We experimentally demonstrate stable trapping of a permanent magnet sphere above a lead superconductor, in vacuum pressures of 4 × 10 −8 mbar. The levitating magnet behaves as a harmonic oscillator, with frequencies in the 4-31 Hz range detected, and shows promise to be an ultrasensitive acceleration sensor. We directly apply an acceleration to the magnet with a current carrying wire, which we use to measure a background noise of ∼ 10 −10 m/ √ Hz at 30.75 Hz frequency. With current experimental parameters, we find an acceleration sensitivity of S 1/2 a = 1.2 ± 0.2 × 10 −10 g/ √ Hz, for a thermal noise limited system. By considering a 300 mK environment, at a background helium pressure of 1 × 10 −10 mbar, acceleration sensitivities of S 1/2 a ∼ 3 × 10 −15 g/ √ Hz could be possible with ideal conditions and vibration isolation. To feasibly measure with such a sensitivity, feedback cooling must be implemented.The ability to detect extremely small forces and accelerations has a diverse range of applications within science and technology, including uses in magnetic resonance force microscopy 1-3 , detection of gravitational waves 4 , measuring short range Casimir forces 5 , gravimetry 6 and measuring gravitational fields of small source masses 7 . Such systems could also be utilized to test fundamental physics, such as testing collapse models which predict extensions to standard quantum mechanics 8,9 , as well as searching for non-Newtonian corrections to our understanding of gravity 10 . State-of-the-art force sensors, based on clamped mechanical resonators, have reached force sensitivities of ∼ 10 −21 N/ √ Hz 11 in cryogenic environments and ∼ 10 −17 N/ √ Hz 12,13 at room temperature. These mechanical resonators are limited in their sensitivity due to the dissipation to the clamping losses. A natural solution to avoid such losses is to levitate the resonator. Indeed, optically levitated dielectric particles 14-20 have shown high quality factors, with force sensitivities of ∼ 10 −20 N/ √ Hz achieved 21,22 and short range interactions between dielectric surfaces and the particle investigated 23,24 . For acceleration measurements, the best performances are obtained with massive systems; impressive sensitivities of < 10 −15 g/ √ Hz in the LISA Pathfinder in-flight experiment 25 have been demonstrated. For commercial uses, superconducting gravimeters, which levitate a centimeter sized type-II superconductor, have achieved acceleration sensitivities of ∼ 10 −10 g/ √ Hz 26 . In principle, magnetically levitated oscillators could provide the most environmentally isolated oscillators; the trapping mechanism is passive, whereas other levitation systems require active fields which limit the Qfactor and the temperature attainable 27 . Due to this promise, magnetically levitated oscillators have been proa) Electronic posed as a route to observing macroscopic superposition states 28-31 , as well as for force and inertial sensing 32 , magnetometry 33 and gravimetry 31 . Experimentally, diamagnetic microparticles have been levitate...
Starting from an idea of S.L. Adler [1], we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥ 10 −26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤ 10 −20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ∼ 10 −21 .
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