  Photon-echo based optical quantum memory schemes often employ intermediate
steps to transform optical coherences to spin coherences for longer storage
times. We analyze a scheme that uses three identical chirped control pulses for
coherence rephasing in an inhomogeneously broadened ensemble of three-level
$\Lambda$-systems. The pulses induce a cyclic permutation of the atomic
populations in the adiabatic regime. Optical coherences created by a signal
pulse are stored as spin coherences at an intermediate time interval, and are
rephased for echo emission when the ensemble is returned to the initial state.
Echo emission during a possible partial rephasing when the medium is inverted
can be suppressed with an appropriate choice of control pulse wavevectors. We
demonstrate that the scheme works in an optically dense ensemble, despite
control pulse distortions during propagation. It integrates conveniently the
spin-wave storage step into memory schemes based on a second rephasing of the
atomic coherences.
