Frequency upconversion of infrared signals via molecular optomechanical cavities

The gist: Molecular optomechanical cavities have emerged as a promising platform for frequency upconversion, enabling the quantum coherent conversion of infrared signal into the visible range.

System Description and Setup

The system considered is a molecular optomechanical system consisting of N identical molecules and a plasmonic nanocavity that supports both VIS and IR modes. The plasmonic nanocavity is realized through a nanoparticle-on-resonator configuration, where an Au nanoparticle is positioned on top of an Au disk, with the N identical molecules placed in the gap between the nanoparticle and the disk. For frequency upconversion of the IR signal of interest, particular types of molecules, e.g., Biphenyl-4-thiol, are selected to couple simultaneously to both the VIS and IR modes within the plasmonic nanocavity. A strong pump field in the visible range, with frequency ωp and amplitude εp, is applied to drive the VIS mode within the nanocavity. The Hamiltonian of the system is given by Hs = ωaa†a + ωcc†c + X N j=1 ωbb†j bj + X N j=1 gaa†a(b†j + bj) + X N j=1 gc(c† + c)(b†j + bj)+ i(εpe−iωpt a † − H.c.). The parameter ga denotes the optomechanical coupling strength between the VIS mode of the cavity and the molecular vibrations, arising from the dispersive interaction mediated by the Raman polarizability. In contrast, gc represents the bilinear coupling strength between the IR mode and the molecular vibrations, which originates from the electric-dipole interaction.

Quantum Langevin Equations and Steady State

The quantum Langevin equations (QLEs) are obtained by substituting Hamiltonian (2) into the Heisenberg equation and accounting for the damping and the corresponding noise terms. The linearized QLEs are obtained by keeping only the first-order term of the quantum fluctuation, resulting in equations like δa˙ = −(i∆ + κa)δa − iGaδB + √2κaain. The system is analyzed using the power spectrum method to solve these linearized QLEs (5). Under the condition of a strong pump field, the steady-state mean values of the operators are obtained using the mean-field approximation. The steady-state mean value for operator 'a' is given by ⟨a⟩ss = εp i∆ + κa.

Conversion Efficiency Analysis

The output spectrum of the VIS mode in the frequency domain is obtained by substituting the input-output relation into Eq. (11). The conversion efficiency from IR signal to VIS range is defined as Sa,out(ω) = T(ω) [Sin(ω) + 1/2]. For the red-detuned pump field, the conversion efficiency T rd ac (ω) is expressed as T rd ac (ω = -ωb). At the first anti-Stokes sideband of the pump field, i.e., ωp + ωb, the conversion efficiency from the IR signal to the VIS range is given by a specific expression involving coupling strengths and decay rates.

Noise Analysis and Stability

The noise spectrum added to the upconverted signal is given by Sa,add(ω) = [Taa(ω) + TaB(ω)] /2. The system stability is determined by the coefficient matrix M, and the system is stable only when the real parts of all the eigenvalues of the coefficient matrix M are positive, as determined by the Routh-Hurwitz criterion. The results show that under red-detuned condition ∆ = ωb, the anti-Stokes sideband exhibits a higher conversion efficiency than the Stokes sideband.

Comparison of Detuning Regimes

The paper compares the performance under red-detuned and blue-detuned pump fields. Under the blue-detuned condition, where amplification of the IR signal is achieved, the conversion efficiency exceeds 1 at both the first Stokes and anti-Stokes sidebands. In contrast, under red-detuned condition ∆ = ωb, the anti-Stokes sideband exhibits a higher conversion efficiency than the Stokes sideband.

Experimental Observations and Conclusions

The results show that under the red-detuned condition ∆ = ωb, the added noise remains below half a quantum. Under the blue-detuned condition, the added noise approaches the quantum limit of one quantum. Compared with the red-detuned regime, the added noise in the blue-detuned regime increases by a factor of 2 to 3, while the conversion efficiency is amplified by three orders of magnitude. The research seeks to establish a theoretical basis to support experimental progress in IR signal upconversion.

Acknowledgments

This work is supported by the Quantum Science and Technology-National Science and Technology Major Project (Grant No. 2023ZD0300700), the National Natural Science Foundation of China (Grants No. 12574387, No. 12405011, and No. U2230402), and the Natural Science Foundation of Hainan Province (Grants No. 125QN210 and No. 125RC631).

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1. Molecular optomechanical cavity systems can be used for quantum coherent conversion of infrared signal into visible range, enabling IR-to-VIS detection without cryogenic cooling. This allows AI systems to perform compact, room-temperature infrared sensing for applications like molecular analysis or thermal imaging.

2. The system exhibits amplification of the infrared signal under blue detuned conditions where the Stokes sideband dominates under the blue-detuned condition, which amplifies the infrared signal. This capability can be leveraged in AI hardware to create a noise-free amplification mechanism for weak IR signals before detection.

3. The added noise approaches the quantum limit of one quantum when the infrared signal is amplified under blue detuning. AI systems can use this knowledge to design algorithms that operate optimally near this quantum limit for enhanced signal fidelity in IR sensing tasks.

4. Conversion efficiencies can reach high values, such as T bd,S ac reaching 103 under specific conditions, which suggests a potential for extremely efficient signal processing pipelines in AI hardware utilizing these molecular systems.

5. The analysis provides theoretical foundations for future experimental advances by showing that the added noise is suppressed by appropriately tuning the coupling strength and decay rates of the system. This allows AI researchers to computationally optimize system parameters to minimize noise in upconversion processes.