Searching for Ultralight Dark Matter with MOLeQuTE: a Massive Optically Levitated Quantum Tabletop Experiment

TL;DR

This work investigates detecting ultralight dark matter (ULDM) via oscillatory forces on a macroscopic, optically trapped sensor. It introduces a novel geometric-optics trap that levitates a mg-scale plate, enabling tunable mechanical frequency and forcing sensitivity, and provides a first-principles optimisation of quantum noises for optically trapped systems. Focusing on vector B-L and scalar neutron couplings, the authors derive expected DM forces, compute the SQL-limited noise budget, and forecast reach surpassing current fifth-force bounds and LIGO in targeted ULDM mass ranges. The study shows that operating off resonance at the SQL yields the best sensitivity, and demonstrates that a 0.2 mg sensor already probes new regions while a future 0.8 g design could explore substantially larger swaths of parameter space, potentially outperforming existing detectors across 50–300 Hz frequencies. Overall, the work outlines a concrete, scalable path toward highly tunable, quantum-limited ULDM sensing with tabletop optics, with broad implications for dark matter phenomenology and precision measurement.

Abstract

Many well theoretically motivated models of ultralight dark matter are expected to give rise to feeble oscillatory forces on macroscopic objects. Optically trapped sensors have high force sensitivities but have remained relatively unexplored in this context. In this work we propose a new, tunable, optically trapped sensor specifically designed to detect such forces. Our design features a high-mass (mg) plate whose weight is supported by a vertical beam. We present the first systematic analysis and optimisation of quantum noises in optically trapped systems and show that our setup has the potential to operate at the standard quantum limit with current off-the-shelf technologies. We demonstrate that our sensor could offer unique access to large regions of uncharted parameter space of vector B-L dark matter, with projected sensitivities that could advance existing limits by several orders of magnitude over a broad range of frequencies.

Figures (4)

• Figure 1: Conceptual perspective view of our proposed setup for sensing forces from dark matter (dashed line) using a silica plate (sensor) with a high-reflectivity coating. The sensor is levitated with a (vertical) optical beam and its motion along $\hat{\bf{x}}$ and $\hat{\bf{y}}$ is trapped independently via pairs of counterpropagating lasers which are focused using cylindrical lenses. Shown here is the final stage (blue-grey suspended plate) of the seismic isolation system to which the lenses are rigidly fixed. The perceived motion of the sensor is that relative to the plate. Not shown here are the first (defocusing) lenses on the horizontal and vertical beams, as well as photodetectors and/or windows necessary to extract non-reflected light from our system. The distances $\bar{x}\pm x$ of each surface to the nearest focus (dotted lines in the $\hat{\bf{y}}$-direction) vary around the average $\bar{x}$. The sensor height $h$ is also shown. Rotation directions of the sensor around the $(\hat{\bf{x}},\hat{\bf{y}},\hat{\bf{z}})$-axes away from the orientation shown here are denoted $(\hat{\bf\theta},\hat{\bf \phi},\hat{\bf{\psi}})$.
• Figure 2: Comparison of both classical and quantum force noise spectra present in our setup for $m=0.2$ mg. Classical noise spectra remain identical for all trapping frequencies, while backaction (red) and shot noise (light blue) are plotted according to Eq. \ref{['eq:min_noise_SFF']}, i.e. are locally correct for any given $\text{f}=\omega_{\rm DM}/(2\pi)$. We ignore the effect of possible additional heating due to the trapping beams above 5 kHz, as quantum noises dominate in this region. The coating's vibrational noise (dark green) and blackbody radiation (orange) are subdominant to quantum noises at all frequencies, while residual gas (dark blue) is subdominant above $5$ Hz by design. Below this point, the seismic noise (solid green) dominates, while vertical beam-induced horizontal recoil noise (lilac) is coincidentally nearly identically to quantum noises at the quantum/seismic transition. For comparison, we show in dashed green the seismic noise for the 3-stage seismic isolation system (dashed green) used in Ref. Deshpande:2024bul. We finally show that levitation is preferable to suspension of our sensor since its noise (dashed, assuming a typical damping rate and a string temperature of $T_s \approx$ 100 K) is significantly larger. See Sec. \ref{['sec:noises']} for further discussion.
• Figure 3: Projected sensitivies to $g_{\rm B-L}$ for our setup for sensors with mass $m=0.2$ mg (green line), and $m=0.8$ g (orange), both with a four stage seismic isolation system. The solid lines indicate the reach assuming the maximum laser power of each of the $\hat{\bf x}$ directed lasers is $P_L = 70$ kW such that the in the case of the 0.8 g sensor the system is only tuned to reach SQL up to $f_{\rm DM} = 270$ Hz. The dashed line indicates the reach if sufficient power were available to reach SQL at every frequency. Note that we ignore the small step-like behaviour between each separate data-taking frequency bin. For comparison to current experiments we show LIGO bounds, as well as bounds from fifth force searches with MICROSCOPE (purple) and Eöt-Wash (blue). For further discussion of these bounds see Sec. \ref{['sec:results']}.
• Figure 4: Projected sensitivies to $y_{n}$ for our setup for $m=0.2$ mg (green line), and $m=0.8$ g (orange), both with a four stage seismic isolation system. The solid lines indicate the reach assuming the maximum laser power of each of the $\hat{\bf x}$ directed lasers is $P_L = 70$ kW such that for the 0.8 g sensor the system is only tuned to reach SQL up to $f_{\rm DM} = 270$ Hz. The dashed line indicates the reach if sufficient power were available to reach SQL at every frequency. We also show projected sensitivities from a scanning strategy focused solely on the region $f\in[50~\text{Hz},500~\text{Hz}]$ (red) in order to maximise the reach of unexplored parameter space. Note we ignore the small step-like behaviour between each separate data-taking frequency bin. For comparison to current experiments we show bounds from fifth force searches with MICROSCOPE (purple) and Eöt-Wash (blue). For further discussion of these bounds see Sec. \ref{['sec:results']}.