Amplifying Frequency Up-Converted Infrared Signals with a Molecular Optomechanical Cavity

Frequency up-conversion, enabled by molecular optomechanical coupling, has recently emerged as a promising approach for converting infrared signals into the visible range through quantum coherent conversion of signals. However, detecting these converted signals poses a significant challenge due to their inherently weak signal intensity. In this work, we propose an amplification mechanism capable of enhancing the signal intensity by a factor of 1000 or more for the frequency up-converted infrared signal in a molecular optomechanical system. The mechanism takes advantage of the strong coupling enhancement with molecular collective mode and the Stokes sideband pump. This work demonstrates a feasible approach for up-converting infrared signals to the visible range.

Figure 1

(a) The molecular optomechanical system consisting of $N$ molecules (with frequency ${\omega }_b$ of the vibrational mode) coupled to both the VIS mode (with frequency ${\omega }_a$ and decay rate ${\kappa }_a$) via the optomechanical interaction and the IR mode (with frequency ${\omega }_c$ and decay rate ${\kappa }_c$) via the bilinear interaction. The VIS mode is driven by a pump field with frequency ${\omega }_p$ and amplitude ${ϵ}_p$. The IR signal of interest with frequency ${\omega }_{\mathrm{ir}}$ and amplitude ${ϵ}_{\mathrm{ir}}$ is incident on the cavity with coupling to the IR mode $c$. (b) Scheme of frequency up-converted IR signals based on the molecular optomechanical system. Here the IR signal of interest is near-resonant with the vibrational frequency of the molecules (as well as the IR mode $c$), and the blue-detuned pump field is near-resonant with the first Stokes sideband of the VIS mode—i.e., ${\omega }_{\mathrm{ir}}\simeq {\omega }_b={\omega }_c$ and ${\omega }_p\simeq {\omega }_a+{\omega }_b$. The input weak IR signal with frequency ${\omega }_{\mathrm{ir}}$ is up-converted as the output VIS signal ($a_{\mathrm{out},-}$) with frequency ${\omega }_p-{\omega }_{\mathrm{ir}}$ via the optomechanical interaction between the VIS mode and the molecular vibration.

Figure 2

(a) The conversion efficiency $T_{ac}$ as a function of the enhanced collective optomechanical coupling strength $|{\mathcal{G}}_a|$ for $N={10}^7$. (b) The conversion efficiency $T_{ac}$ as a function of the number of the molecules $N$ at $g_a/2\pi =0.08\mathrm{GHz}$. Here, we consider the resonance case ${\omega }_{\mathrm{ir}}={\omega }_b={\omega }_c=2\pi \times 30\mathrm{THz}$, and other parameters are $\mathrm{\Delta }=-{\omega }_b$, ${\kappa }_a/2\pi =30\mathrm{THz}$, ${\kappa }_c/2\pi =0.5\mathrm{THz}$, ${\gamma }_B/2\pi =0.16\mathrm{THz}$, ${ϵ}_p/2\pi =500\mathrm{THz}$, and $g_c/2\pi =0.1\mathrm{GHz}$.

Figure 3

(a) The maximum conversion efficiency $T_{ac}^{\max }$ as functions of the decay rates ${\kappa }_a$ and ${\kappa }_c$ at optimal coupling strength $|{\mathcal{G}}_a|=|{\mathcal{G}}_a^{(*)}|\simeq \sqrt{(G_c^2|{\eta }_c^{-1}|+{\kappa }_c{\gamma }_B|{\eta }_B|){\kappa }_a|{\eta }_a|/{\kappa }_c}$. (b) The optimal coupling strength $|{\mathcal{G}}_a^{(*)}|$ as functions of the decay rates ${\kappa }_a$ and ${\kappa }_c$. Here, $N={10}^7$ and other parameters are the same as those in Fig. 2.

Figure 4

(a) The conversion efficiency $T_{ac}$ as a function of the frequency of the IR signal ${\omega }_{\mathrm{ir}}$ for different values of $|{\mathcal{G}}_a|$. (b) The bandwidth $\mathrm{\Gamma }$ as a function of the enhanced collective optomechanical coupling strength $|{\mathcal{G}}_a|$. Here, $N={10}^7$ and other parameters are the same as those in Fig. 2. In panel (b), the unstable region is marked with the gray shadow.