Coherent control of light pulses stored in a Gradient Echo Memory

Abstract

We address the problem of storage and retrieval of a time-bin qubit onto an atomic ensemble of three-level atoms of the Λ - type driven by a far detuned coupling field. The atoms are subject to a longitudinal magnetic field which produces a spatially varying Zeeman splitting of the lower levels along the medium and allows for the spatial encoding of the different angular frequencies of the input pulse during the storage phase. The system operates like a quantum optical memory which is referred to as Gradient Echo Memory (GEM) in analogy to the NMR gradient echo. In the conventional approach to GEM-based devices in Λ − type media, the coupling field co-propagates with the probe field and the magnetic field is reversed after the storage phase, thus an echo signal is released from the medium in the forward direction, in contrast to π-pulse based echo memories which produce a time reversed echo signal in the backward direction. In this work we predict that a backward echo pulse can also be obtained in a GEM schema by making use of a counter-propagating coupling field during the reading phase of the process. In addition, we show that for a proper engineering of the control parameters the system can act as an optical router, i.e., part of the stored signal can be released in the forward direction and the rest in the backward one. The current proposal could have potential applications in quantum information processing.