  A STIRAP-based unitary decelerating (accelerating) process consists of a
train of the standard three-state STIRAP pulse sequences which may act as the
basic unitary decelerating (accelerating) sequences. The present work is
focused on investigating analytically and quantitatively how the momentum
distribution of a momentum superposition state such as a momentum Gaussian
wave-packet state of a single freely moving atom affects the STIRAP state
transfer in these decelerating and accelerating processes. The complete STIRAP
state transfer and the unitarity of these processes are stressed highly in the
investigation. It has been shown that the momentum distribution has an
important influence upon the STIRAP state-transfer efficiency. In the ideal
adiabatic condition these unitary decelerating and accelerating processes for a
freely moving atom are studied in detail, and it is shown that they can be used
to manipulate and control in time and space the center-of-mass position and
momentum of a Gaussian wave-packet motional state of a free atom. Two general
(strict and accurate) adiabatic conditions for the basic STIRAP decelerating
and accelerating processes are derived analytically. With the help of the
STIRAP theory and the unitary quantum dynamics it confirms theoretically that
the time- and space-compressing processes of the quantum control process
(quant-ph/0607144) can be realized almost perfectly by the STIRAP-based unitary
decelerating and accelerating processes in the ideal or nearly ideal adiabatic
condition.
