Some problems in the theory of two-photon processes

Zhidang Chen, Helen S. Freedhoff

Ḱale Oyedeji, Larry B. Petway, Lewis S. Klein +1 more

Chong Wang, Zhu Yong, Liangsheng Li +1 more

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.

Adi R. Bulsara, William C. Schieve

We consider the problem of two-photon transitions between atomic levels having the same parity. The semiclassical theory is developed from Maxwell's equations and the resulting transcendental equations for the pulse envelope solved exactly. They lead to an unstable pulse envelope if the higher-order processes are included. We then treat the laser as a birth/death process, deriving a Markovian (macroscopic) master equation for the probability function, which may be solved exactly in the steady state. By a suitable truncation procedure, this equation predicts a stable steady-state envelope, and is consistent with the microscopic quantum theory when virtual processes are neglected. A comparison is made between the macroscopic (master equation) approach and the microscopic quantum theory at the level of the moment equations. We find that, in the high-gain limit, the fluctuations predicted by the two theories are the same.

Nikolay N. Bogolubov, Fam Le Kien, A.S. Shumovsky

William J. Meath, B. N. Jagatap, A. E. Kondo

The dynamics and the cross sections associated with the excitation of a ground-state dipolar molecule to an excited state, by the simultaneous absorption of two photons, are discussed using the rotating wave approximation and time-dependent perturbation theory. The excitations of ten- and two-energy level representations of model dipolar molecules are used for illustrative purposes. The temporal development of the final state of the excitation process and the two-photon excitation cross sections are discussed as functions of laser intensity, laser–molecule interaction time and the two types of excitation mechanism (which are available for dipolar molecules, relative to the one mechanism for a non-polar molecule). The results are used to discuss the validity of perturbation theory treatments of the problem and various strategies for the enhancement of the intrinsically weak two-photon excitation process.