Strain coupling of a nitrogen-vacancy center spin to a diamond mechanical oscillator

Designing Optically Addressable Nitrogen-Vacancy Centers in Ultrasmall Nanodiamonds: Insights from First-Principles Calculations

Ultrasmall nanodiamonds (USNDs) are promising platforms for fluorescent and quantum-sensing applications. Here we present first-principles electronic structure calculations of nitrogen-vacancy (NV-) centers in USNDs, and we investigate their optical addressability as a function of the surface termination. We consider both isolated nanoparticles and arrays of USNDs with different degrees of packing, and we include quantum vibronic effects in our analysis, using stochastic methods. We find that the NV- can be stabilized in a negative charge state if the nanoparticles are terminated by fluorine, hydroxyl, and ether. While fluorine terminations are useful for fluorescent biotags, we suggest that hydroxyl and ether terminations are beneficial for quantum-sensing applications. We also find that the NV- can be stabilized in arrays of USNDs for interparticle separations larger than the diameter of the nanoparticle. Finally, our results show that in arrays, electron phonon interactions enhance the negative charge stability of NV- centers.

Bright Quantum-Grade Fluorescent Nanodiamonds

Optically accessible spin-active nanomaterials are promising as quantum nanosensors for probing biological samples. However, achieving bioimaging-level brightness and high-quality spin properties for these materials is challenging and hinders their application in quantum biosensing. Here, we demonstrate bright fluorescent nanodiamonds (NDs) containing 0.6-1.3-ppm negatively charged nitrogen-vacancy (NV) centers by spin-environment engineering via enriching spin-less 12C-carbon isotopes and reducing substitutional nitrogen spin impurities. The NDs, readily introduced into cultured cells, exhibited improved optically detected magnetic resonance (ODMR) spectra; peak splitting (E) was reduced by 2-3 MHz, and microwave excitation power required was 20 times lower to achieve a 3% ODMR contrast, comparable to that of conventional type-Ib NDs. They show average spin-relaxation times of T1 = 0.68 ms and T2 = 3.2 μs (1.6 ms and 5.4 μs maximum) that were 5- and 11-fold longer than those of type-Ib, respectively. Additionally, the extended T2 relaxation times of these NDs enable shot-noise-limited temperature measurements with a sensitivity of approximately 0.28 K / Hz . The combination of bulk-like NV spin properties and enhanced fluorescence significantly improves the sensitivity of ND-based quantum sensors for biological applications.

Transition-Metal-Related Quantum Emitters in Wurtzite AlN and GaN

Transition-metal centers exhibit a paramagnetic ground state in wide-bandgap semiconductors and are promising for nanophotonics and quantum information processing. Specifically, there is a growing interest in discovering prominent paramagnetic spin defects that can be manipulated using optical methods. Here, we investigate the electronic structure and magneto-optical properties of Cr and Mn substitutional centers in wurtzite AlN and GaN. We use state-of-the-art hybrid density functional theory calculations to determine level structure, stability, optical signatures, and magnetic properties of these centers. The excitation energies are calculated using the constrained occupation approach and rigorously verified with the complete active space configuration interaction approach. Our simulations of the photoluminescence spectra indicate that Cr Al 1 + in AlN and Cr Ga 1 + in GaN are responsible for the observed narrow quantum emission near 1.2 eV. We compute the zero-field splitting (ZFS) parameters and outline an optical spin polarization protocol for Cr Al 1 + and Cr Ga 1 + . Our results demonstrate that these centers are promising candidates for spin qubits.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9) Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Two-color electromagnetically induced transparency generated slow light in double-mechanical-mode coupling carbon nanotube resonators

We theoretically propose a multiple-mode-coupling hybrid quantum system comprising two-mode-coupling nanomechanical carbon nanotube (CNT) resonators realized by a phase-dependent phonon-exchange interaction interacting with the same nitrogen-vacancy (NV) center in diamond. We investigate the coherent optical responses of the NV center under the condition of resonance and detuning. In particular, two-color electromagnetically induced transparency (EIT) can be achieved by controlling the system parameters and coupling regimes. Combining the spin-phonon interactions and phonon-phonon coupling with the modulation phase, the switching of one and two EIT windows has been demonstrated, which generates a light delay or advance. The slow-to-fast and fast-to-slow light transitions have been studied in different coupling regimes, and the switch between slow and fast light can be controlled periodically by tuning the modulation phase. The study can be applied to phonon-mediated optical information storage or information processing with spin qubits based on multiple-mode hybrid quantum systems.

