Figure 1

Sketch of the system and of the process under consideration. Two levels of a single cascade three-level system are coupled to a single cavity mode. Sketch of the spontaneous decay process $|g⟩\to |s⟩$ in the case of weak and strong coupling (${\Omega }_R/{\omega }_0\ll 1$) (a), and in the USC regime (${\Omega }_R/{\omega }_0\gtrsim 0.1$) (b). In the latter case the spontaneous decay can produce the emission of additional pairs of cavity photons.Reuse & Permissions

Figure 2

Lowest energy levels of the total quantum system (eigenvalues of $H$) as a function of the coupling ${\Omega }_R/{\omega }_0$ and a sketch of the allowed spontaneous transitions in USC. The bending lines as a function of ${\Omega }_R/{\omega }_0$ describes the dressed energy levels ${\omega }_{\tilde{j}}$.Reuse & Permissions

Figure 3

Dynamics of released cavity photons. (a) Time evolution of the intracavity mean photon number $⟨X^{-}{X}^{+}⟩$ calculated for different coupling strengths ${\Omega }_R/{\omega }_0=0.3$ (red line), 0.4 (blue line), 0.6 (black line). Larger signals correspond to larger couplings. The inset in panel (a) shows the population dynamics of level $|\tilde{0}⟩$. (b) $⟨X^{-}{X}^{+}⟩$ for different spontaneous emission decay rates ${\gamma }_{gs}$ (see text) obtained by artificially dropping cavity losses (the signal rises more rapidly for larger ${\gamma }_{gs}$). (c) Time evolution of $⟨X^{-}{X}^{+}⟩$ calculated for two equal artificial atoms with ${\Omega }_R/{\omega }_0=0.65$. (d) Time evolution of $⟨X^{-}{X}^{+}⟩$ after initial state preparation by a $\pi$ pulse with $\sigma =5/{\omega }_0$ (continuous blue line), with $\sigma =1.7/{\omega }_0$ (dotted black line) and comparison with the dynamics originating from the initial state $|\tilde{0}⟩$ (dashed red line) for a single three level system.Reuse & Permissions

Figure 4

(a) Spectrum $S(\omega )$ of spontaneously emitted photons into not-confined electromagnetic modes. (b) Normalized second order correlation function $g^{(2)}(t)$. (c) ${\mathcal{G}}^{(2)}(t,t)=⟨X^{-}(t)X^{+}(t)⟩g^{(2)}(t,t)$. (d) Normalized third-order correlation function $g^{(3)}(t)$.Reuse & Permissions