We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micro-magnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three dimensional trapping with quality factors around one million and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degree of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultra-sensitive metrology.

We theoretically show that a magnet can be stably levitated on top of a punctured superconductor sheet in the Meissner state without applying any external field. The trapping potential created by such induced-only superconducting currents is characterized for magnetic spheres ranging from tens of nanometers to tens of millimeters. Such a diamagnetically levitated magnet is predicted to be extremely well isolated from the environment. We therefore propose to use it as an ultrasensitive force and inertial sensor. A magnetomechanical read-out of its displacement can be performed by using superconducting quantum interference devices. An analysis using current technology shows that force and acceleration sensitivities on the order of 10 −23 N/ √ Hz (for a 100 nm magnet) and 10 −14 g/ √ Hz (for a 10 mm magnet) might be within reach in a cryogenic environment. Such unprecedented sensitivities can be used for a variety of purposes, from designing ultra-sensitive inertial sensors for technological applications (e.g. gravimetry, avionics, and space industry), to scientific investigations on measuring Casimir forces of magnetic origin and gravitational physics.Most modern force and inertial sensors are based on the response of a mechanical oscillator to an external perturbation. Such sensors find applications in a wide range of domains: from measuring accelerations in smartphones and automobiles [1] in present-day technology, to being used on the cutting edge of research for magnetic resonance force microscopy [2][3][4], mass spectroscopy at the single-molecule level [5], and measuring gravitational and Casimir physics at short distances [6][7][8][9][10]. Most force and inertial sensors are based on microfabricated clamped mechanical oscillators, whose sensitivity is ultimately limited by mechanical dissipation due to material and clamping losses [11]. Levitation offers a clear route to avoiding these loss mechanisms. Indeed, the most precise commercial accelerometers are based on levitated systems: the superconducting gravimeter, which levitates a superconducting centimeter-sized sphere in the mixed superconducting state to achieve acceleration sensitivities of 3.1 × 10 −10 g/ √ Hz [12], and the MicroStar accelerometer, which electrostatically levitates a centimeter-sized cube in space leading to 10 −11 g/ √ Hz [13]. In research, different levitated systems are being explored to push into unexplored levels of sensitivity. This includes the demonstration of a record force sensitivity of 4 × 10 , and matter-wave interferometry using clouds of atoms with a sensitivity of ∼ 10 −9 g/ √ Hz [26,27].In this Letter, we aim at exploiting the exquisite isolation from the environment provided by magnetic levitation in a cryogenic environment. In particular, we propose an all-magnetic passively-levitated sensor that can be scaled over a broad range of sizes and is predicted to reach unprecedented ultra-high force and inertial sensitivities of 10 −23 N/ √ Hz and 10 −14 g/ √ Hz, respectively. We show that a spherical particle with a per...

We theoretically show that, despite Earnshaw's theorem, a non-rotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein-de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.According to the Einstein-de Haas and the Barnett effect [1,2], a change in the magnetization of an object is accompanied by a change in its rotational motion. In particular, if the magnetic moment of a magnet is varied by a single Bohr magneton, it must rotate with an angular frequency /I about the magnetic moment axis to conserve angular momentum. Here I is its moment of inertia about the rotation axis. For a Cobalt sphere of radius R, this corresponds to a frequency /I ≈ 2π × 10 6 Hz/(R[nm]) 5 , where R[nm] is the radius in nanometers. This clear manifestation of the quantum spin origin of magnetization, as prescribed by the gyromagnetic relation, is hence boosted at the nanoscale [3][4][5].In this Letter, we explore the role of the quantum spin origin of magnetization in magnetic levitation. Earnshaw's theorem [6], very relevant in this context, prevents magnetic levitation of a non-rotating ferromagnet in a static magnetic field. The theorem can be circumvented by mechanically spinning the magnet, as neatly demonstrated by the Levitron [7][8][9][10], which is a magnetic top of a few centimeters. At the single atom level, magnetic trapping with static fields is also possible by exploiting the fast Larmor precession of its quantum spin [11,12]. In this case, the atom is, from the mechanics point of view, a point particle without rotational degrees of freedom. A magnetic nanoparticle lies in between the Levitron and the atom as both its rotational degrees of freedom and the quantum spin origin of magnetization have to be accounted for. Can a non-rotating magnetic nanoparticle, despite Earnshaw's theorem, be stably levitated with static magnetic fields?We show in this Letter that this is the case. In particular, we predict two stabilization mechanisms that crucially rely on the quantum spin origin of the magnetic moment. At low (large) magnetic fields, the Einstein-de Haas effect (the Larmor precession of its magnetic moment) stabilizes levitation. These results are obtained by deriving a quadratic Hamiltonian which describes the linearized dynamics of the degrees of freedom of the magnet (center-of-mass motion, rotation, and magnetization dynamics) around the equilibrium point. We further show that in the absence of thermal fluctuations, the equilibrium state exhibits both quantum entanglement and squeezing of its degrees of freedom. As discussed in the co...