Dark matter searches with levitated sensors

Despite compelling cosmological evidence for its abundance in the universe, the identification of the nature of dark matter (DM) remains an open challenge.^1,2 While the subject has seen much discourse, to date, no experiment has been able to conclusively prove a dark matter event has been detected with high statistical significance. Theoretical predictions motivate a wide dark matter parameter space, and methods and strategies devised for detection depend strongly on the mass scale of the proposed candidate.

Large-scale experiments have thus far been concentrated on certain well-motivated candidates (see Sec. II); however, due to limitations either on energy resolution or bandwidth, and as parameter space is ruled out in these areas, with no signal due to dark matter having been observed, the following question arises: how else might we probe the fundamental structure and properties of this type of matter?

A novel avenue for dark matter searches in the mid- and the low-mass sector is the use of optomechanical sensors.^3–8 Levitated optomechanics in particular (illustrated in Fig. 1) promises excellent experimental control and manipulation in both translational and rotational degrees of freedom.^9–13 Trapped and motion-cooled silica nanospheres,^14,15 or embedded spin systems such as diamond crystals with nitrogen-vacancy centers, can be used to perform highly precise measurements of accelerations, forces, and momentum transfers, through relative phases arising in interferometric setups^16–20 as well as through decoherence effects. In this work, we discuss how these quantum technologies may benefit dark matter searches.

The anticipated sensitivity of a given experimental setup to any particular dark matter candidate is strongly model-dependent. A potential dark matter signal is governed by a few crucial parameters. The candidate's mass sets the kinematics of interaction and hence local number density and relative velocity with respect to Earth of its theorized particles in the galactic halo.^21–23 Additionally, any predicted non-gravitational couplings will further affect interactions with standard model particles.²⁴ 

In the standard Lambda cold dark matter model (⁠$ΛCDM$⁠), formulated on the assumption that the universe is, in an approximate sense, flat on large scales, isotropic and homogeneous, dark matter is predicted to make up $∼26.8 %$ of the mass-energy content of the universe. This dark matter is non-relativistic, non-baryonic, weakly interacting, and expected to consist of massive particles. A formerly strong contender surfacing naturally through supergravity and supersymmetric models are weakly interacting massive particles (WIMPs), assumed to interact with standard model particles through the gravitational and electroweak force. However, in the predicted mass range of 1 GeV–100 TeV, no such particles have been detected so far, and many WIMP models have been excluded by experiments.²⁵ 

While the standard cosmological model has been successful in explaining a variety of astrophysical observations, it also suffers shortcomings, a prominent one being the statistically significant disagreement between theoretically derived and experimentally measured values of the Hubble constant. Among many such deviations,²⁶ discrepancies like the aforementioned open the field of possible dark matter models.

An alternative model that mimics the behavior of CDM at larger scales but exhibits vastly different phenomenology at small mass scales supposes the existence of ultralight bosonic dark matter (ULDM) with wave-like behavior. Oscillations of such dark matter waves give rise to time-dependent variations of the electron to proton mass ratio, and fundamental constants such as the fine structure constant, both of which are readily measured with atomic clocks. Additionally, a lower limit on the mass of fermionic dark matter $mDM,f≳ 100 eV$ is imposed by the Tremaine–Gunn bound.²⁷ 

Motivated by the expected experimental signal and for ease of discussion, we will split the particulate candidates broadly into two categories. If the number density is sufficiently high (occurring for bosonic dark matter masses $mχ ≲ 1 eV$⁠), then the field can be approximately described by a Bose–Einstein condensate, exhibiting wave-like behavior and coherence over a timescale set by the natural frequency of the field. For candidates with masses larger than $∼ 1 eV$⁠, however, the interactions will be impulse-like in nature, with a momentum transfer dependent on the mass of the candidate.

