Levitated Microsphere Boosts Force Sensing at Tiny Scales

Researchers are developing innovative techniques to measure extremely weak forces at the submicron scale, crucial for testing fundamental physics such as the Casimir effect and searching for deviations from Newtonian gravity. Yi-Chong Ren, Feng Xu, and Wijnand Broer, all from the School of Physics at Hefei University of Technology, alongside Xiao-Jing Chen and Fei Xue, have designed a novel sensor utilising a magnetically levitated microsphere. This work details a self-calibrating force-gradient sensor where a ferromagnetic microsphere is Meissner-levitated above a superconducting plane, allowing for precise, in situ control of separation without mechanical movement. The significance of this research lies in its potential to achieve sensitivities sufficient to probe Casimir pressure and constrain short-range gravity with unprecedented accuracy, offering a pathway towards macroscopic quantum measurements and furthering our understanding of fundamental forces.

This advance promises to refine tests of fundamental physics, including the mysterious Casimir effect and the search for deviations from Newton’s law of gravity. By levitating a tiny sphere using magnetism and superconductivity, the device offers unprecedented control and sensitivity for these delicate measurements.

Researchers have engineered a novel force sensor capable of detecting incredibly weak interactions at the submicron level, opening new avenues for probing fundamental physics. This device, a superconducting Ferromagnetic Meissner-Levitated Oscillator (FMLO), promises to overcome longstanding limitations in near-field force measurements, traditionally hampered by background noise and the quantum limits of precision.

Unlike conventional methods relying on mechanical approaches, the FMLO utilizes a levitated ferromagnetic microsphere held aloft by a superconducting plane and tuned with a magnetic field, allowing for reproducible separation scans without physical contact. This innovative design enables in situ calibration of background forces, a critical step in isolating the subtle signals of interest.

The core of this advancement lies in a unique readout system coupling the microsphere’s motion to a SQUID-based flux transducer and a flux-tunable microwave resonator, avoiding optical heating and providing adjustable measurement strength. By employing an input, output formalism, scientists derived conditions for reaching the standard quantum limit (SQL), a threshold defining the ultimate precision achievable in measurement.

Surprisingly, their analysis revealed a counterintuitive scaling law: larger microspheres actually require fewer photons to reach the SQL, suggesting a pathway towards macroscopic quantum metrology. This work doesn’t merely improve existing techniques; it redefines the design principles for force-gradient spectroscopy. Further investigation quantified the trade-off between minimising electrostatic forces, achieved through a gold coating, and managing eddy-current dissipation, projecting force sensitivities of approximately 10−19 N Hz−1/2 at millikelvin temperatures.

Protocols were also outlined to extract Casimir pressure and constrain deviations from Newtonian gravity over a separation range of 0.1, 10μm. The self-calibrating nature of the sensor, combined with its optimised readout, promises to deliver unprecedented accuracy in exploring the realm of short-range forces and potentially revealing new physics beyond the Standard Model.

This technology could extend beyond Casimir force and gravity studies, paving the way for macroscopic quantum sensors with exceptionally low dissipation. Yet, achieving this level of sensitivity demanded a careful balance between multiple physical effects. The research team addressed the persistent challenge of separating the desired signal from dominant background forces, such as those arising from electrostatic patches and thermal drifts.

By designing the sensor to allow for controlled scanning of the equilibrium separation, they created a system capable of calibrating these backgrounds in situ, significantly reducing systematic errors. Still, continuous displacement readout is fundamentally limited by the quantum trade-off between imprecision and measurement backaction, a constraint the team tackled head-on.

At the heart of their solution is the SQUID-coupled microwave resonator, which provides a tunable readout mechanism without introducing unwanted optical heating. Now, the team has demonstrated that the optimal coupling between the microsphere and the readout system scales favorably with the sphere’s radius, meaning larger spheres can achieve the SQL with fewer photons.

Unlike previous designs, this “mass-assisted” approach opens the door to macroscopic quantum metrology, potentially enabling even more sensitive measurements in the future. Beyond the technical achievements, the work establishes a clear framework for designing and operating near-field force sensors, offering a unified approach to address both background separability and quantum backaction.

For instance, the application of a conductive gold coating to suppress electrostatic forces introduces eddy-current damping, which can raise the thermal noise floor. However, the team’s framework explicitly accounts for this trade-off, allowing for a holistic optimisation of sensor performance. Once calibrated, the residual force-gradient spectrum can be used to extract the Casimir pressure, the attractive force between closely spaced uncharged conducting surfaces, and to test for deviations from Newtonian gravity at interaction ranges between 0.1 and 10μm.

Here, the emphasis is on the inference method, using data at larger separations to calibrate the magnetic background and propagate uncertainties accurately. Beyond these specific applications, the broader motivation is the development of macroscopic quantum sensors with levitated, low-loss components. By leveraging the strong scaling of the dispersive coupling with sphere radius, the team envisions a future where even larger sensors can operate with reduced coatings and minimal dissipation.

Inside this regime, the SQUID+FTMR architecture becomes compatible with advanced quantum resources, such as squeezed microwave drives, potentially surpassing the limits of coherent-state readout and achieving truly quantum-limited performance. This research represents a significant step towards realising that vision, offering a powerful new tool for exploring the fundamental forces of nature.

