Single-Spin Magnetomechanics with Levitated Micromagnets

Selective loading of a micrometer-scale particle into a magneto-gravitational trap by sublimation-activated release

In this paper, we discuss a technique for selectively loading a particle into a magneto-gravitational trap using the sublimation of camphor to release particles from a tungsten probe tip directly into the trapping region. This sublimation-activated release (SAR) loading technique makes use of micropositioners with tungsten probe tips, as well as the relatively fast rate of sublimation of camphor at room temperature, to selectively load particles having diameters ranging from 8 to 100 μm or more. The advantages of this method include its ability to selectively load unique particles or particles in limited supply, its low loss compared to alternative techniques, the low speed of the particle when released, and the versatility of its design, which allows for loading into traps with complex geometries. SAR is demonstrated here by loading a particle into a magneto-gravitational trap, but the technique could also be applicable to other levitated optomechanical systems.

Magnon-Skyrmion Hybrid Quantum Systems: Tailoring Interactions via Magnons

Coherent and dissipative interactions between different quantum systems are essential for the construction of hybrid quantum systems and the investigation of novel quantum phenomena. Here, we propose and analyze a magnon-skyrmion hybrid quantum system, consisting of a micromagnet and nearby magnetic skyrmions. We predict a strong-coupling mechanism between the magnonic mode of the micromagnet and the quantized helicity degree of freedom of the skyrmion. We show that with this hybrid setup it is possible to induce magnon-mediated nonreciprocal interactions and responses between distant skyrmion qubits or between skyrmion qubits and other quantum systems like superconducting qubits. This work provides a quantum platform for the investigation of diverse quantum effects and quantum information processing with magnetic microstructures.

Magnomechanically induced transparency and tunable slow-fast light via a levitated micromagnet

In this paper, we theoretically investigate the magnomechanically induced transparency (MIT) phenomenon and slow-fast light propagation in a microwave cavity-magnomechanical system which includes a levitated ferromagnetic sphere. Magnetic dipole interaction determines the interaction between the photon, magnon, and center of mass motion of the cavity-magnomechanical system. As a result, we find that apart from coupling strength, which has an important role in MIT, the levitated ferromagnetic sphere's position provides us a parameter to manipulate the width of the transparency window. In addition, the control field's frequency has crucial influences on the MIT. Also this hybrid magnonic system allows us to demonstrate MIT in both the strong coupling and intermediate coupling regimes. More interestingly, we demonstrate tunable slow and fast light in this hybrid magnonic system. In other words, we show that the group delay can be adjusted by varying the control field's frequency, the sphere position, and the magnon-photon coupling strength. These parameters have an influence on the transformation from slow to fast light propagation and vice versa. Based on the recent experimental advancements, our results provide the possibility to engineer hybrid magnonic systems with levitated particles for the light propagation, and the quantum measurements and sensing of physical quantities.

Measurement of the Earth Tides with a Diamagnetic-Levitated Micro-Oscillator at Room Temperature

The precise measurement of the gravity of Earth plays a pivotal role in various fundamental research and application fields. Although a few gravimeters have been reported to achieve this goal, miniaturization of high-precision gravimetry remains a challenge. In this work, we have proposed and demonstrated a miniaturized gravimetry operating at room temperature based on a diamagnetic levitated micro-oscillator with a proof mass of only 215 mg. Compared with the latest reported miniaturized gravimeters based on microelectromechanical systems, the performance of our gravimetry has substantial improvements in that an acceleration sensitivity of 15  μGal/sqrt[Hz] and a drift as low as 61  μGal per day have been reached. Based on this diamagnetic levitation gravimetry, we observed Earth tides, and the correlation coefficient between the experimental data and theoretical data reached 0.97. Some moderate foreseeable improvements can develop this diamagnetic levitation gravimetry into a chip size device, making it suitable for mobile platforms such as drones. Our advancement in gravimetry is expected to facilitate a multitude of applications, including underground density surveying and the forecasting of natural hazards.

Scanning Nitrogen-Vacancy Magnetometry of Focused-Electron-Beam-Deposited Cobalt Nanomagnets

Focused-electron-beam-induced deposition is a promising technique for patterning nanomagnets in a single step. We fabricate cobalt nanomagnets in such a process and characterize their content, saturation magnetization, and stray magnetic field profiles by using a combination of transmission electron microscopy and scanning nitrogen-vacancy (NV) magnetometry. We find agreement between the measured stray field profiles and saturation magnetization with micromagnetic simulations. We further characterize magnetic domains and grainy stray magnetic fields in the nanomagnets and their halo side-deposits. This work may aid in the evaluation of Co nanomagnets produced through focused electron-beam-induced deposition for applications in spin qubits, magnetic field sensing, and magnetic logic.

Fast quantum interference of a nanoparticle via optical potential control

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 108 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10-10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.

