Page 154 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN003H-565 June 13, 2001 20:37

216 Coherent Control of Chemical Reactions

wave packet in a two-electronic state model. In this di-
agram, X g0 represents the lowest vibrational state of the
(1)
ground electronic state, X (0) is the excited-state wave
e
(1)
packet created from X g0 by an optical excitation, X (τ)
e
(2)
is the wave packet at time τ, and X (τ) represents the
g
ground-state wave packet created by stimulated emission
from X (1) (τ). Superscripts of X denote the order of the
e
photon-molecule interactions that are used in calculating
these wave packets.
ThetotalHamiltonian H(t)isgivenwithinthesemiclas-
sical treatment of the molecule-laser field interaction as
H(t) = H 0 − µ · ε(t). (23)
Here H 0 is the molecular Hamiltonian, and µ · ε(t)is
the interaction between the molecule and the laser field
in the dipole approximation, where µ is the transition
dipole moment of the molecule. Time evolution of the
system is determined by the time-dependent Schr¨odinger
equation,
∂
ih | (t) = H(t)| (t) . (24)
∂t

FIGURE 9 Potential energy curves of HI. The insert shows the
3
rotational structure of the b 1 Rydberg state, which is predis-
1
sociated by the A valence state. [Reproduced with permission
from Fiss, J. A., Khachatrian, A., Truhins, K., Zhu, L., Gordon, R.
J., and Seideman, T. (2000). Phys. Rev. Lett. 85, 2096.]

caused by inelastic coupling to a continuum, have also
been observed.

IV. WAVE PACKET CONTROL

A. Introduction
Recent progress in laser technology has led to the
widespreaduse ofultrafast lasers with pulse widths shorter
than the vibrational periods of most chemical bonds. A
localized state, called a nuclear wave packet, is created
on a potential surface by exciting a molecule with ul-
trashort pulses of radiation. The time-evolution of such
wave packets can be directly utilized to observe the tran-
sition states of chemical reactions. This development FIGURE 10 The effect of an intermediate resonance on the
is one of the major accomplishments of femtosecond phase lag for the photoionization of HI. Shown are (a) the
+
chemistry. phase lag of HI + relative to H 2 S , (b) the three-photon ioniza-
tion spectrum of HI, and the one-photon ionization spectra of
To understand how wave packets are created by ultra-
(c) HI and (d) H 2 S. [Reproduced with permission from Fiss, J.
short pulses, consider a molecule interacting with a pulsed A., Khachatrian, A., Truhins, K., Zhu, L., Gordon, R. J., and Sei-
laser field ε(t). Figure 12 shows the time evolution of a deman, T. (2000). Phys. Rev. Lett. 85, 2096.]