Electron spin control of optically levitated nanodiamonds in vacuum

Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum

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 at pressures below 10-5 Torr. We have driven a nanodiamond to rotate up to 20 MHz (1.2 × 109 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.

Luminescence Thermometry Beyond the Biological Realm

As the field of luminescence thermometry has matured, practical applications of luminescence thermometry techniques have grown in both frequency and scope. Due to the biocompatibility of most luminescent thermometers, many of these applications fall within the realm of biology. However, luminescence thermometry is increasingly employed beyond the biological realm, with expanding applications in areas such as thermal characterization of microelectronics, catalysis, and plasmonics. Here, we review the motivations, methodologies, and advances linked to nonbiological applications of luminescence thermometry. We begin with a brief overview of luminescence thermometry probes and techniques, focusing on those most commonly used for nonbiological applications. We then address measurement capabilities that are particularly relevant for these applications and provide a detailed survey of results across various application categories. Throughout the review, we highlight measurement challenges and requirements that are distinct from those of biological applications. Finally, we discuss emerging areas and future directions that present opportunities for continued research.

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.

Nanothermometry in rarefied gas using optically levitated nanodiamonds

Heat transfer in gases in the continuum regime follows Fourier's law and is well understood. However, it has been long understood that in the subcontinuum, rarefied gas regime Fourier's law is no longer valid and various models have been proposed to describe heat transfer in these systems. These models have very limited experimental exploration for spherical geometries due to the difficulties involved. Optically levitated nanoparticles are presented as the ideal experimental system to study heat transfer in rarefied gases due to their isolation from their environment. Nanodiamonds with nitrogen-vacancy centers are used to measure temperature. As the pressure decreases so does the heat transfer to the rarefied gas and the nanodiamond temperature increases by over 200 K. These experiments demonstrate the utility of optically levitated nanoparticles to study heat transfer in any gas across a wide range of pressures. In the future, these measurements can be combined with models to empirically determine the energy accommodation coefficient of any gas.

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems

We study the enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric, with the two involved cavities being dissipatively coupled via the waveguide. The anti-PT symmetry may break down when a weak waveguide-mediated coherent coupling is introduced. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity measured by an enhancement factor is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the enhancement factor shows resistance to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength and has potential applications in high-precision measurements with systems involving Kerr-type nonlinearity.

Interaction between an Optically Levitated Nanoparticle and Its Thermal Image: Internal Thermometry via Displacement Sensing

We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal fluctuations of the dipole. The resulting force is orders of magnitude stronger than the thermal gradient force, and it strongly depends on the internal temperature of the nanoparticle for a particle-to-surface distance greater than two micrometers. We argue that it is experimentally feasible to use displacement sensing of a levitated nanoparticle in front of a surface as an internal thermometer in ultrahigh vacuum. Experimental access to the internal physics of a levitated nanoparticle in vacuum is crucial to understanding the limitations that decoherence poses to current efforts devoted to preparing a nanoparticle in a macroscopic quantum superposition state.

Highly sensitive gyroscope based on a levitated nanodiamond

A gyroscope is one of the core components of an inertial navigation system. Both the high sensitivity and miniaturization are important for the applications of the gyroscope. We consider a nitrogen-vacancy (NV) center in a nanodiamond, which is levitated either by an optical tweezer or an ion trap. Based on the Sagnac effect, we propose a scheme to measure the angular velocity with ultra-high sensitivity through the matter-wave interferometry of the nanodiamond. Both the decay of the motion of the center of mass of the nanodiamond and the dephasing of the NV centers are included when we estimate the sensitivity of the proposed gyroscope. We also calculate the visibility of the Ramsey fringes, which can be used for estimating the limitation of gyroscope sensitivity. It is found that the sensitivity ∼6.86×10^-7 r a d/s/H z can be achieved in an ion trap. As the working area of the gyroscope is extremely small (∼0.01~μm²), it could be made on-chip in the future.

