  In this paper, we identify a many-particle phonon expectation value $\zeta$
with the ability to induce collective dynamics in a non-interacting atomic gas
inside an optical cavity. We then propose to utilise this expectation value to
enhance the laser cooling of many atoms through a cyclic two-stage process
which consists of cooling and displacement stages. During cooling stages, short
laser pulses are applied. These use $\zeta$ as a resource and decrease the
vibrational energy of the atomic gas by a fixed amount. Subsequent displacement
stages use the asymmetry of the trapping potential to replenish the
many-particle phonon expectation value $\zeta$. Alternating both stages of the
cooling process is shown to transfer the atomic gas to a final temperature
which vanishes in the infinitely-many particle limit.
