Fig. 1. (a) Sketch of the single atom–cavity QED system driven by a broadband squeezed vacuum with central frequency ${\omega }_{\mathrm{sq}}$. The resonance frequency of this two-level atom ${\omega }_A={\omega }_e-{\omega }_g$ with $\hslash {\omega }_{\alpha }(\alpha =e,g)$ being the energy of state $|\alpha \rangle$. Here, $g$ is the coupling constant between the atom and cavity. $\mathit{\gamma }$ and $\mathit{\kappa }$ are the decay rates of the atom and cavity, respectively. Panels (b) and (c) demonstrate the energy levels and the corresponding transition pathways for the empty cavity and the atom–cavity QED system, respectively.

Fig. 2. Panels (a) and (b) show the cavity excitation spectrum, i.e., the mean photon number $\langle a^{†}a\rangle$, and the quantum fluctuation of cavity photons $|\langle aa\rangle {|}^2$ with $r=0.2$. For the empty cavity (blue dashed curves), the cavity mode frequency is fixed, and ${\mathrm{\Delta }}_{\mathrm{cav}}={\omega }_{\mathrm{cav}}-{\omega }_{\mathrm{sq}}$. In the presence of the atom (red solid curves), we assume ${\omega }_{\mathrm{cav}}={\omega }_{\mathrm{sq}}$ and ${\mathrm{\Delta }}_A={\mathrm{\Delta }}_{\mathrm{cav}}={\omega }_A-{\omega }_{\mathrm{sq}}$. The system parameters are given by $g/\kappa =15$ and $\gamma /\kappa =1$.

Fig. 3. (a) Quantum states and transition pathways of the single atom–cavity QED system driven by a squeezed vacuum. (b) Mean photon number and probabilities of one- and two-photon excitations versus the squeezing parameter $r$.

Fig. 4. Probabilities of one- and two-photon Fock states (a) $P_1$ and (b) $P_2$ versus the squeezing parameter $r$ and the normalized coupling constant $g/\kappa$ with $\gamma =\kappa$.

Fig. 5. Mean photon number and probabilities of one- and two-photon excitations versus the squeezing parameter $r$.