Introducing lighter mass dark matter candidates into the standard model can often be achieved through the addition of a single ultralight field, commonly in the form of a spin 0 scalar or pseudo-scalar field, or a spin 1 vector or axial-vector field.²⁸ The choice of these specific spin values is informed by theoretical models and observational constraints. Higher spin values, such as spin 2 and above, introduce significant complexities in dark matter models, often leading to theoretical challenges and inconsistencies, particularly in their coupling and interaction with gravitational fields.^29,30 In reference to Fig. 2, these candidates typically lie in the blue-shaded $≲ 1 eV$ mass range. The interaction mechanism of these fields with standard model particles dictates the experimental observables, which may include variations in fundamental constants, spin torque coupling, electromagnetic effects, or dark matter-induced accelerations.

These fields are often treated as having monochromatic oscillations due to their coherent wave-like nature within a narrow frequency range, arising from their extremely light mass.³¹ The term “monochromatic” in this context refers to this narrow energy spread. Despite the diversity of the possible experimental observables, certain induced matter effects, such as differential accelerations in materials with different nuclear compositions, are detectable with levitated sensors. Both scalar and vector fields can couple to standard model nucleons, making levitated mechanical sensors of varying material composition well-suited for narrow-band searches for these dark matter candidates (for an expanded discussion, see Sec. III).

For a given local mass density (⁠$ρ ∼ 0.3 GeV/cm3$⁠), heavier dark matter candidates (in the $>1 eV$ mass range as shown in Fig. 2) have a lower number density, ruling out wave-like behavior due to insufficient density. Their interactions with standard model particles are impulse-like in nature, leading to energy deposition and recoil of the target nucleus. Typically, dark matter interactions are inferred from this energy deposition, observable through atomic excitation or scintillation. However, two issues arise for such candidates: first, the momentum transfer p during the interaction is small (⁠$p=mχ vχ$⁠, with $vχ$ representing the velocity of dark matter candidates, assumed to be non-relativistic), leading to a requirement for highly sensitive detection thresholds. Second, the rarity of these recoils—attributed to the low local number density and theorized small interaction cross sections—necessitates large target sizes for feasible experimental timeframes. To address these challenges, large-scale noble element detectors are employed to exploit the advantage of size,²⁵ while small mechanical sensors are utilized for their low detection thresholds.²⁴ 

The roots of levitated optomechanics trace back to the pioneering work of Arthur Ashkin in 1971 with the development of optical tweezers and their application to the levitation of a dielectric particle in vacuum.³² In recent years, the field has rapidly matured and the quantum ground state of the center-of-mass motion has been reached in one and two dimensions.^10–12,33

Levitated optomechanics^9,34 is a very appealing field to employ for dark matter searches. Experiments are typically performed in ultrahigh vacuum (with gas pressures as low as $10−11 mbar$⁠),³⁵ thus suppressing the Brownian motion noise from collisions with ambient gas. Levitated systems interact predominantly with the optical, electric, or magnetic fields employed to trap, control, and measure their motion, as well as any residual gas molecules. As they are largely isolated from the environmental sources of noise, they offer unparalleled force sensitivities, down to zeptoNewton scales and below.¹⁹ 

Another notable advantage of the levitated systems is that the motional modes (⁠$x, y ,and z$⁠) for the 3D center-of-mass motion lie along a Cartesian axial frame, allowing simultaneous probing of all the components of an applied external force, and determination of its precise orientation. It should be emphasized that although the small size of levitated sensors relative to standard noble element detectors may imply reduced coupling between dark matter and the oscillators, this may be compensated for, especially by the ability for directional detection and, depending on the candidate, additional enhancement factors in the cross section due to coherent scattering.

Optical levitation has been the most explored technique thus far. Here, silica nanospheres of diameter $70–200 nm$ have been trapped with a mass of $≈ 10−18–10−16 kg$ and oscillation frequencies on the order of $30–300 kHz$⁠. These dielectric nanoparticles are levitated in optical tweezer traps obtained via tightly focusing laser beams: typically, a Gaussian laser beam is tightly focused by a high numerical aperture (NA) lens to form a diffraction-limited beam focus. The nanoparticles are then attracted to the beam focus by a gradient force, which ultimately traps them.

