Group delay of single-photon transmission in a waveguide side coupled with a Jaynes-Cummings chain

Using a real-space model Hamiltonian, we have theoretically studied the single-photon transmission in a waveguide side coupled with a Jaynes-Cummings chain (JCC). The JCC can induce the photon group advancement (GA) and group delay (GD) in different frequency ranges determined by JCC eigenmodes. For GA and GD, there exist different optimal JCC lengths. At certain frequency, the GAs maximum value as usual increases with decreasing the cavity dissipation, whereas the GDs eventually reaches saturation. For a 1.55 -μm photon, our calculation indicates that the GDs maximum value is about 400 ps simultaneously with a large transmission.