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Optically active spin defects in solids are leading candidates for quantum sensing and quantum networking. Recently, single spin defects were discovered in hexagonal boron nitride (hBN), a layered van der Waals (vdW) material. Due to its two-dimensional structure, hBN allows spin defects to be positioned closer to target samples than in three-dimensional crystals, making it ideal for atomic-scale quantum sensing, including nuclear magnetic resonance (NMR) of single molecules. However, the chemical structures of these defects remain unknown, and detecting a single nuclear spin with an hBN spin defect has been elusive. In this study, we created single spin defects in hBN using $^{13}$C ion implantation and identified three distinct defect types. We observed both $S=1$ and $S=1/2$ spin states within a single hBN spin defect, with only the $S=1/2$ states showing strong hyperfine interactions with nearby $^{13}$C nuclear spins. For the first time, we demonstrated atomic-scale NMR and coherent control of individual nuclear spins in a vdW material. By comparing experimental results with density-functional theory calculations, we propose chemical structures for these spin defects. Our work advances the understanding of single spin defects in hBN and provides a pathway to enhance quantum sensing using hBN spin defects with nuclear spins as quantum memories., Comment: 9 pages, 5 figures

Levitated optomechanics, a rapidly expanding field that employs light to monitor and manipulate the mechanical motion of levitated objects, is increasingly relevant across physics, engineering, and other fields. This technique, which involves levitating micro- and nano-scale objects in a vacuum where they exhibit high-quality motion, provides an essential platform for precision measurements. Noted for their ultra-high sensitivity, levitated particles hold potential for a wide range of real-world applications. This perspective article briefly introduces the principle of optical levitation and the dynamics of levitated particles. It then reviews the emerging applications of levitated particles in ultrasensitive force and torque measurements, acceleration and rotation sensing, electric and magnetic field detection, scanning probe microscopy, localized vacuum pressure gauging, acoustic transduction, and chemical and biological sensing. Moreover, we discuss the present challenges and explore opportunities to minimize and integrate levitation systems for broader applications. We also briefly review optomechanics with ion traps and magnetic traps which can levitate particles in high vacuum without laser heating., Comment: Perspective article, 20 pages, 12 figures

Optical refrigeration of solids with anti-Stokes fluorescence has been widely explored as a vibration-free cryogenic cooling technology. A minimum temperature of 87 K has been demonstrated with rare-earth ion doped crystals using optical refrigeration. However, the depletion of the upper-lying energy levels in the ground state manifold hinders further cooling to below liquid nitrogen (LN$_2$) temperatures, confining its applications. In this work, we introduce a Purcell enhanced optical refrigeration method to circumvent this limitation. This approach enhances the emission of high energy photons by coupling to a nearby nanocavity, blue shifting the mean emission wavelength. Such Purcell enhanced emission facilitates cooling starting from a lower energy level in the ground state manifold, which exhibits a higher occupation below LN$_2$ temperatures. Using our experimentally measured optical coefficients, our theoretical analysis predicts a minimum achievable temperature of 38 K for a Yb$^{3+}$:YLiF$_{4}$ nanocrystal near a cavity under realistic conditions. The proposed method is applicable to other rare-earth ion doped materials and semiconductors, and will have applications in creating superconducting and other quantum devices with solid-state cooling., Comment: 6 pages

Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.

Optically addressable spin defects in three-dimensional (3D) crystals and two-dimensional (2D) van der Waals (vdW) materials are revolutionizing nanoscale quantum sensing. Spin defects in one-dimensional (1D) vdW nanotubes will provide unique opportunities due to their small sizes in two dimensions and absence of dangling bonds on side walls. However, optically detected magnetic resonance of localized spin defects in a nanotube has not been observed. Here, we report the observation of single spin color centers in boron nitride nanotubes (BNNTs) at room temperature. Our findings suggest that these BNNT spin defects possess a spin $S=1/2$ ground state without an intrinsic quantization axis, leading to orientation-independent magnetic field sensing. We harness this unique feature to observe anisotropic magnetization of a 2D magnet in magnetic fields along orthogonal directions, a challenge for conventional spin $S=1$ defects such as diamond nitrogen-vacancy centers. Additionally, we develop a method to deterministically transfer a BNNT onto a cantilever and use it to demonstrate scanning probe magnetometry. Further refinement of our approach will enable atomic scale quantum sensing of magnetic fields in any direction., Comment: 9 pages, 5 figures

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate below $10^{-5}$ Torr. Impressively, we have driven a nanodiamond to rotate up to 20 MHz ($1.2 \times 10^{9}$ rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena., Comment: 11+13 pages; 5+8 figures