Free-space versus cavity optomechanics: two distinct approaches are widely used within optical levitation for control: (i) with active control, time-dependent “feedback” forces (usually electric) are applied to damp the motion along the $x, y,and z$ axes allowing quantum cooling regimes to be achieved in 1D “free-space”^11,12 and (ii) with passive control, the tweezer trap is coupled to an optical cavity comprising of a pair of highly reflective mirrors. The resultant coupling of the motions to the optical mode of the cavity has provided a powerful method for cooling and read-out, allowing quantum ground state cooling regimes both in 1D¹⁰ and 2D.³³ 

In the latter case, the motion is detected via the cavity mode light that is transmitted through the cavity, then interfered with a strong reference beam via a technique termed homodyne or heterodyne detection.

In the former case, the $x, y, z$ motions are detected in real-time interferometrically by measuring the interference between the light scattered from the particle and the light used to illuminate it. This causes modulations of the propagating light, which are detected using photodiodes, converting this to a voltage modulation. Calibration of this voltage signal gives a real-time measurement of the particle's position.³⁶ For non-spherical particles, their rotational motion modifies the polarization of the scattered light, which can also be measured.³⁷ 

In both cases, Fourier transformation of the time signal to the frequency domain provides information on the particle's oscillation frequency, temperature, and damping. Once a steady state is achieved, the power spectral density (PSD) is a standard tool of analysis.

The minimum detectable force in levitated optomechanics is comparable to the background thermal noises (such as the Brownian noise from background gas) that heat the particle's motion. A widely used expression for the minimum force is readily obtained³⁸  $Fmin=Sff b=2 kB m Γ TCM b$⁠, where m is the mass of the oscillator, $kB$ is Boltzmann's constant, $Γ$ is the damping rate determined by the active or passive damping method employed, and $TCM$ is the center-of-mass temperature. The parameter b is the measurement bandwidth, which in levitated experiments is effectively the inverse of the experimental integration time. A simple reading of this expression reveals the surprising fact that quantum cooling is unimportant for force sensitivity: the product $Γ TCM$ is constant since $TCM ∝ Γ−1$⁠. Hence, some of the highest force sensitivities to date have been demonstrated near $TCM ∼ 300 K$⁠, i.e., with modest cooling, used simply to stabilize levitation.¹⁹ 

Nevertheless, a goal for many experiments is to reach quantum regimes where quantum coherent effects, possibly in the multi-mode and multi-particle regimes, offer further enhancements. In addition, cooling remains important for sensing using correlations between motional modes.³⁸ 

The standard quantum limit (SQL) of displacement sensing is a key goal for non-levitated and levitated optomechanics. For the harmonic oscillator modes of the mechanical motion, their zero point fluctuation $xzpf=ℏ/(2 m ωx)$ sets a fundamental limit to displacement sensing. However, any realistic sensing must, in addition, allow for the measurement disturbance. For optical sensing, employing a weaker optical probe enhances the effect of quantum shot noise due to the random arrival of the photons; conversely, using a stronger optical probe reduces the effect of shot noise but enhances the back action noise (from photon recoil in free-space experiments or dynamical coupling to the cavity mode for cavity-based optomechanics). Minimizing the combined effect of shot noise and back action noise sets the so-called standard quantum limit for displacement sensing. To date, measurements within about $20 %$ of the SQL have been achieved in a levitated setup.¹¹ 

It is nevertheless still possible to go beyond the SQL by employing squeezed light modes arising from the coupled cavity-mechanical motion dynamics (ponderomotive squeezing)³⁹ or by directly using a squeezed source of light as a probe.⁴⁰ As forces are measured via the displacements, these advances are relevant to force sensitivity.

The types of forces typically detected via levitated sensors are constant, static forces; impulse, “kick”-like forces; and harmonic forces, oscillating at a particular frequency. A more recent study also investigates the measured effect of a directed, stochastic force.³⁸ How these forces are measured depends upon the type of force and the length of interaction. A pictorial representation of the particle interaction for each force, and the experimental signals to be measured as a result, can be seen in Fig. 3.

A constant force results in a change in the probability distribution of the position of the particle, i.e., a shift in its mean position.

