Search for Dark Matter Scattering from Optically Levitated Nanoparticles

TL;DR

Levitated optomechanical sensors are used to detect impulsive forces on silica nanospheres to search for particle-like dark matter scattering via a long-range neutron coupling. The authors calibrate impulse responses in situ, operate near the standard quantum limit for impulse sensing, and analyze data from two nanospheres to set 95% CL limits on the DM-neutron coupling across a wide DM mass range, including virialized and thermalized populations, and composite DM scenarios. They demonstrate directional sensitivity to separate potential DM signals from backgrounds and discuss prospects for large sensor arrays to improve sensitivity by orders of magnitude, potentially probing light DM and neutrino-like interactions. The work showcases a novel DM probe exploiting ultra-sensitive, low-threshold, directionally discriminating mechanical sensors.

Abstract

The development of levitated optomechanics has enabled precise force sensors that operate in the quantum measurement regime, opening up unique opportunities to search for new physics whose weak interactions may have evaded existing sensors. We demonstrate the detection of impulsive forces acting on optically levitated nanoparticles, where the dominant noise source is provided by measurement backaction. Using these sensors, we search for momentum transfers that may originate from scattering of passing particlelike dark matter. For dark matter that couples to Standard Model neutrons via a generic long-range interaction, this search constrains a range of models in the mass range $1$-$10^7~\mathrm{GeV/}c^2$, placing upper limits on single neutron coupling strength as low as $\leq 1 \times 10^{-7}$ at the 95% confidence level. We also demonstrate the ability of using the inherent directional sensitivity of these sensors to separate possible dark matter signals from backgrounds. Future extensions of the techniques developed here can enable searches for light dark matter and massive neutrinos that can reach sensitivity several orders of magnitude beyond existing searches.

Figures (14)

• Figure 1: Overview of the experimental setup and illustration of the impulse measurement. (a) Simplified schematic showing the major features of the experimental setup, as described in the text (see Appendix \ref{['sec:detailed_setup']} for a full schematic). (b) Scattering of a dark matter particle with a levitated nanosphere via a light mediator $\phi$ that couples to neutrons, producing an observable momentum transfer $\vec{q}$. The range of the interaction is approximately $\hbar/m_\phi c$, where $m_\phi$ is the mediator mass. (c) The impulse detection is achieved by continuously monitoring the center-of-mass motion via photons scattered off the nanosphere.
• Figure 2: Heating rate measurement at various pressures. (Left) A trapped nanosphere is repeatedly released from feedback at various pressures with its $z$-position continuously monitored. The increase in averaged phonon occupancy, $\Delta n \equiv n-n_0$, averaged over 1200 measurements, versus time is shown (plotted in colored bands), with linear fits shown as solid lines. (Right) Measured heating rates as a function of pressure. The horizontal error bars are dominated by systematic uncertainties in the specified accuracy of the pressure gauge. The uncertainties of the measured heating rates are dominated by systematic errors in the charge-based position calibration. The rates are fit to a model with a constant plus a linear component that represents heating from photon recoil and gas collisions, respectively (dashed line). The red band corresponds to the expected contribution of gas collisions (see Appendix \ref{['sec:app_gas']}), for residual gas dominated by H$_2$O (upper edge) or H$_2$ (lower edge).
• Figure 3: Noise spectral densities measured at $(2 \pm 1) \times 10^{-8}$ mbar and the estimated noise budget. (Left) Single-sided amplitude spectral density of the $z$ displacement noise. The contribution of backaction and gas collisions is estimated from the derived heating rate, independent of the position measurement. Narrow features such as vibrational sidebands that are 1.25 kHz away from the resonant frequency are not modeled here. (Right) Amplitude spectral density of the effective force noise. The contribution of zero-point fluctuations is below the plot range. The dashed black line represents the ideal case at the current readout power, in which the imprecision noise is improved by having a measurement efficiency $\eta_m = 1$ and thermal noise eliminated. The dotted black line shows the noise spectrum when the impulse SQL (Eq. \ref{['eq:impulse_sql']}) is reached in the idealized situation in which the readout power can be freely tuned without affecting the mechanical response.
• Figure 4: Example data demonstrating net charge control in ultrahigh vacuum and impulse calibration. (a) Measurement of the net electric charge of a levitated nanosphere as a function of time, with a heated tungsten filament (top) and illumination of a pulsed UV laser (bottom). Discrete steps indicating changes of an elementary charge, $e$, are observed in both cases. The data presented here are taken at a pressure $(2 \pm 1) \times 10^{-8}$ mbar. (b) Example position (top panels, blue) and reconstructed impulse amplitude versus time (bottom panels, gray) from electric impulse calibrations. In each calibration, an electric pulse indicated by a solid black line is applied in the $z$-direction at time $t=0$, with an amplitude $\Delta p = 1.1 \pm0.1$ MeV/$c$. The light red lines in the bottom panels represent the reconstructed waveform averaged over 1,200 calibrations.
• Figure 5: (a) Example distributions of the reconstructed amplitudes for applied impulses at various sizes. The solid lines represent Gaussian fits to the measured distributions. The yellow shaded region shows the reconstructed amplitude distribution when the same reconstruction algorithm is applied to noise-only data (i.e., when no calibration impulses are applied). The distribution of the random force amplitudes estimated from the noise-only data is indicated in gray, which represents the force noise level in the absence of search bias, with a Gaussian fit to this distribution shown by the dashed gray line. (b) Reconstructed momentum resolution, $\sigma_p$, measured for calibration impulses at different amplitudes. The blue shaded region shows where the impulse amplitude is below $5\sigma_p$, with $\sigma_p = 130 \pm 10~\mathrm{keV/}c$ measured from the noise distribution in the left figure. The blue and black dotted lines indicate the impulse sensitivity estimated from the measured force noise in Sec. \ref{['sec:noise_analysis']} ($\Delta p_{\mathrm{meas}} = 65 \pm 9 \ \mathrm{keV/}c$) and the impulse standard quantum limit (Eq. \ref{['eq:impulse_sql']}), respectively. (c) Average reconstructed amplitude versus true impulse amplitude. The dashed line is a fit to a model showing the linearity of the response above the reconstruction threshold, but accounting for the expected nonlinearity from the search bias for amplitudes $\Delta p \lesssim 500~\mathrm{keV/}c$.