Renormalization: single-photon processes of two-level system in free space

The investigation on quantum radar requires accurate computation of the state vectors of the single-photon processes of the two-level system in free space. However, the traditional Weisskopf-Wigner(W-W) theory fails to deal with those processes other than spontaneous emission. To solve this problem, we provide a new method based on the renormalization theory. We evaluate the renormalized time-ordered Green functions associated with the single-photon processes, and relate them to the corresponding state vectors. It is found that the ultraviolet divergences generated by the Lamb shift and higher-order interactions can be systematically subtracted in the state vectors. The discussions on spontaneous emission and single-photon absorption are then presented to illustrate the proposed method. For spontaneous emission, we obtain the same results of the W-W theory. For single-photon absorption where W-W theory fails, we find that the two-level electric dipole first gets excited rapidly and then decays exponentially, and that the efficiency of the single-photon absorption declines as the bandwidth of the incident photon becomes narrow. The proposed method can improve the investigation on quantum radar.