For an impulse-like event, the particle experiences a transfer of momentum over a time much shorter than its oscillation period, resulting in a sudden increase in amplitude of its oscillations. These short, transient interactions are, hence, considered temporally.

When the interaction time is longer than the oscillation period, it is instead best to study the dynamics in the frequency domain, through changes in spectral densities such as the PSD, where random fluctuations due to residual gas and photon scattering are averaged over. In the presence of a harmonic force, a sharp “delta” peak appears in the PSD at the frequency of the harmonic oscillations, in addition to the (usually broader) peak at the trap frequency. The height of the sharp peak is dependent on the size of the force. For a stochastic broadband force, the force operates over a wide range of frequencies and results in an increase in the height of the PSD, with the increase dependent on the size of the force. However, when this stochastic force is directional, additional information can be extracted by considering the correlations induced via the cross-correlation mechanical spectra. This is discussed further in Sec. IV.

Decoupling from the environment enables levitated oscillators to exhibit high Q factors, making them excellent force sensors, with a force sensitivity of $4.34 zN/Hz1/2$ having been measured experimentally with an optically levitated nanoparticle.¹⁹ 

While optical levitation through the use of a high-NA lens has achieved the highest force sensitivity, the size, and material used for the test particle are limited. The size of the particle in a high-NA optical tweezer is limited by the increased scattering force with an increased size to the point that the particle can no longer be stably trapped. The possible materials that can be used are limited due to absorption of the high-intensity light used to levitate the particle. This absorption results in the increase in internal temperature at high vacuum as the gas is no longer present in the chamber to thermalize the levitated particle. This can result in internal temperatures up to 1000 K (Ref. 41) and lead to the melting of the nanoparticle.⁴² 

However, the size range of possible particles that can be levitated is expanded by utilizing gravito-optical traps,^43–45 or trapping via electric^46–48 or magnetic fields.^49–52 These techniques allow the levitation of micron-sized spheres,^16–18 and this large mass $∼ 10−6–10−9 g$ has enabled a measured acceleration sensitivity of $9×10−12 g/Hz1/2$⁠.⁵³ The only requirement for electric field levitation is a specific charge-to-mass ratio determined by the trap design. Hence, there is significantly more freedom in the choice of material for the levitated object, allowing for higher densities and use of materials with unique properties, for example, NV centers.⁵⁴ For electrical and magnetic trapping, the oscillation frequencies can be as low as a few Hz up to approximately tens of kilohertz.

The capacity to confine particles with substantially concentrated mass, thereby enhancing the coupling potential, is especially beneficial for bosonic ULDM searches.⁵⁵ Diamagnetically levitated micromechanical oscillators have been proposed to investigate ULDM, utilizing the coupling to the $B−L$ charge (baryon number minus lepton number).⁵⁶ This study predicts improved limits to the $gB−L$ coupling constant by an order of magnitude compared to previous results, and sensitivity to $gB−L ∼ O(10−25)$ in the frequency range of 0.1–100 Hz (see Table I).

A levitated particle benefits from a high mass concentration, which couples well to the dark matter candidate while being small enough that interactions with a light candidate can be considered coherent across the particle.

Additionally, while a single mechanical oscillator has maximum sensitivity at a single resonant frequency, an array of levitated particles, facilitated through the use of electrodynamic traps,^57,58 allows for probing of a much wider ultralight dark matter spectral range. This would allow for a broadband search for dark matter of this type, increasing interaction cross section and reducing the time needed to conduct a search of this type.

Non-spherical, asymmetric particles have also been investigated. Through levitation, this kind of particle is free to rotate around its principle axes and can be driven by circularly polarized light to rotate at $∼GHz$ frequencies.^59–61 These ultrahigh rotation frequencies make these devices excellent torque sensors⁶² with a torque sensitivity of $(4.2 ± 1.2)×10−27 N m/Hz1/2$ having been achieved. Combining all the different systems mentioned before means that the levitated optomechanical toolbox is able to investigate a wide range of phenomena with high sensitivity.

