Cavity-modified oscillating bound states with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Λ</mml:mi></mml:math>-type giant emitter in a linear waveguide

We study a system composed of a three-level giant atom (3GA), a waveguide initially in the vacuum state, and a single-mode cavity. The 3GA-cavity system is in a strong-coupling regime, and the distance between the coupling points is comparable to the coherent length of a spontaneously emitted photon. The dynamics of the 3GA and its radiative field in the waveguide for long times are analyzed in each subspace with only one excitation exchanged between the waveguide and the 3GA cavity. Besides the steady value, we also found an oscillatory character of the excited-state population, a signature of oscillating bound states which is generated by the superposition of two bound states in the continuum. The radiative field propagates in the cavitylike geometry formed by the coupling points. When one bound state is emergent, a sinelike interference pattern is visible for the emitted photon distribution in spacetime. An oscillatory character in time and a beat in space for the emitted photon distribution are observed when two bound states are emergent in a subspace. The wavelengths and the periods are controlled by the number of photons in the cavity.