Giant atoms have exhibited counterintuitive but interesting phenomena such as non-exponential decays which would benefit quantum information processing. However, recent experiments on electromagnetically induced transparency (EIT) of giant atoms observed standard spectra only. In this letter, we present a full quantum model for observing EIT in a single giant atom rather than a semi-classical one in recent works. With this model and a quantum transport theory in real space, a class of non-Markovian EIT can be observed which has not been witnessed before. This new phenomenon results from spatial non-locality of a multiple distant coupling structure in the giant atom, which physically forces propagating fields between the coupling points behaving as standing waves. We also show that the spatial non-locality induced non-Markovianity can be represented by a time-delayed master equation where widely-used Born approximation in the existing works breaks down.
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