Unlike atomic systems, macroscopic particles also possess an internal bulk temperature. This internal temperature can be measured via changes in the particle's refractive index,⁴¹ changes in fluorescent light,^63–65 or microwave resonances.⁶⁶ This internal temperature can also be cooled by solid-state laser refrigeration to as low as $130 K$ (Refs. 63 and 64) with further enhancements proposed to reach cryogenic temperatures.⁶⁷ 

A variety of searches for different dark matter candidates have already been undertaken using levitated optomechanics. In general, interest in lower-mass candidates has grown as parameter space for direct detection of weakly interacting massive particles (WIMPs) is further excluded by large-scale noble element detectors.²⁵ Levitated optomechanical systems possess concentrations of mass ranging approximately from $1010 to 1015$ atomic masses, significantly enhancing the probability of interaction with select dark matter candidates.

The first realization of an experimental search for dark matter with levitated particles utilized not an interaction with galactic dark matter candidates, but millicharged dark matter bound to standard model particles.⁶⁸ Control of the net charge of a levitated object can be obtained through the use of UV light or corona discharge.⁶⁹ The neutralization of a microsphere has enabled the possibility of excluding partial charges larger than $10−4 e (GeV–TeV)$⁠, marking a two-order-of-magnitude enhancement compared to the state of the art of the time.

Further dark matter searches have been undertaken, looking for momentum transfers provided by self-interacting composite dark matter particles (nuggets), which interact with standard model nucleons via a light mediator through a Yukawa-like potential.⁷⁰ This specific model benefits from the microsphere being a highly localized collection of nucleons enhancing the interaction cross section and experimentally excluding new parameter space, with $σχ n (cm2) ∼ 10−28$ for $103$–$104 GeV$ dark matter mass. Impulse sensitivity can be increased by considering levitated nanoparticles at the standard quantum limit, when $Δp=ℏm ω0/2$⁠, where m is the mass of the oscillation and $ω0$ the oscillation frequency.⁷¹ As mentioned, working with levitated nanoparticles also offers enhancement via coherent scattering across the size of the nanoparticle (⁠$≈15$ nm),¹⁴ enabling the investigation into low mass particle dark matter with projected sensitivity of $σSI (cm2) ∼ 10−30 (mχ ∼ 0.1 –100 MeV)$ for a 10 by 10 array. Given this increase in cross section, levitated nanoparticles have also been proposed, in conjunction with the use of scintillator panels instrumented with Silicon Photomultiplier (SiPM) arrays, for investigating heavy sterile neutrinos (another dark matter candidate), through examination of the products of radioactive decays and reconstructing neutrino mass.⁷² This method has a projected sensitivity of $|Ue4|2 ∼ 10−4–10−6$ $(for mχ ∼ 10 keV to 1 MeV$⁠) for 1000 nanospheres. Both approaches utilize the advantages that come with the levitation of multiple particles. Levitated sensors are becoming increasingly sensitive to impulse kicks to such an extent that they are approaching the ability to resolve individual gas collisions.^11,73

Levitated ferromagnets in a superconducting trap have been shown to be excellent magnetometers, surpassing the energy resolution limit and demonstrating the highest reported sensitivity in terms of bare energy per unit volume.⁷⁴ This level of sensitivity to magnetic fields has been suggested for the study of axions and axion-like dark matter via its coupling to the electron spins of the ferromagnetic magnetometer with a projected sensitivity of $gaee ∼ O(10−14) (mχ∼ 10−13 to 10−18 eV)$⁠. Levitated superconductors in a magnetic trap have also been proposed for investigating axions and dark photons via perturbations of the levitated superconductor's equilibrium position due to the oscillating magnetic field caused by the ultralight dark matter.⁷⁵ For axions, the projected sensitivity is $gaγ (GeV−1) ∼ O(10−10) (ma∼ 10−12 to 10−14 eV)$ and the projection for dark photons $ϵ ∼ O(10−8)(mA′ ∼ 10−12 to 10−14 eV)$⁠. Magnetically levitated objects have also been proposed and utilized to investigate dark energy, ruling out the basic chameleon model as a candidate for dark energy.^76,77

An extremely useful feature of levitated probes for dark matter searches is that the measured signals have a straightforward geometrical interpretation. For a spherical particle, the typical signals measured correspond to the particle's motional normal modes in a Cartesian frame (⁠$x, y, z$⁠). This simple description is useful when considering dark matter interactions. A dark matter interaction should exhibit a known directionality deriving from the Earth's motion relative to the galactic reference frame.⁷⁸ This directionality enables discrimination against background events that either (a) interact in a direction not expected or (b) exhibit no directionality at all.

