Field correlations and effective two-level atom-cavity systems

We analyze the properties of the second-order correlation functions of the electromagnetic field in atom-cavity systems that approximate two-level systems. It is shown that a recently developed polariton formalism can be used to account for all the properties of the correlations, if the analysis is extended to include two manifolds—corresponding to the ground state and the states excited by a single photon—rather than just two levels.

Figure 1

Energy levels in $\left(a\right)$ Jaynes-Cummings and $\left(b\right)$ EIT-Kerr schemes. $\delta$ and $\Delta$ are the detunings of the field modes from the atomic resonance, and ${\gamma }_j$’s are spontaneous emission decay rates for the given decay channel.

Figure 2

Second-order correlation functions in Jaynes-Cummings and EIT-Kerr schemes. Left column (“Exact”) is obtained from the exact models, while right column (“Polariton”) from the effective two-manifold models. In the Exact case, parameters for the extended JC are $\gamma =0.1\kappa$, $\theta =g$ and $g=6\kappa$, ${\mathcal{E}}_p=0.1\kappa$ for the dashed curve; $g=20\kappa$, ${\mathcal{E}}_p=0.5\kappa$ for the solid curve. For the EIT-Kerr scheme, parameters are ${\gamma }_j=0.1\kappa$, $g_j=6\kappa$, $\Delta =0$ and $\delta =0.2\kappa$, ${\mathcal{E}}_p=0.7\kappa ,{\Omega }_c=6\kappa$ (dashed); $\delta =4\kappa$, ${\mathcal{E}}_p=0.1\kappa$, ${\Omega }_c=12\kappa$ (solid). The same parameters are used in the Polariton case. In the EIT-Kerr case, this amounts to ${\epsilon }_{+}=8.59\kappa$, ${\epsilon }_{-}=-8.39\kappa$, ${\Omega }_{+}=-0.696\kappa$, ${\Omega }_{-}=-0.704\kappa$, ${\Omega }_R=0.99\kappa$, ${\Gamma }_{+}=0.348\kappa$, ${\Gamma }_{-}=0.352\kappa$ and ${\Gamma }_0=0.5\kappa$ (dashed); ${\epsilon }_{+}=15.56\kappa$, ${\epsilon }_{-}=-11.56\kappa$, ${\Omega }_{+}=-0.06\kappa$, ${\Omega }_{-}=-0.06\kappa$, ${\Omega }_R=0.18\kappa$, ${\Gamma }_{+}=0.2\kappa$, ${\Gamma }_{-}=0.2\kappa$, and ${\Gamma }_0=0.8\kappa$ (solid).