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

Abstract

Gradient echo memory (GEM) stores and retrieves photon wave packet in forward direction with high efficiency and fidelity using photon-echo mechanism. It is an important technique for quantum memory applications. By breaking the continuity of the gradient absorption structure, the scheme becomes gradient frequency 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 derive its exact analytical solution in a medium of arbitrary optical thickness subjecting to any linear gradient of transition frequency, and discuss its physical processes. Based on this solution, we further suggest and analysis two types of GFC, one with stepwise gradient and the other with discontinuous gradient.

Nuclear quantum memory for hard x-ray photon wave packets

“…In contrast to the efficiency, the fidelity cannot be easily translated into a photon number quantity. However, an upper boundary can be estimated, which is nonetheless close to the complex amplitudebased fidelity for static frequency combs as used in this work (12,43). The complex amplitude-based fidelity of the kth echo is defined in (12,53) where ℇ cav (t) and ℇ out (t) are the complex wave packet amplitudes of the photon decay from the cavity mode and from the combined setup (cavity plus NFC), respectively.…”

“…Because of the lack of phase information in our measurements, only a photon counting–based fidelity is calculable. Because nuclear forward scattering is inherently coherent, for static NFCs, the phases of the echoes are predicted to be well preserved, rendering the intensity fidelity a good approximation for the complex amplitude-based fidelity ( 12 , 43 ).…”

“…The complex amplitude-based fidelity of the kth echo is defined in (12,53) where ℇ cav (t) and ℇ out (t) are the complex wave packet amplitudes of the photon decay from the cavity mode and from the combined setup (cavity plus NFC), respectively. The normalization constants are given by: This intensity fidelity (43),  (k) int , is plotted in Fig. 4.…”