“…Over the last decade, modified photon echo techniques have been intensively studied and applied to quantum memory applications to overcome the fundamental limitation of population inversion in conventional photon echoes, for which the population inversion excited by an optical π pulse results in quantum noises caused by spontaneous and/or stimulated emissions [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. Photon echo has also been experimentally studied in a highly doped crystal Tm:YAG [ 18 ] and in ruby upon excitation through an optical fiber [ 19 ]. Although some of these techniques have been successful for quantum state storage and retrieval [ 8 , 9 , 10 , 11 , 12 , 13 ], the understanding of collective atom phase control is still limited, where absorptive photon echoes have been involved in controlled atomic frequency comb (AFC) echoes [ 8 , 9 ] and doubly rephased (DR) photon echoes [ 10 , 11 , 12 , 13 ].…”