eq. 23) i is the electronic transition dipole moment between the th and the kth adiabatic electronic dressed states. Here τ (1) (R, (t)) = τ (3) (R, (t)) = 0 when the electric-field polarized adiabatic electronic eigenfunction φ (r; R, (t)) is made a real function.

3) are satisfied. For the state-to-state transition probability optimal control problem based on the expansion Eq. 6) k at the control field terminal time T . By invoking Eqs. 5), the corresponding TBQCP performance index, Eq. 8) k and 2 (0) Pi f (T ) (0) ∗ (R)ψ f k (R, 0)dR ψik = Pi f (0) = . 9) k Similarly, Eq. -S. Ho, H. -I. 11) α which couples the th and kth field-free adiabatic electronic states due to the presence of the control field. The equations of motion for the nuclear wave functions ψk (R, t)’s can be derived by substituting the expansion in Eq.

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