High Spatial Resolution 2D Imaging of Current Density and Pressure for Graphene Devices under High Pressure Using Nitrogen-Vacancy Centers in Diamond

Current density imaging is helpful for discovering interesting electronic phenomena and understanding carrier dynamics, and by combining pressure distributions, several pressure-induced novel physics may be comprehended. In this work, noninvasive, high-resolution two-dimensional images of the current density and pressure gradient for graphene ribbon and hBN-graphene-hBN devices are explored using nitrogen-vacancy (NV) centers in diamond under high pressure. The two-dimensional vector current density is reconstructed by the vector magnetic field mapped by the near-surface NV center layer in the diamond. The current density images accurately and clearly reproduce the complicated structure and current flow of graphene under high pressure. Additionally, the spatial distribution of the pressure is simultaneously mapped, rationalizing the nonuniformity of the current density under high pressure. The current method opens a significant new avenue to investigate electronic transport and conductance variations in two-dimensional materials and electrical devices under high pressure as well as for nondestructive evaluation of semiconductor circuits.

Sensing at the Nanoscale Using Nitrogen-Vacancy Centers in Diamond: A Model for a Quantum Pressure Sensor

The sensing of stress under harsh environmental conditions with high resolution has critical importance for a range of applications including earth's subsurface scanning, geological CO2 storage monitoring, and mineral and resource recovery. Using a first-principles density functional theory (DFT) approach combined with the theoretical modelling of the low-energy Hamiltonian, here, we investigate a novel approach to detect unprecedented levels of pressure by taking advantage of the solid-state electronic spin of nitrogen-vacancy (NV) centers in diamond. We computationally explore the effect of strain on the defect band edges and band gaps by varying the lattice parameters of a diamond supercell hosting a single NV center. A low-energy Hamiltonian is developed that includes the effect of stress on the energy level of a ±1 spin manifold at the ground state. By quantifying the energy level shift and split, we predict pressure sensing of up to 0.3 MPa/Hz using the experimentally measured spin dephasing time. We show the superiority of the quantum sensing approach over traditional optical sensing techniques by discussing our results from DFT and theoretical modelling for the frequency shift per unit pressure. Importantly, we propose a quantum manometer that could be useful to measure earth's subsurface vibrations as well as for pressure detection and monitoring in high-temperature superconductivity studies and in material sciences. Our results open avenues for the development of a sensing technology with high sensitivity and resolution under extreme pressure limits that potentially has a wider applicability than the existing pressure sensing technologies.

Qudit-based high-dimensional controlled-not gate

High-dimensional quantum systems expand quantum channel capacity and information storage space. By implementing high-dimensional quantum logic gates, the speed of quantum computing can be practically enhanced. We propose a deterministic 4 × 4-dimensional controlled-not (CNOT) gate for a hybrid system without ancillary qudits required, where the spatial and polarization states of a single photon serve as a control qudit of four dimensions, whereas two electron-spin states in nitrogen-vacancy (NV) centers act as a four-dimensional target qudit. As the control qudits are easily operated employing simple optical elements and the target qudits are available for storage, the CNOT gate works in a deterministic way, and it can be flexibly extended to n × n-dimensional (n > 4) quantum gates for other hybrid systems or different photonic degrees of freedoms. The efficiency and fidelity of the CNOT gate are analyzed aligning with current technological capabilities, finding that they have satisfactory performances.

