Semiclassical and cavity-QED treatments of optical nonlinearity are compared with each other for a two-level system embedded in a cavity. The semiclassical treatment leads to qualitative incorrectness even if applied field is coherent.
The effect of a cavity on the third-order optical nonlinearity, is studied for a two-level system with excitation frequency ω 0 , as a function of the Q factor, coupling constant g, and longitudinal (γ 1 ) and pure transverse (γ 2 ) damping constants. The largest enhancement is found in the strong-coupling regime with γ 1 + 2γ 2 = ω 0 /2Q. Large enhancement is also achieved in the weak-coupling regime satisfying the condition ω 0 /Q = (g 2 /γ 1 )[ 1 + 8γ 1 /(γ 1 + 2γ 2 ) - 1], and the intensity depends on damping constants only. The calculation is based on the cavity QED because the semiclassical treatment of the cavity quasimode leads to incorrect optical 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 present a numerical study comparing semiclassical and quantum models of a damped, strongly interacting cavity QED system composed of a single two-level atom interacting with a single quantized cavity mode driven externally by a tunable monochromatic field. We compute the steady state transmission spectrum of the coupled system under each model and show that in the strong coupling regime, the two models yield starkly different results. The fully quantum mechanical model of the system correctly yields the expected multiphoton transmission spectra while the semiclassical approach results in a bistable spectrum.