A levitated non-spherical nanoparticle in a vacuum is ideal for studying quantum rotations and is an extremely sensitive torque and force detector. It has been proposed to probe fundamental particle-surface interactions such as the Casimir torque and the rotational quantum vacuum friction, which require it to be driven to rotate near a surface at sub-micrometer separations. Here, we optically levitate a silica nanodumbbell in a vacuum at about 430 nm away from a sapphire surface and drive it to rotate at GHz frequencies. The relative linear speed between the tip of the nanodumbbell and the surface reaches 1.4 km/s at a sub-micrometer separation. The rotating nanodumbbell near the surface demonstrates a torque sensitivity of $(5.0 \pm 1.1) \times 10^{-26} {\rm NmHz}^{-1/2}$ at room temperature. Moreover, we levitate a nanodumbbell near a gold nanograting and use it to probe the near-field intensity distribution beyond the optical diffraction limit. Our numerical simulation shows it is promising to detect the Casimir torque between a nanodumbbell and a nanograting., Comment: 4 figures

We experimentally study the interference of dipole scattered light from two optically levitated nanoparticles in vacuum, which present an environment free of particle-substrate interactions. We illuminate the two trapped nanoparticles with a linearly polarized probe beam orthogonal to the propagation of the trapping laser beams. The scattered light from the nanoparticles are collected by a high numerical aperture (NA) objective lens and imaged. The interference fringes from the scattered vector light for the different dipole orientations in image and Fourier space are observed. Especially, the interference fringes of two scattered light fields with polarization vortex show the {\pi} shift of the interference fringes between inside and outside the center region of the two nanoparticles in the image space. As far as we know, this is the first experimental observation of the interference of scattered vector light fields from two dipoles in free space. This work also provides a simple and direct method to determine the spatial scales between optically levitated nanoparticles by the interference fringes.

We experimentally observe the dipole scattering of a nanoparticle using a high numerical aperture (NA) imaging system. The optically levitated nanoparticle provides an environment free of particle-substrate interaction. We illuminate the silica nanoparticle in vacuum with a 532 nm laser beam orthogonally to the propagation direction of the 1064 nm trapping laser beam strongly focused by the same high NA objective used to collect the scattering, which results in a dark background and high signal-noise ratio. The dipole orientations of the nanoparticle induced by the linear polarization of the incident laser are studied by measuring the scattering light distribution in the image and the Fourier space (k-space) as we rotate the illuminating light polarization. The polarization vortex (vector beam) is observed for the special case, when the dipole orientation of the nanoparticle is aligned along the optical axis of the microscope objective. Our work offers an important platform for studying the scattering anisotropy with Kerker conditions.

We report an experimental observation of a record-breaking ultra-high rotation frequency about 6 GHz in an optically levitated nanoparticle system. We optically trap a nanoparticle in the gravity direction with a high numerical aperture (NA) objective lens, which shows significant advantages in compensating the influences of the scattering force and the photophoretic force on the trap, especially at intermediate pressure (about 100 Pa). This allows us to trap a nanoparticle from atmospheric to low pressure ($10^{-3}$ Pa) without using feedback cooling. We measure a highest rotation frequency about 4.3 GHz of the trapped nanoparticle without feedback cooling and a 6 GHz rotation with feedback cooling, which is the fastest mechanical rotation ever reported to date. Our work provides useful guides for efficiently observing hyperfast rotation in the optical levitation system, and may find various applications such as in ultrasensitive torque detection, probing vacuum friction, and testing unconventional decoherence theories., Comment: 5 pages, 5 figures

We theoretically and experimentally study the effect of the coupled-resonator-induced transparency in the Michelson interferometer with the dual-recycled configuration, which is equivalent to the adjustable coupled resonator. The coupling strength, corresponding to the splitting of the reflection spectrum and associated with the width of the coupled-resonator-induced transparent window,can be controlled by adjusting the arm lengths, i.e., the relative phase of the interference arms on the 50/50 beam splitter. Thus, this tunability of the coupling strength can be very fast, and the absorptive and dispersive properties can be effectively controlled. This work provides a new system to coherently control and storage optical field.

We experimentally study a protocol of using the broadband high frequency squeezed vacuum to detect the low-frequency signal. In this scheme, the lower sideband field of the squeezed light carries the low frequency modulation signal and the two strong coherent light fields are applied as the bichromatic local oscillator in the homodyne detection to measure the quantum entanglement of the upper and lower sideband for the broadband squeezed light. The power of one of the local oscillators for detecting the upper sideband can be adjusted to optimize the conditional squeezing in the low frequency regime by subtracting the photocurrent of the upper sideband field of the squeezed light from that of the low sideband field. By means of the quantum correlation of the upper and lower sideband for the broadband squeezed light, the low frequency signal beyond the standard quantum limit is measured. This scheme is appropriate for enhancing sensitivity of the low frequency signal by the aid of the broad squeezed light, such as gravitational waes detection, and does not need directly produce the low frequency squeezing in the optical parametric process.