Levitated optomechanics is, thus, uniquely suited to searches looking to measure $x, y, z$ components of an external force. However, it is essential that the $x, y, z$ motional modes are accurately aligned with the frame $Xlab, YLab, ZLab$ of the laboratory detectors.

For a free-space scheme, where the particle is held in a tweezer trap, the tweezer axes must be carefully aligned with the detectors as illustrated in Fig. 4. Any misalignment will result in a spurious (uninteresting) correlation between the normal modes that masks more interesting, externally induced correlations between the modes.

For cavity-based schemes, the strong coupling between the cavity mode and the motion, as well as the sensitivity of cavity-based detection, is extremely advantageous for quantum cooling: the first quantum ground state experiments were reported using a cavity setup¹⁰ in 1D, corresponding to the cavity axis. However, the alignment between the orientation of the mechanical normal modes and the laboratory detection axes is complicated by the back-action from the cavity optical mode. A study of the cavity-mediated coupling of the mechanical modes showed that cross heating due to mode hybridization could significantly affect 1D quantum cooling experiments.⁷⁹ 

Hybridization between the mechanical modes results in a geometric rotation of the normal mode⁸⁰ orientation relative to the lab frame. If both modes are well coupled to the cavity, one mode rotates so it becomes a dark mode, orthogonal to the cavity field, so cannot be cooled. The other mode, in contrast, rotates into alignment with the cavity, forming a bright mode that is strongly cooled. This is illustrated in Fig. 4. A study of 2D quantum cooling of the $x−y$ plane⁸⁰ found it was only possible in a “Goldilocks” zone, where cavity coupling is strong enough for quantum ground state cooling, but not strong enough for the formation of dark/bright modes. A recent experiment³³ in the Goldilocks parameter regime achieved 2D quantum cooling.

Another recent experimental study investigated the back-action induced rotation of the particle's normal modes.⁸¹ A particular trapping position where the back-action induced rotation is canceled by an interference with the trapping field⁷⁹ was demonstrated. At this point, externally induced correlations are exposed since the misalignment caused by these (parameter-sensitive) mode rotations is eliminated. Levitated nanospheres in a Fabry–Perot cavity have been proposed to investigate charged dark matter bound to ordinary matter via the cavity's output light.⁸² 

In a recent study,³⁸ it was proposed and experimentally verified that there is a technique that is well adapted to detect—in the steady state—a dark matter candidate that appears as a source of stochastic white noise, but from a preferred direction. Such a source might normally be difficult to distinguish from the ordinary thermal noises that heat the particle, especially if the source is weak.

Figure 5 illustrates this concept. The standard approach to detect the effect of thermal noises uses PSDs $Sxx(ω)=⟨|x(ω)|2⟩andSyy(ω)=⟨|y(ω)|2⟩$ where the angled brackets denote an average over an ensemble of measured spectra. The area under the curve yields the temperature of the x and y modes, respectively. The behavior of the PSDs is qualitatively similar whether the bath is uncorrelated or not: the directional force appears simply as yet another thermal source. There is a quantitative effect but it may easily be confused with a change in multiple other thermal heating sources present in the experiment. A directional signal can also be easily masked by uncertainties in directional heating rates that arise from slight particle asymmetries.

