Microwave multiphoton conversion via coherently driven permanent dipole systems

We investigate the multiphoton quantum dynamics of a leaking single-mode quantized cavity field coupled with a resonantly driven two-level system possessing permanent dipoles. The frequencies of the interacting subsystems being considered are very different, e.g., the microwave range for the cavity and the optical domain for the frequency of the two-level emitter, respectively. In this way, the emitter couples to the resonator mode only via its diagonal dipole moments. Furthermore, the generalized Rabi frequency resulting from the external coherent driving of the two-level subsystem is also assumed to be different from the resonator's frequency or its multiples. As a consequence, this highly dispersive interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from the optical to microwave range, respectively.

Figure 1

The schematic of the model: A coherently pumped two-level emitter couples with a single-mode resonator of frequency $\omega$ via its nonzero diagonal dipoles $d_{\alpha \alpha }$, with $\alpha \in \{1,2\}$. Here, $\mathrm{\Omega }$ is the corresponding Rabi frequency due to the off-diagonal dipole moment $d_{21}$ whereas ${\omega }_L, {\omega }_L\gg \omega$, is the frequency of the resonantly applied external field. The emitter-resonator coupling strength is denoted by $g$, while $\kappa$ is the resonator's decay rate. Also are sketched some processes which may occur, namely, emission or absorption of a cavity photon (or two, three, etc.) followed by the spontaneous decay $\gamma$.

Figure 2

(a) The steady-state mean cavity photon number $\langle n\rangle \equiv \langle {\overline{b}}^{†}\overline{b}\rangle$ as well as (b) its second-order correlation function $g^{\left(2\right)}\left(0\right)$ as a function of $\eta =g/\left(2\mathrm{\Omega }\right)$. The blue long-dashed lines are plotted for single-photon processes, $N=1$, while the solid green ones for two-photon processes, $N=2$, respectively. Here, $\overline{n}={10}^{-1}, \kappa /\gamma ={10}^{-3}$, and $\xi =0$.

Figure 3

(a) The steady-state mean cavity photon number $\langle n\rangle \equiv \langle {\overline{b}}^{†}\overline{b}\rangle$ as well as (b) its second-order correlation function $g^{\left(2\right)}\left(0\right)$ as a function of $\eta =g/\left(2\mathrm{\Omega }\right)$. The solid green curves are plotted for two-photon processes, $N=2$, while the short-dashed black ones for three-photon processes, $N=3$. Other parameters are as in Fig. 2.

Figure 4

The cavity photon distribution function $P_n$ in the steady state. The green thin curve is plotted for $\eta =0.09$, while the thick blue one for $\eta =0.07$, respectively. Other parameters are as in Fig. 2.