Enhancing optomechanical force sensing utilizing synthetic magnetism

Abstract

In precision force sensing of multi-mechanical mode optomechanical systems, coherent interference can decouple certain degenerate vibrational modes from the cavity field, leading to incomplete information regarding the measured signal. In this paper, we propose a scheme to enhance and control the detection bandwidth in optomechanical force sensing by exploiting synthetic magnetism achieved through tuning phonon hopping interactions. By toggling between broken and unbroken dark mode, this approach effectively manages the response bandwidth and exhibits intriguing additional noise characteristics. Specifically, when the dark mode remains unbroken, the thermal noise is robust and reduced to half of that of a standard device. In contrast, when the dark mode is broken, thermal noise increases substantially at mechanical resonance but remains the same as when the dark mode is unbroken at effective detection frequencies. Moreover, our scheme offers the dual benefit of amplifying the mechanical response while suppressing additional noise, with the potential to surpass the standard quantum limit.

Figures (6)

• Figure 1: The schematic diagram of the optomechanical force sensor model. The system consists of an optical cavity and two mechanically coupled oscillators, with their coupling dependent on the phase. The coupling strength, denoted by $V$, and the coupling phase, denoted by $\phi$, serve as probes for detecting ideal impulsive forces. The right-end mirror is a perfect cavity mirror, free of dissipation, while the transmitted light at the left-end mirror passes through an amplitude spectrum filter. The output from the homodyne detection setup can detect external force signals. The homodyne detection setup includes a beam splitter, photodiode, local oscillator light with a phase $\theta$, and a subtractor.
• Figure 2: The dimensionless additional noise power spectral density $N_{\text{add}}^{\phi}(\omega)$ (a) and the mechanical response $R_{m}^{\phi}(\omega)$ (b) as functions of the normalized frequency $\omega/\omega_m$ for various coupling phases $\phi$. The system parameters are based on those provided in Table \ref{['tab:parameters']} with $V = 0.01 \omega_m$ and $G' = 4.5 \times 10^{-3} \, \omega_m$.
• Figure 3: (a) The effective coupling strengths $\tilde{G}_{\pm}$ as functions of $\phi$. The dimensionless additional noise power spectral density $N_{\rm{add}}^{\phi}(\omega)$ (b) and the mechanical response $R_{m}^{\phi}(\omega)$ (c) as functions of the normalized frequency $\omega/\omega_m$ for various coupling phases $\phi$. Here the parameters are consistent with Fig. \ref{['fig:2']} and $V = 0.02 \omega_m$.
• Figure 4: The dimensionless additional noise power spectral density $N_{\text{add}}^{\phi}$ as the function of $\omega/\omega_m$ for different coupling phases $\phi = 0$ (a), $\phi = \frac{\pi}{2}$ (b), and $\phi = \pi$ (c) for different coupling strength $V$, respectively. The parameters are taken from Table \ref{['tab:parameters']}, and $G' = 4.5 \times 10^{-3} \omega_m$.
• Figure 5: (a) The dimensionless additional noise power spectral density $N_{\text{add}}^{\phi}$ at $\omega_\text{eff}$ as the function of $G'/\omega_m$ for various coupling $\phi$, with $\kappa = 0.1 \omega_m$.(b) The dimensionless added noise power spectral density $N_{\text{add}}^{\phi}$ at $\omega_\text{eff}$ as the function of $\kappa/\omega_m$ for different coupling phases, with $G' = 4.5 \times 10^{-3} \omega_m$. The parameters for both (a) and (b) are taken from Table \ref{['tab:parameters']}, and the coupling strength of the two oscillator $V = 0.02 \, \omega_m$.