However, the signature of the cross-correlation spectrum $Sxy(ω)=⟨ x*(ω) y(ω) ⟩$ is unambiguous. As shown in Fig. 5(c), provided there are no misalignments between the laboratory detectors and the normal modes, an uncorrelated stochastic noise bath yields a zero cross-correlation spectrum. However, if the noise has a preferred direction, there is a distinctive spectral signature. Since $Sxy(ω)∝cos Ψsin Ψ ∝ sin 2Ψ$⁠, the spectra are sensitive to quadrant: their shapes flip for $±Ψ$⁠.

Cooling is important for the detection of cross-correlation spectra: in order to generate $x−y$ cross correlations, one requires that the damping rates $Γx,y ∼ |ωx−ωy|$⁠.³⁸ This is in sharp contrast to standard force sensing where the sensitivity is largely independent of the experimental cooling rate (see discussion of $Fmin$ in Sec. III).

Additionally, a directional signal due to dark matter will modulate yearly due to the Earth's movement through the galactic reference frame, resulting in a sign change in the correlation signal when the direction passes through $Ψ=0$⁠. This sign change (due to the changing direction of a directional stochastic noise source) has already been measured experimentally.³⁸ Hence, the correlations between different motional modes are potentially valuable as a discriminant in searching for directional dark matter signals.

In summary, the cross-correlation technique complements current methods. It offers a promising new approach to detect a dark matter signal that is not a simple harmonic force or a source of strong but infrequent recoils, but rather a source of white noise that may be missed with current methods. It might correspond to a stream of weak impacts, individually undetectable but frequent enough to generate correlations. Alternatively, it might correspond to a broadband spectrum of harmonic coherent sources, across a range of frequencies.

A recently popularized approach for direct searches for dark matter candidates, extending beyond the current experimental status of levitated optomechanics, is rooted in the creation of quantum superposition states. Novel experimental protocols using embedded single spins,⁸³ the typical example of one such physical system being nitrogen-vacancy centers in diamond crystals, may be utilized to induce a separation of the motional wavepacket of nanocrystals. Similarly, optical field couplings in trapped atom–nanoparticle hybrid systems,⁸⁴ or tunneling effects in ferrimagnetic nanoparticles can be explored to produce non-classical states.⁸⁵ 

Regardless of the choice of the physical system, the methodology for future matter–wave interferometric experiments is largely the same. Once the mesoscopic quantum system is initialized in a superposition of its center-of-mass motion and a state of the form $|ψ(t)⟩=(1/2)(|ψL(t)⟩+|ψR(t)⟩)$ has been created, with L and R symbolically representing left- and right-propagating wavepackets, it is often beneficial to keep the separation $Δ x$ between the superposed components constant during most of the experiment time. Relative phases $Δϕ$ accumulated between the arms of the superposition can finally be measured after the interferometer is closed. In quantum systems featuring embedded spins, the phases are particularly easily inferred from measurements performed solely on the spin states.

Stern–Gerlach interferometers based on spin-mechanical mesoscopic objects have been richly discussed in the context of general relativity and gravitational physics, where they have been proposed as sensors for gravitational waves, spacetime curvature,⁸⁶ tests of the equivalence principle,⁸⁷ and quantum gravity theories.^83,88 In addition to their suitability as detectors of fields, such classes of large mass interferometers have also been considered as detectors for elusive particles.^89–91 A possible advantage of quantum superposition sensors over classical sensors is the prospect of enhanced sensitivity,⁹² since quantum superposition sensors, harnessing the inherent quantum nature of the sensing object, may surpass the SQL.

In summary, we have presented a perspective on the prospect of employing levitated sensors for dark matter searches. Following an overview of select classes of dark matter models, we discussed the possibility of levitated free space and cavity-based large-mass systems being used for the detection of both ultralight and hidden-sector candidates, emphasizing the potential sensitivity enhancement of recently introduced cross-correlation techniques. We further highlighted theoretical proposals for future interferometric techniques, based on superpositions of massive levitated objects, for sensing certain types of dark matter through their scattering decoherence signatures as well as coherent phases accumulating between superposed components.

