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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.
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This chapter is intended as a pedagogical introduction to the dynamics of optically levitated nanoparticles with a focus on the study of single particle thermodynamics. Much of the work studying thermodynamics with nano- and micro-particles has taken place in liquid, and this chapter will avoid reviewing this impressive body of work, focussing instead on studies of thermodynamics with nanoparticles levitated in a gas. For a recent literature review we refer the reader to Gieseler & Millen Entropy 20, 326 (2018). The authors will discuss extensions into the quantum regime where relevant throughout the chapter.
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 $10^{-23}text{N}/sqrt{text{Hz}}$ (for a 100 nm magnet) and $10^{-14}g/sqrt{text{Hz}}$ (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 (i.e. gravimetry, avionics, and space industry), to scientific investigations on measuring Casimir forces of magnetic origin and gravitational physics.
Electron and nuclear spins associated with point defects in insulators are promising systems for solid state quantum technology. While the electron spin usually is used for readout and addressing, nuclear spins are exquisite quantum bits and memory systems. With these systems single-shot readout of nearby nuclear spins as well as entanglement aided by the electron spin has been shown. While the electron spin in this example is essential for readout it usually limits nuclear spin coherence. This has set of the quest for defects with spin-free ground states. Here, we isolate a hitherto unidentified defect in diamond and use it at room temperature to demonstrate optical spin polarization and readout with exceptionally high contrast (up to 45%), coherent manipulation of an individual excited triplet state spin, and coherent nuclear spin manipulation using the triplet electron spin as a meta-stable ancilla. By this we demonstrate nuclear magnetic resonance and Rabi oscillations of the uncoupled nuclear spin in the spin-free electronic ground state. Our study demonstrates that nuclei coupled to single metastable electron spins are useful quantum systems with long memory times despite electronic relaxation processes.
In this comment, we agree with the formulas derived in Refs. [1,2] but show that the results are not due to interference between spatially separated states of the center of mass of a mesoscopic harmonic oscillator.
We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite of the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.
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