Spontaneous emission dynamics of giant atom controlled by quantum coherent feedback

We investigated the spontaneous emission of a giant atom coupled with a semi-infinite waveguide. Our model considers the giant atom a two-level system coupled to the semi-infinite waveguide at two points. Based on the Hamiltonian in real space, the first-order delay-differential equation for the atomic excitation amplitude is obtained using the Schrodinger equation. Furthermore, the dynamics of spontaneous emission controlled by quantum coherent feedback due to the semi-infinite waveguide in the non-Markov regime are discussed in two cases, with the coupling strengths between the giant atom and the semi-infinite waveguide at the two coupling points being identical in one case and having a phase difference in the other case. The spontaneous emission exhibits partial decay due to multiple excitations from the quantum feedback and two-point coupling. When the coupling strengths are identical, the decay of the atomic excitation can be either increased or inhibited substantially, even forming a steady state, due to the self-interference due to the two-point coupling. The quantum coherent feedback can either further increase the decay of the excited state or maintain the steady state formed by self-interference. Moreover, a new steady state can be built due to quantum coherent feedback, which cannot exist in the self-interference system. The decay rates can also be increased or decreased by manipulating the phase difference between the coupling strengths at the two coupling points. It can destroy the steady state formed by self-interference or build a steady state based on the chosen phase difference. One can leverage quantum coherent feedback to manipulate the steady state value of the population of the excited states by adjusting the phase difference. The dissipation can increase the decay rates of the excited states. Furthermore, it also destroys steady states. Our results may find applications in developing quantum devices such as quantum memory based on giant atom-waveguide systems.