Recent progress with rare-earth-ion ensemble quantum memories has resulted in a family of echo-memory protocols which use sequences of pulsed light fields to recall a pulse stored in the ensemble earlier. The simplest of these protocols, the two-pulse photon echo, has been deemed too noisy to operate in the single-photon regime.In this work we introduce and investigate the LiSPER protocol, which involves using off-resonant pulses to control the recall of the stored pulse from the ensemble. In the LiSPER protocol, two off-resonant pulses dynamically tune the resonant frequencies of the ions in the ensemble such that an unwanted noisy echo is suppressed and a less noisy echo of the input pulse is emitted at a later time. A theoretical basis for LiSPER is formed with analytical calculations and numerical simulations, and the dependence of the protocol efficiency on parameters of the off-resonant pulses is characterised. Also presented are the results of experiments performed using a praseodymium ion ensemble. These results agree qualitatively with the theoretical work, although the entire LiSPER protocol is not demonstrated.
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