本文从量子梯度回声存储器(GEM)存储光脉冲时的麦克斯韦-布洛赫方程组出发,推导了GEM在k空间的极化声子描述及其满足的微分方程。我们解出了k空间行波通解,得到极化声子演化规律的数学表达式,加深了对已有的实验和数值模拟结果的理解。然后,我们考虑了实际原子系综量子态的退相干效应,解出了带有退相干参数的通解,发现了退相干效应对存储失真影响的定量关系。基于此,我们提出了GEM存储的一个优化方案。这个优化方案不但使存储的保真度有所提高,还缩短了翻转梯度外场与回声脉冲读取的时间间隔,为量子存储器走向实际应用提供了理论帮助。 Based on the Maxwell-Bloch equations when the light pulse is stored in the Quantum Gradient Echo Memory (GEM), the phonon description and its differential equations for the GEM in k-space are deduced. We solve the traveling wave general solution in k-space and get the mathematical expression of the phonon evolution law, deepening the understanding of the existing experimental and numerical simulation results. Then, we consider the decoherence effect of the actual atomic quantum state, solve the general solution with the decoherence parameter, and find the quantitative relationship between the decoherence effect and the storage distortion. Based on this, we propose a GEM storage optimization program. This optimization scheme not only improves the fidelity of the memory, but also shortens the time interval between the flipping gradient field and echo pulse reading, which provides theoretical help for the practical application of quantum memory.