Coherent Control of Spontaneous Emission for a giant driven $\Lambda $-type three-level atom

Quantum optics with giant atoms provides a new approach for implementing optical memory devices at the atomic scale. Here, we theoretically study the relaxation dynamics of a single driven three-level atom interacting with a one-dimensional waveguide, via two coupling points. Under certain conditions, after the long-time dynamics, we found that the population of giant atom can either maintain stable values or exhibit regular periodic oscillation behavior, while photons can be trapped in the region of giant atoms. This phenomenon is not achievable using a two-level atom with two legs. It is worth noting that the atomic excitation probability of a stable bound state is a constant value, which is determined by the size of the atom. Crucially, the size of the atom (the distance between the two coupling points) is much larger than the wavelength of the light field, which is a necessary condition for the existence of oscillating bound states.