Biocompatible Nanotomography of Tightly Focused Light

Tightly focusing a spatially modulated laser beam lays the foundations for advanced optical techniques, such as a holographic optical tweezer and deterministic super-resolution imaging. Precisely mapping the subwavelength features of those highly confined fields is critical to improving the spatial resolution, especially in highly scattering biotissues. However, current techniques characterizing focal fields are mostly limited to conditions such as under a vacuum and on a glass surface. An optical probe with low cytotoxicity and resistance to autofluorescence is the key to achieving in vivo applications. Here, we use a newly emerging quantum reference beacon, the nitrogen-vacancy (NV) center in the nanodiamond, to characterize the focal field of the near-infrared (NIR) laser focus in Caenorhabditis elegans (C. elegans). This biocompatible background-free focal field mapping technique has the potential to optimize in vivo optical imaging and manipulation.

Levitodynamics: Levitation and control of microscopic objects in vacuum

[Figure: see text].

Laser refrigeration of optically levitated sodium yttrium fluoride nanocrystals

Solid state laser refrigeration can cool optically levitated nanocrystals in an optical dipole trap, allowing for internal temperature control by mitigating photothermal heating. This work demonstrates cooling of ytterbium-doped cubic sodium yttrium fluoride nanocrystals to 252 K on average with the most effective crystal cooling to 241 K. The amount of cooling increases linearly with the intensity of the cooling laser and is dependent on the pressure of the gas surrounding the nanocrystal. Cooling optically levitated nanocrystals allows for crystals prone to heating to be studied at lower pressures than currently achievable and for temperature control and stabilization of trapped nanocrystals.

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.

Motional Dynamical Decoupling for Interferometry with Macroscopic Particles

We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations.

Single-Spin Magnetomechanics with Levitated Micromagnets

We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micromagnets 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 1×10^{6} 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 degrees 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 ultrasensitive metrology.

Quantum Acoustomechanics with a Micromagnet

We show theoretically how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state or to enter into the strong quantum coupling regime. The center of mass can thus be used to probe and manipulate an acoustic mode, thereby opening new possibilities for out-of-equilibrium quantum mesoscopic physics. Our results hold for experimentally feasible parameters and apply to levitated micromagnets as well as micromagnets deposited on a clamped nanomechanical oscillator.

Optomechanics with levitated particles

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro- and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent low-dissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 10⁶ amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing.

Room temperature "optical nanodiamond hyperpolarizer": Physics, design, and operation

Dynamic Nuclear Polarization (DNP) is a powerful suite of techniques that deliver multifold signal enhancements in nuclear magnetic resonance (NMR) and MRI. The generated athermal spin states can also be exploited for quantum sensing and as probes for many-body physics. Typical DNP methods require the use of cryogens, large magnetic fields, and high power microwave excitation, which are expensive and unwieldy. Nanodiamond particles, rich in Nitrogen-Vacancy (NV) centers, have attracted attention as alternative DNP agents because they can potentially be optically hyperpolarized at room temperature. Here, unraveling new physics underlying an optical DNP mechanism first introduced by Ajoy et al. [Sci. Adv. 4, eaar5492 (2018)], we report the realization of a miniature "optical nanodiamond hyperpolarizer," where ¹³C nuclei within the diamond particles are hyperpolarized via the NV centers. The device occupies a compact footprint and operates at room temperature. Instrumental requirements are very modest: low polarizing fields, low optical and microwave irradiation powers, and convenient frequency ranges that enable miniaturization. We obtain the best reported optical ¹³C hyperpolarization in diamond particles exceeding 720 times of the thermal 7 T value (0.86% bulk polarization), corresponding to a ten-million-fold gain in averaging time to detect them by NMR. In addition, the hyperpolarization signal can be background-suppressed by over two-orders of magnitude, retained for multiple-minute long periods at low fields, and deployed efficiently even to ¹³C enriched particles. Besides applications in quantum sensing and bright-contrast MRI imaging, this work opens possibilities for low-cost room-temperature DNP platforms that relay the ¹³C polarization to liquids in contact with the high surface-area particles.

Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous studies only focused on adiabatic limit, where the rotating frequency is much smaller than the spin frequency. Here we propose to use a levitated nano-diamond with a built-in nitrogen-vacancy (NV) center to study the dynamics and the geometric phase of a rotating electron spin without adiabatic approximation. We find that the transition between the spin levels appears when the rotating frequency is comparable to the spin frequency at zero magnetic field. Then we use Floquet theory to numerically solve the spin energy spectrum, study the spin dynamics and calculate the geometric phase under a finite magnetic field, where the rotating frequency to induce resonant transition could be greatly reduced.

High-precision gravimeter based on a nano-mechanical resonator hybrid with an electron spin

We show that the gravitational acceleration can be measured with the matter-wave Ramsey interferometry, by using a nitrogen-vacancy center coupled to a nano-mechanical resonator. We propose two experimental methods to realize the similar Hamiltonian, by using either a cantilever resonator or a trapped nanoparticle. The scheme is robust against the thermal noise, and could be realized at the temperature much higher than the quantum regime. The effects of decoherence on the interferometry fringe visibility is calculated, considering both the mechanical motional decay and dephasing of the nitrogen-vacancy center. In addition, we demonstrate that under the various sources of random and systematic noises, our gravimeter can be made on-chip and achieve a high measurement of precision. Under experimental feasible parameters, the proposed gravimeter could achieve 10^-10 relative precision.

Observation of the linewidth broadening of single spins in diamond nanoparticles in aqueous fluid and its relation to the rotational Brownian motion

Capturing the fast rotational motion of single nanoparticles has been hindered owing to the difficulty of acquiring directional information under the optical diffraction limit. Here, we report the linewidth broadening of the electron spin resonance of single nitrogen vacancy (NV) centers that matches the rotational diffusion constant of the host nanodiamonds. When nanodiamonds are gradually detached from the substrates that they were fixed to, their optically detected spin resonance peaks are broadened by 1.8 MHz, which corresponds to the rotational diffusion constant of nanoparticles with a diameter of 11.4 nm from the Einstein–Smoluchowski relation.

Sensitivity of displacement detection for a particle levitated in the doughnut beam

Displacement detection of a spherical particle in focused laser beams with a quadrant photodetector provides a fast and high precision way to determine the particle location. In contrast to the traditional Gaussian beams, the sensitivity of displacement detection using various doughnut beams is investigated. The sensitivity improvement for large spherical particles along the longitudinal direction is reported. With appropriate vortex charge l of the doughnut beams, they can outperform the Gaussian beam to get more than one order of magnitude higher sensitivity and, thus, have potential applications in various high-precision measurements. By using the levitating doughnut beam to detect the particle displacement, the result will also facilitate the recent proposal of levitating a particle in doughnut beams to suppress the light absorption.

Ramsey Interferences and Spin Echoes from Electron Spins Inside a Levitating Macroscopic Particle

We report on observations of Ramsey interferences and spin echoes from electron spins inside a levitating macroscopic particle. The experiment is realized using nitrogen-vacancy (NV) centers hosted in a micron-sized diamond stored in a Paul trap both under atmospheric conditions and under vacuum. Spin echoes are used to show that the Paul trap preserves the coherence time of the embedded electron spins for more than microseconds. Conversely, the NV spin is employed to demonstrate high angular stability of the diamond even under vacuum. These results are significant steps towards strong coupling of NV spins to the rotational mode of levitating diamonds.

Printed-circuit-board linear Paul trap for manipulating single nano- and microparticles

Levitation of very small but macroscopic objects is a rapidly developing interrogation technique for nanooptics and optomechanics. Paul traps are one mechanism for levitation of charged particles, which enables interrogation of novel materials or optically active samples in a virtually interaction-free environment, providing a test-bed for completely new experiments. Elementary traps have already been demonstrated for nano- and microparticles as a proof-of-principle for such experiments. We present a linear, segmented Paul trap with a printed-circuit-board-based design for levitation of nano- and microparticles, as a step toward the more sophisticated tools needed for advanced experiments. We describe the trap design, construction, and characterization and address the challenging phenomena associated with such a system. This trap provides a step toward designing an ideal environment for studies using a variety of isolated particles to enable advances in areas including magnetometry, thermodynamics, and optomechanics.

