Long-range optomechanical interactions in SiN membrane arrays

Abstract

Optomechanical systems using a membrane-in-the-middle configuration can exhibit a long-range type of interaction similar to how atoms show collective motion in an optical potential. Photons bounce back and forth inside a high-finesse Fabry-Pérot cavity and mediate the interaction between multiple membranes over a significant distance compared to the wavelength. Recently, it has been demonstrated that off-resonant coupling between light and the inter-membrane cavity can lead to coherent mechanical noise cancellation. On-resonance coupling of light with both the Fabry-Pérot and inter-membrane cavities, predicted to enhance the single photon optomechanical coupling, have to date not been experimentally demonstrated, however. In our experiment, a double-membrane system inside a Fabry-Pérot cavity resonantly enhances the cavity field, resulting in a stronger optomechanical coupling strength from the increased radiation pressure. The resonance condition is first identified by analyzing the slope of the dispersion relation. Then, the optomechanical coupling is determined at various chip positions over one wavelength range. The optimum coupling conditions are obtained and enhancement is demonstrated for double membrane arrays with three different reflectivites, reaching nearly four-fold enhancement for the collective motion of $R=65\%$ double membranes. The cavity losses at the optimum coupling are also characterized and the potential of reaching the single-photon strong coupling regime is discussed.

Figures (17)

• Figure 1: a) Microscope image of a SiN double-membrane trampoline device. The membrane on the backside is visible as a white shadow. The lateral offset between membranes on the front- and backside of the chip is less than 35µm, which is much smaller than the extent of the PhC pad and does not cause significant optical losses, as the cavity beam waist is only 33µm. b) Side-view schematic of the identical membrane array device and collective mechanical oscillation in orthogonal basis, where the top panel shows the mechanical center-of-mass mode (oscillates in-phase), while the bottom panel shows the mechanical breathing mode (oscillates with opposite phase). c) Schematic of the optical field off- (top) and on-resonance (bottom) with the inter-membrane cavity. The light field increases inside the inter-membrane cavity compared to the off-resonance case, yielding a higher radiation pressure across both membranes and resulting in an enhanced optomechanical coupling strength.
• Figure 2: Characterization of the $R = 35\%$ double membrane device. a) Dispersion curve close to the resonance of the inter-membrane cavity. b) Dispersion curve off-resonance. The maximum linear coupling strength is 2.17MHz/nm. c) Zoom-in of the dispersion curve from a), showing that the dispersion tends to flatten (0.04MHz/nm) when $\lambda$ is close to the resonance of the inter-membrane cavity. The additional first transversal mode of the cavity is due to small alignment imperfections. a) and b) are measured with a broader wavelength scan of approximately 42pm. c) is a finer scan, to accurately identify the inter-membrane resonance condition ($\lambda_\mathbf{res}$). d) Normalized dispersion curve height vs. input wavelength. The blue solid line is the numerical simulation of a fixed membrane spacing based on Li2016. The different data points represent the normalized height of the dispersion curve measured for different membranes when scanning the wavelength of the laser. One device (green, round dots) is on-resonance within the laser operating wavelength range. $\lambda_\mathrm{res}$ is 1550.41nm, shown in a) and c).
• Figure 3: Optical and mechanical characterization of DM with $R=35%$. a) PDH error signal without (top) and with a membrane (bottom), both using the same y-axis scale. Blue dotted lines are raw data and the orange lines are a fit. b) Dependence of the cavity linewidth on optical input power. The lines (orange) show a linear regression. Error bars represent standard deviation obtained from the fit. c) Mechanical spectra showing the two fundamental modes of the membranes, all characterized at the chip position $0.25\lambda$ (cf. Fig. \ref{['fig: Dispersion_curve']}c). The spectra are equally vertically shifted for visualization. The two gray vertical dashed lines indicate the intrinsic fundamental modes of the trampoline membranes.
• Figure 4: Optomechanical coupling strength $g_\mathrm{0}$ ($g_\mathrm{c}$ for DMs) and cavity loss $\kappa$ as a function of the chip position. a) and b) are for SM and c) and d) are for DM, respectively. $g_\mathrm{0}$ is fitted by $|\sin(\theta/2)|^2$ for the SM and by Eq. \ref{['eq:g0_norm']} for the DMs. The blue shaded area in a) and c) indicates the fitting uncertainty of $g_\mathrm{0}$. Error bars represent standard deviation obtained from the fit.
• Figure 5: Enhancement of optomechanical coupling strength (black circles) and corresponding increase in cavity linewidth (blue squares) vs. membrane reflectivities. The black solid curve represents the enhancement in $g_\mathrm{c}$ and the blue curve illustrates the $\kappa_\mathrm{empty}$ and material absorption ($\kappa_\mathrm{abs}$) limited total cavity losses, applying adapted models from Newsom2020 using our experimental parameters -- membrane thickness $d$ of 200nm and complex refractive index of $2+10^{-5}i$, where the imaginary part indicates absorption. The two dashed lines highlight potential improvements in $\kappa$ by thinning down $d$ to 100nm or reducing Im(n) to $10^{-6}$karuza2012tunable, respectively. Error bars of $g_\mathrm{c} /g_0$ are standard deviation derived from the fit.