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Gradient echo memory (GEM) stores and retrieves photon wave packet in forwarddirection with high efficiency and fidelity using photon-echo mechanism. It isan important technique for quantum memory applications. By breaking thecontinuity of the gradient absorption structure, the scheme becomes gradientfrequency comb (GFC), which is a hybrid of GEM and atomic frequency comb (AFC).To elucidate the non-trivial field-atom evolution of gradient echo, we deriveits exact analytical solution in a medium of arbitrary optical thicknesssubjecting to any linear gradient of transition frequency, and discuss itsphysical processes. Based on this solution, we further suggest and analysis twotypes of GFC, one with stepwise gradient and the other with discontinuousgradient.

Exact solution of gradient echo memory and analytical treatment of gradient frequency comb