Resonance-antiresonance line shape for transmission in quantum waveguides with resonantly coupled cavities

We investigate the line shape of the transmission probability in quantum waveguides with resonantly coupled cavities. Resonance and antiresonance features in the vicinity of each quasibound state can be characterized by a zero-pole pair in the complex-energy plane, which leads to asymmetrical transmission peaks. We have found a generalization of the familiar symmetrical Lorentzian line shape. Using several examples, we demonstrate the utility of our proposed line shape to extract the lifetime of the quasibound state by a fit to the data. We also discuss the asymmetrical line shapes in the context of Fano resonances.