High-Q Magnetic Levitation and Control of Superconducting Microspheres at Millikelvin Temperatures

We report the levitation of a superconducting lead-tin sphere with 100  μm diameter (corresponding to a mass of 5.6  μg) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 Hz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6×10^{7}. We also demonstrate 3D magnetic feedback control of the motion of the sphere. The setup is housed in a dilution refrigerator operating at 15 mK. By implementing a cryogenic vibration isolation system, we can attenuate environmental vibrations at 200 Hz by approximately 7 orders of magnitude. The combination of low temperature, large mass, and high quality factor provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times.

Levitated Optomechanics with Meta-Atoms

We propose to introduce additional control in levitated optomechanics by trapping a meta-atom, i.e., a subwavelength and high-permittivity dielectric particle supporting Mie resonances. In particular, we theoretically demonstrate that optical levitation and center-of-mass ground-state cooling of silicon nanoparticles in vacuum is not only experimentally feasible but it offers enhanced performance over widely used silica particles in terms of trap frequency, trap depth, and optomechanical coupling rates. Moreover, we show that, by adjusting the detuning of the trapping laser with respect to the particle's resonance, the sign of the polarizability becomes negative, enabling levitation in the minimum of laser intensity, e.g., at the nodes of a standing wave. The latter opens the door to trapping nanoparticles in the optical near-field combining red and blue-detuned frequencies, in analogy to two-level atoms, which is of interest for generating strong coupling to photonic nanostructures and short-distance force sensing.

Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

Levitated Micromagnets in Superconducting Traps: A New Platform for Tabletop Fundamental Physics Experiments

Magnetically levitated microparticles have been proposed as mechanical sensors with extreme sensitivity. In particular, micromagnets levitated above a superconductor can achieve very low levels of dissipation and thermal noise. In this paper, we review recent initial experiments and discuss the potential for using these systems as sensors of magnetic fields and rotational motion, as well as possible applications to fundamental physics.

Diamagnetic Composites for High-Q Levitating Resonators

Levitation offers extreme isolation of mechanical systems from their environment, while enabling unconstrained high-precision translation and rotation of objects. Diamagnetic levitation is one of the most attractive levitation schemes because it allows stable levitation at room temperature without the need for a continuous power supply. However, dissipation by eddy currents in conventional diamagnetic materials significantly limits the application potential of diamagnetically levitating systems. Here, a route toward high-Q macroscopic levitating resonators by substantially reducing eddy current damping using graphite particle based diamagnetic composites is presented. Resonators that feature quality factors Q above 450 000 and vibration lifetimes beyond one hour are demonstrated, while levitating above permanent magnets in high vacuum at room temperature. The composite resonators have a Q that is >400 times higher than that of diamagnetic graphite plates. By tuning the composite particle size and density, the dissipation reduction mechanism is investigated, and the Q of the levitating resonators is enhanced. Since their estimated acceleration noise is as low as some of the best superconducting levitating accelerometers at cryogenic temperatures, the high Q and large mass of the presented composite resonators positions them as one of the most promising technologies for next generation ultra-sensitive room temperature accelerometers.

Spin-Controlled Quantum Interference of Levitated Nanorotors

We describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particle's three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology.

Position Measurement of a Levitated Nanoparticle via Interference with Its Mirror Image

Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of 1.7×10^{-12}  m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.

Imaging-based feedback cooling of a levitated nanoparticle

Imaging-based detection of the motion of levitated nanoparticles complements a widely used interferometric detection method, providing a precise and robust way to estimate the position of the particle. Here, we demonstrate a camera-based feedback cooling scheme for a charged nanoparticle levitated in a linear Paul trap. The nanoparticle levitated in vacuum was imaged using a complementary metal-oxide semiconductor (CMOS) camera system. The images were processed in real-time with a microcontroller integrated with a CMOS image sensor. The phase-delayed position signal was fed back to one of the trap electrodes, resulting in cooling by velocity damping. Our study provides a simple and versatile approach applicable for the control of low-frequency mechanical oscillators.

Precision Calibration of the Duffing Oscillator with Phase Control

The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to an external excitation. When changing the amplitude or frequency of the external excitation, a sudden jump in the response function reveals the nonlinear dynamics prominently. However, this bistability leaves part of the full response function unobserved, which limits the precise measurement of the system parameters. Here, we exploit the often unknown fact that the response of a Duffing oscillator with nonlinear damping is a unique function of its phase. By actively stabilizing the oscillator's phase we map out the full response function. This phase control allows us to precisely determine the system parameters. Our results are particularly important for characterizing nanoscale resonators, where nonlinear effects are observed readily and which hold great promise for next generation of ultrasensitive force and mass measurements. We demonstrate our approach experimentally with an optically levitated particle in high vacuum.

