We investigate the dynamics of a $\mathrm{\Lambda }$-type giant atom (GA) whose two transitions are coupled to the guided modes of a one-dimensional waveguide at two spatially separated points, with the GA initially excited and the electromagnetic modes of the waveguide in vacuum. The spontaneous emission properties of this GA are investigated by solving the delay-differential equation for the amplitude of the three-level GA in its excited state. Signatures of non-Markovian behavior manifest in the population trapping in the excited state of the GA in the regime where the distance $d$ of the coupling points is smaller than or comparable to the coherent length $L$ characterizing the width of the emitted wave packet. And an exact Markovian dynamics is also found when $d\ge L$ via the inference from adjusting the energy spacing and the inherent time delay in addition to the complex phases in the atom-light coupling, matching the behavior of a small atom coupled to a waveguide.

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• Quantum optics
• Spontaneous emission