Interference trapping of populations in a semi-infinite coupled-resonator waveguide

We study the energy structure and dynamics of a two-level emitter (2LE) locally coupled to a semi-infinite one-dimensional (1D) coupled-resonator array (CRA). The energy spectrum in the single-excitation subspace features a continuous band with scattering states, discrete levels with bound states, and a quantum phase transition characterized by the change of the number of bound states. The number of bound states is revealed by the behavior of the excited-state population at long times with quantum beat, residual oscillation, a constant with either non-zero or zero.