Table I summarizes the already sizable body of work in the literature, which includes both experimental results setting new limits, and projections for the sensitivity of future experiments. For instance, the search for hypothesized millicharged dark matter carrying electrical charge as conducted⁶⁸ with optically trapped nanoparticles has set new limits on their abundance by probing the mass to fractional charge parameter space. Capable of searching for electric charges as small as $10−4e$⁠, this experimental approach is uniquely suited to explore regions in the parameter space beyond the scope of present large-scale underground and accelerator experiments. This provides a strong motivation for further development of levitated sensors for dark matter searches. A similar experiment⁷⁰ looking for impulse-like signatures of composite dark matter candidates in the TeV mass regime has also placed novel limits on dark matter–neutron interactions and dramatically exceeded the sensitivity of prior searches.

Proposed future experiments for directional searches using optically trapped femtogram masses (or possibly arrays thereof) that exploit large enhancements in the cross section for spin-independent scattering due to coherent scattering of the dark matter candidates from the entire sensor, are expected to show increased sensitivity to dark matter masses below 1 GeV.¹⁴ Approaches capable of full momentum reconstruction may also be used to conduct searches for sterile neutrinos,⁷² possibly yielding novel limits to the mixing matrix element $|Ue4|2$⁠, an extended form of the famed Pontecorvo–Maki–Nakagawa–Sakata matrix, placing new constraints in the neutrino mass range $0.1–1 MeV$⁠.

Magnetically trapped micron-sized ferrimagnets have been proposed for probes of axion dark matter in the galactic halo model⁷⁴ in the mass regime $10−18–10−13 eV$⁠. Although current magnetometers are not yet able to surpass the bounds set by existing astrophysical observations and solar axion searches¹⁰⁵ for the coupling of axions to electrons, $gaee$⁠, the use of larger magnets is expected to offer comparable and potentially increased sensitivity. Levitated superconducting particles⁷⁵ have been studied for ultralight dark matter detection in mass regimes $4×10−15 ≲mχ ≲ 4×10−12 eV$ and they may be employed to constrain the dark photon coupling $ϵ$ and the axion–photon coupling $gaγ$⁠, with a predicted achievable sensitivity comparable to other laboratory probes. Diamagnetic levitated sensors with a changeable resonance frequency have been suggested for ultralight dark matter detection in a similar mass range of $10−16 ≲ mχ ≲ 10−13 eV$ for dark matter vector fields coupling to the standard model through baryon-minus-lepton number channels,⁵⁶ claiming a possible tenfold improvement in $gB−L$ limits.

Given the already experimentally demonstrated successes of levitated setups to place new constraints on dark matter parameter spaces as well as the exciting possibilities outlined by proposals for future experiments, quantum technologies based on large-mass levitated systems are able to probe regions beyond the capabilities of present-day large-scale experiments and offer strong complementary approaches to other dark matter searches.

E.K. would like to acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC: Grant No. EP/L015242/1) and an EPSRC Doctoral Prize Fellowship Grant (EP/W524335/1). M.T. would like to acknowledge funding by the Leverhulme Trust (RPG-2020-197). S.B. would like to acknowledge funding from the EPSRC (Grant Nos. EP/N031105/1 and EP/S000267/1) and Science and Technology Facilities Council (STFC; Grant No. ST/W006227/1). M.R., J.M.H.G., F.A., A.P., and P.F.B. acknowledge funding from the EPSRC and STFC via Grant Nos. EP/N031105/1, EP/S000267/1, EP/W029626/1, EP/S021582/1, and ST/W006170/1. C.G. would like to acknowledge STFC Grant No. ST/W006227/1 and additional support from the Cosmoparticle Initiative. J.H.I. and T.S.M. acknowledge funding from the EPSRC Grant No. EP/W029626/1.

The authors have no conflicts to disclose.

Eva Kilian: Conceptualization (lead); Investigation (equal); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Markus Rademacher: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Jonathan M. H. Gosling: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Julian H. Iacoponi: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Fiona Alder: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Marko Toroš: Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Antonio Pontin: Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Chamkaur Ghag: Supervision (equal). Sougato Bose: Conceptualization (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Tania S. Monteiro: Conceptualization (equal); Data curation (equal); Investigation (equal); Methodology (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). P. F. Barker: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.