"In the case of a temporal double pulse analysed with a spectrometer, dispersion is used to broaden the individual pulses in time so much that they overlap and, with the which-pulse information now erased, interference may be observed. The modulation frequency in the interference pattern depends on the temporal separation of the pulses, analogous to the spatial double slit.
In our case, we do not require a spectrometer to observe interference. Successive pulses stored using Gradient Echo Memory (GEM) overlap spatially in the atomic ensemble. They interfere and create a spatial fringe pattern within the atomic spinwave. The spacing of the fringes is determined by the temporal separation of the pulses and the atomic frequency gradient, which adds a spatially varying phase to the spinwave over time. We normally take this intra-memory spatial interference for granted, since using GEM for both storage and recall amounts to a double Fourier transform meaning the output is just a scaled version of the input. The interference only becomes apparent when the spinwave is retrieved with Electromagnetically Induced Transparency (EIT), and the fringe pattern appears as a function of time in the output light. In this case, the two pulses that were initially separated in time emerge together with their which-pulse information erased, so that interference fringes are 6 now observed in the temporal profile of the output light." CC:
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