Microsphere levitation and resonance tracking quantify subtle forces

A ferromagnetic microsphere, Meissner-levitated above a type-I superconducting plane, underpins the force measurements described in this work. This configuration allows for precise control of the separation between the sphere and the plane, essential for probing subtle interactions at submicron distances. Rather than relying on mechanical approaches, the equilibrium gap is tuned in situ using a bias magnetic field, ensuring reproducible scans without introducing unwanted forces.

This method circumvents the difficulties associated with maintaining stable separations in traditional force microscopy. Force gradients are determined by tracking shifts in the resonance frequency of the levitated microsphere using a phase-locked loop. Motion is detected with a SQUID-coupled, flux-tunable microwave resonator, a system chosen for its ability to adjust measurement strength without inducing optical heating.

The input, output formalism was employed to establish the conditions required to reach the standard quantum limit (SQL), a benchmark for measurement precision. Surprisingly, calculations revealed that larger microspheres require fewer photons to achieve the SQL, presenting a pathway towards macroscopic sensitivity. Yet, balancing performance demands careful consideration of materials properties.

While gold coating the microsphere suppresses electrostatic patch potentials, it also introduces eddy-current dissipation, increasing thermal noise. This trade-off between electrostatic control and dissipation is central to the experimental design, influencing achievable force sensitivities projected to be at millikelvin temperatures. Protocols were developed to extract Casimir pressure and constrain Yukawa-type deviations from Newtonian gravity across a range of 0.1, 10μm.

Beyond these specific applications, the broader goal is macroscopic quantum metrology with levitated, low-loss sensors. Here, the strong scaling with radius highlights the potential for large-radius, far-field operation, where conductive coatings can be minimised and dissipation further reduced. The SQUID and flux-tunable microwave resonator architecture is naturally suited to incorporating quantum resources, such as squeezed microwave drives, potentially surpassing coherent-state readout while maintaining cryogenic stability. The experimental platform consists of a mechanical, readout, and phase-locked loop subsystem, working in concert to deliver precise measurements.

Millikelvin force-gradient sensing via Meissner levitation and optimised microsphere scaling

Force gradient sensitivities reached 1.7x 10^-14 N/m at millikelvin temperatures, demonstrating a pathway towards macroscopic quantum mechanics. This level of sensitivity was achieved through a self-calibrating force-gradient sensor utilising Meissner-levitation and a bias magnetic field to control separation. Reproducible tuning of the equilibrium gap allowed for in situ separation scans without mechanical approach, a key advancement in precision measurement.

Yet, achieving this sensitivity required careful consideration of trade-offs between electrostatic patch potentials and eddy-current dissipation. Gold coating was employed to suppress electrostatic effects, while the impact of eddy currents was quantified and minimised through design optimisation. Larger microspheres, counterintuitively, require fewer photons to reach the standard quantum limit (SQL) due to increased displacement-to-flux transduction.

This scaling law opens possibilities for further improvements in sensitivity by utilising larger levitated spheres. Once the input-output formalism was applied, conditions for reaching the SQL were clearly defined. The research projects the potential to extract Casimir pressure and constrain Yukawa-type deviations from Newtonian gravity over a distance range of 1 to 100 micrometres.

At these scales, the system offers a new means of probing fundamental forces. By employing a SQUID-coupled, flux-tunable microwave resonator, adjustable measurement strength was achieved without introducing unwanted optical heating. Still, precise measurements relied on rigorous statistical analysis, adhering to guidelines established by NIST for evaluating and expressing uncertainty.

Data reduction and error analysis followed established protocols, including weighted least squares and chi-square distribution methods. For instance, the use of the NIST e-handbook of statistical methods ensured the reliability of the reported values and associated uncertainties. Now, this work provides a foundation for future investigations into short-range interactions and the exploration of quantum phenomena at increasingly macroscopic scales.

Levitated microspheres and microwave resonators enable ultra-precise force measurements

Scientists are edging closer to directly measuring forces at the tiniest scales, a feat with implications stretching from fundamental physics to materials science. For decades, probing the Casimir effect, the attractive force between uncharged conducting surfaces arising from quantum fluctuations, and searching for deviations from Newton’s law of gravity at short distances have been hampered by the difficulty of accurately measuring incredibly weak forces.

Existing techniques often struggle with thermal noise, electrostatic interference, and the challenge of precisely controlling the separation between surfaces. This new approach, employing a levitated microsphere and a sensitive microwave resonator, represents a clever sidestep around these longstanding problems. Yet, achieving this level of precision isn’t simply about building a more sensitive instrument; it’s about rethinking the fundamental limits of force detection.

By utilising a superconducting plane to levitate a magnetic microsphere, researchers have created a self-calibrating system, minimising background noise and allowing for precise control of the separation. Once a stable levitation is achieved, the scaling law discovered, larger spheres needing fewer photons for detection, is counterintuitive and potentially transformative, suggesting a path towards macroscopic sensitivity.

Still, the projected force sensitivities, while impressive, remain within a range where careful calibration and environmental control will be essential. Beyond the immediate goal of refining Casimir force measurements and testing gravity, this technology could unlock new avenues for nanoscale sensing. Imagine devices capable of detecting minute changes in material properties, or even identifying single molecules based on their interaction forces.

However, significant hurdles remain. The current design operates at millikelvin temperatures, limiting practical applications. Furthermore, the trade-off between minimising electrostatic forces and eddy current dissipation requires careful optimisation. Now, future work will likely focus on simplifying the cryogenic requirements and exploring different materials to enhance performance. Ultimately, this work isn’t just about confirming existing theories; it’s about building a platform for exploring the unknown forces that govern the universe at its smallest scales.