Microwave optical limiting via an acoustic field in a diamond mechanical resonator

We investigate the generation and control of the reverse saturable absorption (RSA) and optical limiting (OL) at microwave (mw) range in high-Q single-crystal diamond mechanical resonator (DMR) embedded with many nitrogen-vacancy (NV) centers. The strain-induced acoustic modes enable mechanical manipulation of NV centers. On the basis of strain-coupling mechanism, it is shown that the saturable absorption (SA) switches to the RSA by applying the acoustic field, leading to induce the OL in the diamond through the cross-Kerr effect. We demonstrate that the OL characteristics such as, threshold, efficiency, and dynamic range can be controlled by changing either the intensity or frequency of the acoustic field. Moreover, we show that this optical limiter can amplify noiselessly the low intensity of the mw field input to the sensors and also attenuate any gain-induced noise and increase in the intensity of the mw field if it exceeds the intensity threshold. In addition, it is shown that by increasing either the number of NV centers or length of the diamond, the optical limiter can be more efficient. The physical mechanism of the OL establishment is explained using the analytical expressions, which are in good agreement with the numerical results. Our proposed acoustic-induced optical limiter can be a scheme for protecting different optical and electronic devices in mw range, remote sensing, navigation, communications, microwave heating and thermo/laser therapy.

Absorption and birefringence study for reduced optical losses in diamond with high nitrogen-vacancy concentration

The use of diamond colour centres such as the nitrogen-vacancy (NV) centre is increasingly enabling quantum sensing and computing applications. Novel concepts like cavity coupling and readout, laser-threshold magnetometry and multi-pass geometries allow significantly improved sensitivity and performance via increased signals and strong light fields. Enabling material properties for these techniques and their further improvements are low optical material losses via optical absorption of signal light and low birefringence. Here, we study systematically the behaviour of absorption around 700 nm and birefringence with increasing nitrogen- and NV-doping, as well as their behaviour during NV creation via diamond growth, electron beam irradiation and annealing treatments. Absorption correlates with increased nitrogen doping yet substitutional nitrogen does not seem to be the direct absorber. Birefringence reduces with increasing nitrogen doping. We identify multiple crystal defect concentrations via absorption spectroscopy and their changes during the material processing steps and thus identify potential causes of absorption and birefringence as well as strategies to fabricate chemical vapour deposition diamonds with high NV density yet low absorption and low birefringence. This article is part of the Theo Murphy meeting issue 'Diamond for quantum applications'.

Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates

The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.

Hypersound tomography of graphitized layers buried into diamond matrix

Acoustic properties of buried graphitized layers in diamond formed by ion implantation followed by annealing were studied using the picosecond ultrasonic technique with spatial resolution. Two methods of elastic pulse generation were used: heating an aluminum film deposited on a diamond sample by femtosecond laser pulses and direct illumination of the graphitized layers by these pulses. We applied a multilayered model of the acousto-optical response to fit experimental results and estimate the distribution of the acoustical parameters (wave resistance, viscoelastic damping, and longitudinal sound speed) of the structures under study in depth. It was found that unique sets of spectral lines are present in the Fourier spectra of measured responses in regions with different internal structures. Mapping of the Fourier spectra made it possible to visualize regions with different internal structures. The combined use of depth profiling and mapping can serve as a tool for hypersound tomography.

NV microscopy of thermally controlled stresses caused by thin Cr2O3 films

Many modern applications, including quantum computing and quantum sensing, use substrate-film interfaces. Particularly, thin films of chromium or titanium and their oxides are commonly used to bind various structures, such as resonators, masks, or microwave antennas, to a diamond surface. Due to different thermal expansions of involved materials, such films and structures could produce significant stresses, which need to be measured or predicted. In this paper, we demonstrate imaging of stresses in the top layer of diamond with deposited structures of Cr₂O₃ at temperatures 19°C and 37°C by using stress-sensitive optically detected magnetic resonances (ODMR) in NV centers. We also calculated stresses in the diamond-film interface by using finite-element analysis and correlated them to measured ODMR frequency shifts. As predicted by the simulation, the measured high-contrast frequency-shift patterns are only due to thermal stresses, whose spin-stress coupling constant along the NV axis is 21±1 MHz/GPa, that is in agreement with constants previously obtained from single NV centers in diamond cantilever. We demonstrate that NV microscopy is a convenient platform for optically detecting and quantifying spatial distributions of stresses in diamond-based photonic devices with micrometer precision and propose thin films as a means for local application of temperature-controlled stresses. Our results also show that thin-film structures produce significant stresses in diamond substrates, which should be accounted for in NV-based applications.