Optically Levitated Nanodumbbell Torsion Balance and GHz Nanomechanical Rotor

Levitated optomechanics has great potential in precision measurements, thermodynamics, macroscopic quantum mechanics, and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell. This levitated nanodumbbell torsion balance is a novel analog of the Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1 GHz, which is the fastest nanomechanical rotor realized to date. Smaller silica nanodumbbells can sustain higher rotation frequencies. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

Quantum measurement of a rapidly rotating spin qubit in diamond

A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realizing a single qubit that can be measured and controlled during physical rotation is experimentally challenging. We demonstrate quantum control of a single nitrogen-vacancy (NV) center within a diamond rotated at 200,000 rpm, a rotational period comparable to the NV spin coherence time T₂. We stroboscopically image individual NV centers that execute rapid circular motion in addition to rotation and demonstrate preparation, control, and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame and paves the way for the realization of single-qubit diamond-based rotation sensors.

An efficient fluorescent single-particle position tracking system for long-term pulsed measurements of nitrogen-vacancy centers in diamond

A simple and convenient design enables real-time three-dimensional position tracking of nitrogen-vacancy (NV) centers in diamond. The system consists entirely of commercially available components (a single-photon counter, a high-speed digital-to-analog converter, a phase-sensitive detector-based feedback device, and a piezo stage), eliminating the need for custom programming or rigorous optimization processes. With a large input range of counters and trackers combined with high sensitivity of single-photon counting, high-speed position tracking (upper bound recovery time of 0.9 s upon 250 nm of step-like positional shift) not only of bright ensembles, but also of low-photon-collection-efficiency single to few NV centers (down to 10³ s^-1) is possible. The tracking requires position modulation of only 10 nm, which allows simultaneous position tracking and pulsed measurements in the long term. Therefore, this tracking system enables measuring a single-spin magnetic resonance and Rabi oscillations at a very high resolution even without photon collection optimization. The system is widely applicable to various fields related to NV center quantum manipulation research such as NV optical trapping, NV tracking in fluid dynamics, and biological sensing using NV centers inside a biological cell.

Magnetometry via spin-mechanical coupling in levitated optomechanics

We analyze magnetometry using an optically levitated nanodiamond. We consider a configuration where a magnetic field gradient couples the mechanical oscillation of the diamond with its spin degree of freedom provided by a nitrogen vacancy center. First, we investigate the measurement of the position spectrum of the mechanical oscillator. We find that conditions of ultrahigh vacuum and feedback cooling allow a magnetic field gradient sensitivity of 1μTm^-1/Hz. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100mTm^-1/Hz. Subsequently, we characterize the magnetic field gradient sensitivity obtainable by maneuvering the spin degrees of freedom using Ramsey interferometry. We find that this technique can offer photon-shot noise and spin-projection noise limited magnetic field gradient sensitivity of 100μTm^-1/Hz. We conclude that this hybrid levitated nanomechanical magnetometer provides a favorable and versatile platform for sensing applications.

Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions

We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9}  amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

Torsional Optomechanics of a Levitated Nonspherical Nanoparticle

An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tensor. The torsional vibration frequency can be 1 order of magnitude higher than its center-of-mass motion frequency, which is promising for ground state cooling. We propose a simple yet novel scheme to achieve ground state cooling of its torsional vibration with a linearly polarized Gaussian cavity mode. A levitated nonspherical nanoparticle in vacuum will also be an ultrasensitive nanoscale torsion balance with a torque detection sensitivity on the order of 10^{-29}  N m/sqrt[Hz] under realistic conditions.