Enhancing Gravitational Interaction between Quantum Systems by a Massive Mediator

In 1957 Feynman suggested that the quantum or classical character of gravity may be assessed by testing the gravitational interaction due to source masses in superposition. However, in all proposed experimental realizations using matter-wave interferometry, the extreme weakness of this interaction requires pure initial states with extreme squeezing to achieve measurable effects of nonclassical interaction for reasonable experiment durations. In practice, the systems that can be prepared in such nonclassical states are limited to small masses, which in turn limits the strength of their interaction. Here we address this key challenge-the weakness of gravitational interaction-by using a massive body as an amplifying mediator of gravitational interaction between two test systems. Our analysis shows that this results in an effective interaction between the two test systems that grows with the mass of the mediator, is independent of its initial state and, therefore, its temperature. This greatly reduces the requirement on the mass and degree of delocalization of the test systems and, while still highly challenging, brings experiments on gravitational source masses a step closer to reality.

On the Significance of Interferometric Revivals for the Fundamental Description of Gravity

We show that an interaction between a harmonic oscillator and a two-level test mass (TLTM) mediated by a local operations and classical communication (LOCC) channel produces a signature that in (D. Carney et al., PRX Quantum 2, 030330 (2021)) is claimed to be exclusively reserved for channels that can transmit quantum information. We provide an explicit example based on a measurement-and-feedback channel, explain where the proof of Carney et al. fails, discuss to what degree setups of this type can test the nature of the gravitational interaction and remark on some fundamental implications that an LOCC model of gravity may have in black hole physics.

Intensive Cavity-Magnomechanical Cooling of a Levitated Macromagnet

We describe microwave cavity-magnomechanical center-of-mass cooling of a levitated magnetic sphere. The standing magnetic component of the electromagnetic wave within a microwave cavity exerts a dynamical force on a magnonic crystalline sphere and dissipates the mechanical energy through scattering into the magnon mode. The coupling is established by the magnetic dipole interaction and enriched by the collective spin motion. We find that the final cooled phonon occupation achieved is an intensive property independent of the mass and size of the sphere, in contrast to standard optomechanical couplings. This is of particular importance for testing quantum mechanics with macroscopic objects.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Surpassing the Energy Resolution Limit with Ferromagnetic Torque Sensors

We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit. We find that the energy resolution limit, pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Spin-Mechanics with Nitrogen-Vacancy Centers and Trapped Particles

Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser light radiation pressure, have had tremendous success. In particular, the motion of levitating objects can be manipulated at the quantum level thanks to their very high isolation from the environment under ultra-low vacuum conditions. To enter the quantum regime, schemes using single long-lived atomic spins, such as the electronic spin of nitrogen-vacancy (NV) centers in diamond, coupled with levitating mechanical oscillators have been proposed. At the single spin level, they offer the formidable prospect of transferring the spins' inherent quantum nature to the oscillators, with foreseeable far-reaching implications in quantum sensing and tests of quantum mechanics. Adding the spin degrees of freedom to the experimentalists' toolbox would enable access to a very rich playground at the crossroads between condensed matter and atomic physics. We review recent experimental work in the field of spin-mechanics that employ the interaction between trapped particles and electronic spins in the solid state and discuss the challenges ahead. Our focus is on the theoretical background close to the current experiments, as well as on the experimental limits, that, once overcome, will enable these systems to unleash their full potential.

Ground-State Cooling of Levitated Magnets in Low-Frequency Traps

We present a ground-state cooling scheme for the mechanical degrees of freedom of mesoscopic magnetic particles levitated in low-frequency traps. Our method makes use of a binary sensor and suitably shaped pulses to perform weak, adaptive measurements on the position of the magnet. This allows us to precisely determine the position and momentum of the particle, transforming the initial high-entropy thermal state into a pure coherent state. The energy is then extracted by shifting the trap center. By delegating the task of energy extraction to a coherent displacement operation, we overcome the limitations associated with cooling schemes that rely on the dissipation of a two-level system coupled to the oscillator. We numerically benchmark our protocol in realistic experimental conditions, including heating rates and imperfect readout fidelities, showing that it is well suited for magnetogravitational traps operating at cryogenic temperatures. Our results pave the way for ground-state cooling of micron-scale particles.

Search for Composite Dark Matter with Optically Levitated Sensors

Results are reported from a search for a class of composite dark matter models with feeble long-range interactions with normal matter. We search for impulses arising from passing dark matter particles by monitoring the mechanical motion of an optically levitated nanogram mass over the course of several days. Assuming such particles constitute the dominant component of dark matter, this search places upper limits on their interaction with neutrons of α_{n}≤1.2×10^{-7} at 95% confidence for dark matter masses between 1 and 10 TeV and mediator masses m_{ϕ}≤0.1  eV. Because of the large enhancement of the cross section for dark matter to coherently scatter from a nanogram mass (∼10^{29} times that for a single neutron) and the ability to detect momentum transfers as small as ∼200  MeV/c, these results provide sensitivity to certain classes of composite dark matter models that substantially exceeds existing searches, including those employing kilogram- or ton-scale targets. Extensions of these techniques can enable directionally sensitive searches for a broad class of previously inaccessible heavy dark matter candidates.