Single-Spin Readout and Quantum Sensing Using Optomechanically Induced Transparency

Solid-state spin defects are promising quantum sensors for a large variety of sensing targets. Some of these defects couple appreciably to strain in the host material. We propose to use this strain coupling for mechanically mediated dispersive single-shot spin readout by an optomechanically induced transparency measurement. Surprisingly, the estimated measurement times for negatively charged silicon-vacancy defects in diamond are an order of magnitude shorter than those for single-shot optical fluorescence readout. Our scheme can also be used for general parameter-estimation metrology and offers a higher sensitivity than conventional schemes using continuous position detection.

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.

Fluorescence modulation of nanodiamond NV- centers for neurochemical detection

Nanodiamond (ND) with nitrogen vacancy (NV-) color centers has emerged as an important material for quantum sensing and imaging. Fluorescent, carboxylated ND (140 nm) is investigated for the detection of dopamine (DA), caffeine (CA), and ascorbic acid (AA). Over a 200 nM range, DA and CA quenched the ND fluorescence by 7.1 and 9.8%, respectively. For AA, fluorescence was quenched (2.9%) at nM concentrations and enhanced at μM concentrations. The quenching fit well to Langmuir adsorption isotherms. For DA-CA mixtures, the CA at nM concentrations did not affect DA quenching but interfered when at μM concentrations. The DA at nM or μM concentrations lessened CA quenching. For DA-AA mixtures with DA at mM concentrations, AA quenched fluorescence throughout the nM and μM range, with increased quenching in the nM range. These studies support ND fluorescence modulation as a possible sensor modality for bioanalyte detection.

Structural Optimization and MEMS Implementation of the NV Center Phonon Piezoelectric Device

The nitrogen-vacancy (NV) center of the diamond has attracted widespread attention because of its high sensitivity in quantum precision measurement. The phonon piezoelectric device of the NV center is designed on the basis of the phonon-coupled regulation mechanism. The propagation characteristics and acoustic wave excitation modes of the phonon piezoelectric device are analyzed. In order to improve the performance of phonon-coupled manipulation, the influence of the structural parameters of the diamond substrate and the ZnO piezoelectric layer on the phonon propagation characteristics are analyzed. The structure of the phonon piezoelectric device of the NV center is optimized, and its Micro-Electro-Mechanical System (MEMS) implementation and characterization are carried out. Research results show that the phonon resonance manipulation method can effectively increase the NV center's spin transition probability using the MEMS phonon piezoelectric device prepared in this paper, improving the quantum spin manipulation efficiency.

Strain Quantum Sensing with Spin Defects in Hexagonal Boron Nitride

Hexagonal boron nitride is not only a promising functional material for the development of two-dimensional optoelectronic devices but also a good candidate for quantum sensing thanks to the presence of quantum emitters in the form of atom-like defects. Their exploitation in quantum technologies necessitates understanding their coherence properties as well as their sensitivity to external stimuli. In this work, we probe the strain configuration of boron vacancy centers (VB^-) created by ion implantation in h-BN flakes thanks to wide-field spatially resolved optically detected magnetic resonance and submicro Raman spectroscopy. Our experiments demonstrate the ability of VB^- for quantum sensing of strain and, given the omnipresence of h-BN in 2D-based devices, open the door for in situ imaging of strain under working conditions.

Uncovering the morphological effects of high-energy Ga+ focused ion beam milling on hBN single-photon emitter fabrication

