The nonlinear interaction between two photons in general atom-cavity systems is investigated. Using the analytic two-photon propagator, the optimum pulse shape for inducing large nonlinearity is clarified for both weak and strong coupling regimes.
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.
A two-level system interacting with a cavity field is an important model for investigating the photon blockade (PB) effect. Most work on this topic has been based on the assumption that the atomic transition frequency is resonant with the fundamental mode frequency of the cavity. We relax this constraint and reexamine PB in a more general atom--cavity system with arbitrary atomic and cavity detunings from a driving field. The results show that when the signs of the atomic and cavity detunings are the same, PB occurs only in the strong-coupling regime, but for opposite signs of the atomic and cavity detunings, strong photon antibunching is observed in both the weak- and strong-coupling regimes and a better PB effect is achieved compared with the case when the signs are the same. More interestingly, we find that this PB arises from quantum interference for both weak and strong nonlinearities. These results deepen our understanding of the underlying mechanism of PB and may be help in the construction of single-photon sources with higher purity and better flexibility using atom--cavity systems.
In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical nonlinearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant thus generalizing our previous results. We can thus investigate quantitatively new features associated with the resonant behavior of the system. We also propose an effective nonlinear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.
We investigate theoretically the photon statistics in a coupled cavity system mediated by a two-level atom. The system consists of a linear cavity weakly driven by a continuous laser, and a nonlinear cavity containing an atom inside. We find that there exists a photon blockade in the linear cavity for both parameter regimes where the coupling strength between the atom and the nonlinear cavity is greater (or less) than the dissipation rate of the linear cavity. We also extend our model by pumping the two cavities simultaneously and find that the conventional photon blockade is apparent in the linear cavity, whereas the unconventional photon blockade appears in the nonlinear cavity. These results show that our work has potential applications for a single photon source in a weakly nonlinear system.