  A near perfect, storage time-extended photon echo-based quantum memory
protocol has been analyzed by solving the Maxwell-Bloch equations for a
backward scheme in a three-level system. The backward photon echo scheme is
combined with a controlled coherence conversion process via control Rabi
flopping to a third state, where the control Rabi flopping collectively shifts
the phase of the ensemble coherence. The propagation direction of photon echoes
is coherently determined by the phase matching condition between the data
(quantum) and the control (classical) pulses. Herein we discuss the classical
controllability of a quantum state for both phase and propagation direction by
manipulating the control pulses in both single and double rephasing photon echo
schemes of a three-level system. Compared with their well-understood use for
two-level photon echoes, the Maxwell-Bloch equations to a three-level system
have a critical limitation regarding the phase change when interacted with an
arbitrary control pulse area.
