Acceleration sensing with magnetically levitated oscillators above a superconductor

Abstract

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...

Ultralow Mechanical Damping with Meissner-Levitated Ferromagnetic Microparticles

“…While higher quality factors have been reported in several systems, both in optically levitated nanoparticles [21] and in clamped ultrastressed membranes [14], values exceeding 10 7 are not easily obtained. Compared to previous attempts of magnetically levitating a ferromagnetic particle above a superconductor [34,35] we obtain quality factors 3 orders of magnitude higher.…”

“…This suggests that different levitation methods, such as Paul traps [28][29][30][31], or magnetic traps [32][33][34][35] could outperform optical levitation in applications requiring the lowest possible noise level. In particular, magnetic levitation appears very promising because of the unique combination of two properties: a completely passive trapping by static magnetic fields, and the possibility of using SQUIDs to detect the motion with ultralow power dissipation.…”

“…Magnetic levitation can be implemented using diamagnetic [32,33] or superconducting particles [27] in external static fields, or ferromagnetic particles above superconductors [34,35]. Interestingly, these systems have been proposed not only for ultrasensitive force and inertial sensing [34,36], but also to test quantum mechanics in currently inaccessible regimes [4], to enable quantum technologies such as quantum magnetomechanics [27] and acoustomechanics [37] and for ultrasensitive magnetometry [11]. In particular, it has been suggested that a levitated micromagnet can overcome the standard quantum limitations to the resolution per unit volume of a magnetometer [11,38].…”

Testing Fundamental Physics by Using Levitated Mechanical Systems

“…Furthermore the trap frequencies can be quite low, in the Hz range. Three possible schemes can be devised: levitation of a diamagnetic insulating nanoparticle with strong external field gradients [49,50], levitation of a superconducting particle using external currents [8,[51][52][53], and levitation of a ferromagnetic particle above a superconductor [54].…”

“…Then dipole force becomes so strong to form a deep optical trap and optical fields can be used for controlling single particle motions again, which gave rise to the development of the new research field levitated optomechnaics [4], based on early pioneering work by Arthur Ashkin (Nobel Prize in Physics in 2018) [5] and already then in close relation to the then soon to be called cold atomic and optical physics. By now the field of levitated large-mass particle systems has seen the implementation of other than optical forces for trapping and manipulation, namely time-varying electrical fields in Paul traps [6] and magnetic traps [7], sometimes including superconductors [8]. All such technical developments give rise to the hope to soon perform experiments with truly macroscopic quantum systems, outperforming existing paradigms of large-mass matterwave interferometry [9].…”