Double-sphere enhanced optomechanical spectroscopy constrains symmetron dark energy

Abstract

Screened scalar fields such as the symmetron provide a viable description of dark energy yet their laboratory detection remains challenging. We propose an optomechanical scheme to constrain symmetron interactions using two optically levitated nanospheres inside a cavity. The symmetron-mediated interaction induces an effective coupling which leads to a measurable splitting in the optomechanical resonance spectrum. We forecast constraints in the regime $μ\sim 10^{-2}$eV-$10^{-4}$ eV, which shows that this approach can improve existing laboratory bounds by up to several orders of magnitude, demonstrating the sensitivity of optomechanical spectroscopy to screened fifth forces.

Figures (7)

• Figure 1: Schematic diagram of the experimental setup. The system consists of two optically trapped silica nanospheres (A and B) with the same radius $R=0.5\mu$m, which are confined inside a Fabry--Pérot cavity formed by two mirrors separated by a distance $L$. A strong pump beam together with a weak probe beam is injected through the left mirror to drive and probe the cavity field. These two nanospheres are localized at the opposite sides of a high-reflection membrane placed at the cavity center. The distance between the two nanospheres is denoted by $d=4\mu$m. And the membrane also serves as a reflective mirror that isolates the two trapping regions.
• Figure 2: Transmission $\mathcal{T}^2$ of the probe field as a function of $\delta-\omega_0$ for different values of the effective coupling parameter $\Omega$. (a) In the absence of the symmetron-induced interaction ($\Omega=0$), a single sharp resonance peak appears at $\delta-\omega_0=0$. (b) The original resonance splits into two distinct peaks located symmetrically around the central frequency for $\Omega=-2\times10^{-3}\mathrm{Hz}$. (c) The situation for $\Omega=-4\times10^{-3}\mathrm{Hz}$.(d) A magnified view of the resonance around $\delta-\omega_0=-2\times10^{-3}\,\mathrm{Hz}$ for $\Omega=-2\times10^{-3}\mathrm{Hz}$, where the full width at half maximum (FWHM) is extracted as $1.501\times10^{-7}\,\mathrm{Hz}$, setting the achievable frequency resolution of the system.
• Figure 3: The transmission resonance $\mathcal{T}^2$ of the probe field. The blue solid curve shows the situation without the consideration of dipole coupling ($\Psi=0$), while the black dashed curve corresponds to the case with the coupling strength $\Psi\approx0.8\,\mathrm{Hz}$. The two spectra almost overlap, showing only a very small frequency shift. This shift is far below the minimum resolvable frequency scale of $\sim10^{-7}\,\mathrm{Hz}$ and therefore does not affect the final sensitivity or the resulting constraints.
• Figure 4: Constraints on the symmetron parameters $M$ and $\mu$. The shaded regions correspond to parameter spaces restricted by different theoretical and physical requirements, while the overlap region highlighted in dark grey represents the final experimental allowed parameter space.
• Figure 5: Expected constraints on the symmetron parameters $\mu$ and $\lambda$. The color map shows the predicted frequency shift $\omega_{\rm sp}$ induced by the symmetron interaction as a function of $\mu,\lambda$. The white dashed line corresponds to the contour $\omega_{\rm sp}=1.501\times10^{-7}\,\mathrm{Hz}$, which represents the projected experimental sensitivity and thus defines the detectability threshold. Parameter regions above this curve yield splittings below the sensitivity limit and are therefore not accessible to our system.