The nonlinear dynamics of a classical photon pulse occurring at a two-sided cavity QED system in the weak-coupling regime is investigated theoretically. It is shown that this system functions as a single-photon filter.
We have investigated two-photon nonlinearity in general cavity QED systems, which cover both weak- and strong-coupling regimes and include the radiative loss from an atom. One- and two-photon propagators are obtained in analytical forms. By surveying both coupling regimes, we have revealed the conditions on a photonic pulse for yielding large nonlinear effects, depending on the cavity Q value. We also discuss the effects of radiative loss on nonlinearity.
Exploiting the field-amplification effect of a cavity, the possibility of optical nonlinearity by only two photons was indicated experimentally. In the present article, we review our recent analysis of the two-photon dynamics in a cavity quantum electrodynamics (QED) system. Since a cavity-QED system is highly dispersive around its resonances, the shapes of photonic pulses are significantly deformed through interaction with the system. Thus, the present analysis is based on a formalism beyond single-mode approximations. The external photon field is treated rigorously as a continuum, which enables us to handle the two-photon wavefunction in the space representation. The degree of optical nonlinearity in a two-photon state is quantified by comparing the output wavefunction with the linear output wavefunction. It is revealed that the semiclassical optical response theory can be applied for evaluation of the two-photon optical nonlinearity. The two-photon nonlinearity appears not purely as a phase shift in the output wavefunction. The degradation of the fidelity between the output wavefunction and the linear output wavefunction always occurs, which hinders the application of this nonlinear effect as a quantum phase gate. The optimum condition for maximizing the two-photon nonlinearity is clarified, suggesting that pulse shape control is more essential than the Q-value control of the cavity QED system.
We study analytically the dynamics of cavity QED nodes in a practical quantum network. Given a single 3-level Λ-type atom or quantum dot coupled to a micro-cavity, we derive several necessary and sufficient criteria for the coherent trapping and generation of a single photon pulse with a given waveform to be realizable. We prove that these processes can be performed with practical hardware -- such as cavity QED systems which are operating deep in the weak coupling regime -- given a set of restrictions on the single-photon pulse envelope. We systematically study the effects of spontaneous emission and spurious cavity decay on the transfer efficiency, including the case where more than one excited state participates in the dynamics. This work should open the way to very efficient optimizations of the operation of quantum networks.