Measuring gravity with milligram levitated masses (2303.03545v2)

Abstract: Gravity differs from all other known fundamental forces since it is best described as a curvature of spacetime. For that reason it remains resistant to unifications with quantum theory. Gravitational interaction is fundamentally weak and becomes prominent only at macroscopic scales. This means, we do not know what happens to gravity in the microscopic regime where quantum effects dominate, and whether quantum coherent effects of gravity become apparent. Levitated mechanical systems of mesoscopic size offer a probe of gravity, while still allowing quantum control over their motional state. This regime opens the possibility of table-top testing of quantum superposition and entanglement in gravitating systems. Here we show gravitational coupling between a levitated sub-millimeter scale magnetic particle inside a type-I superconducting trap and kg source masses, placed approximately half a meter away. Our results extend gravity measurements to low gravitational forces of attonewton and underline the importance of levitated mechanical sensors. Specifically, at a frequency of 26.7 Hz, a mass of 0.4 mg and showing Q-factors in excess of 10$^7$, we obtained a force noise of 0.5 $fN\sqrt{Hz}$ . We simultaneously detect the other 5 rotational and translational degrees of freedom.

• The paper introduces a superconducting setup that levitates milligram masses to detect gravity at sub-attonewton sensitivity.
• It achieved a damping linewidth of 2.9 µHz and a quality factor of 9.13×10⁶, enabling precise gravitational coupling measurements.
• The technique isolates environmental vibrations, paving the way for testing gravitational decoherence and quantum gravity theories.

Measuring Gravity with Milligram Levitated Masses

The paper "Measuring gravity with milligram levitated masses" introduces a novel approach to gravitational measurement using a magnetically levitated sub-milligram test mass, achieving sub-attonewton force sensitivity. This work extends the field of table-top gravitational experiments, which traditionally have employed larger masses, into a domain involving significantly smaller test masses. The experimental setup leverages the unique properties of a type-I superconducting trap to minimize decoherence, enabling precise gravitational measurements at low thermal noise levels within a cryogenic environment.

Summary of Key Findings and Methodology

The authors demonstrate gravitational coupling by employing a superconducting setup, wherein a magnetic particle is levitated within a trap formed of tantalum cooled to below 100 mK. A source mass of 2.4 kg is used to generate a gravitational signal. The superconducting setup, along with the use of magnetically levitated particles, allows for the measurement of gravitational forces at the attonewton level. The setup includes a SQUID-based detection mechanism to quantify the particle's displacement due to gravitational interaction.

Notable Results:

• Measurement of gravitational coupling at forces as low as 30 aN.
• A damping linewidth as narrow as 2.9 µHz, corresponding to a quality factor (Q) of around 9.13 × 10^6 for the z-mode of the particle.
• Isolation of environmental vibrations through the use of advanced multi-stage mechanical isolation within a cryostat mounted on a large concrete block, ensuring highly stable conditions for sensitive measurements.

Implications and Future Directions

The paper presents significant implications for the ongoing effort to test the intersection of quantum mechanics and general relativity. By pushing gravitational measurement into the mesoscopic regime, it offers a platform to experimentally probe decoherence mechanisms and wave function collapse theories such as the Continuous Spontaneous Localization (CSL) model and the Di{o}si-Penrose model at lower mass scales.

Theoretical Implications:

• The work suggests potential tests of gravitational-induced decoherence and deviations from standard gravitational models.
• It opens pathways to investigating the quantum state manipulation of gravitationally interacting systems.

Practical Implications:

• The demonstrated approach could lead to the development of ultrasensitive sensor technologies based on magnetomechanics with applications in gravimetry and fundamental physics research.

Future work could expand this framework by utilizing different sources or experimenting with even smaller source masses, potentially approaching the Planck mass scale. Such developments could allow the examination of gravitational fields sourced from quantum superpositions, thereby experimentally exploring the quantum aspects of gravity.

Conclusion

This paper contributes a significant methodological advance in precision gravitational measurements, achieved by employing levitated mechanical systems under low thermal noise and high isotropy conditions. It provides a basis for further exploration into the quantum mechanical nature of gravity and the implementation of magnetomechanically-based sensors in precise metrological applications. Through these advancements, the paper enhances our experimental prowess in probing fundamental physical laws and refining the bridge between quantum theory and general relativity.