Many techniques to fabricate complex nanostructures and quantum emitting defects in low dimensional materials for quantum information technologies rely on the patterning capabilities of focused ion beam (FIB) systems. In particular, the ability to pattern arrays of bright and stable room temperature single-photon emitters (SPEs) in 2D wide-bandgap insulator hexagonal boron nitride (hBN) via high-energy heavy-ion FIB allows for direct placement of SPEs without structured substrates or polymer-reliant lithography steps. However, the process parameters needed to create hBN SPEs with this technique are dependent on the growth method of the material chosen. Moreover, morphological damage induced by high-energy heavy-ion exposure may further influence the successful creation of SPEs. In this work, we perform atomic force microscopy to characterize the surface morphology of hBN regions patterned by Ga+ FIB to create SPEs at a range of ion doses and find that material swelling, and not milling as expected, is most strongly and positively correlated with the onset of non-zero SPE yields. Furthermore, we simulate vacancy concentration profiles at each of the tested doses and propose a qualitative model to elucidate how Ga+ FIB patterning creates isolated SPEs that is consistent with observed optical and morphological characteristics and is dependent on the consideration of void nucleation and growth from vacancy clusters. Our results provide novel insight into the formation of hBN SPEs created by high-energy heavy-ion milling that can be leveraged for monolithic hBN photonic devices and could be applied to a wide range of low-dimensional solid-state SPE hosts.

Scanning gradiometry with a single spin quantum magnetometer

Quantum sensors based on spin defects in diamond have recently enabled detailed imaging of nanoscale magnetic patterns, such as chiral spin textures, two-dimensional ferromagnets, or superconducting vortices, based on a measurement of the static magnetic stray field. Here, we demonstrate a gradiometry technique that significantly enhances the measurement sensitivity of such static fields, leading to new opportunities in the imaging of weakly magnetic systems. Our method relies on the mechanical oscillation of a single nitrogen-vacancy center at the tip of a scanning diamond probe, which up-converts the local spatial gradients into ac magnetic fields enabling the use of sensitive ac quantum protocols. We show that gradiometry provides important advantages over static field imaging: (i) an order-of-magnitude better sensitivity, (ii) a more localized and sharper image, and (iii) a strong suppression of field drifts. We demonstrate the capabilities of gradiometry by imaging the nanotesla fields appearing above topographic defects and atomic steps in an antiferromagnet, direct currents in a graphene device, and para- and diamagnetic metals.

Enhanced Phonon Antibunching in a Circuit Quantum Acoustodynamical System Containing Two Surface Acoustic Wave Resonators

We propose a scheme to implement the phonon antibunching and phonon blockade in a circuit quantum acoustodynamical system containing two surface acoustic wave (SAW) resonators coupled to a superconducting qubit. In the cases of driving only one SAW resonator and two SAW resonators, we investigate the phonon statistics by numerically calculating the second-order correlation function. It is found that, when only one SAW cavity is resonantly driven, the phonon antibunching effect can be achieved even when the qubit–phonon coupling strength is smaller than the decay rates of acoustic cavities. This result physically originates from the quantum interference between super-Poissonian statistics and Poissonian statistics of phonons. In particular, when the two SAW resonators are simultaneously driven under the mechanical resonant condition, the phonon antibunching effect can be significantly enhanced, which ultimately allows for the generation of a phonon blockade. Moreover, the obtained phonon blockade can be optimized by regulating the intensity ratio of the two SAW driving fields. In addition, we also discuss in detail the effect of system parameters on the phonon statistics. Our work provides an alternative way for manipulating and controlling the nonclassical effects of SAW phonons. It may inspire the engineering of new SAW-based phonon devices and extend their applications in quantum information processing.

Generation of Spin Defects by Ion Implantation in Hexagonal Boron Nitride

Optically addressable spin defects in wide-band-gap semiconductors as promising systems for quantum information and sensing applications have recently attracted increased attention. Spin defects in two-dimensional materials are expected to show superiority in quantum sensing due to their atomic thickness. Here, we demonstrate that an ensemble of negatively charged boron vacancies (VB -) with good spin properties in hexagonal boron nitride (hBN) can be generated by ion implantation. We carry out optically detected magnetic resonance measurements at room temperature to characterize the spin properties of ensembles of VB - defects, showing a zero-field splitting frequency of ∼3.47 GHz. We compare the photoluminescence intensity and spin properties of VB - defects generated using different implantation parameters, such as fluence, energy, and ion species. With the use of the proper parameters, we can successfully create VB - defects with a high probability. Our results provide a simple and practicable method to create spin defects in hBN, which is of great significance for realizing integrated hBN-based devices.

Strong single-photon optomechanical coupling in a hybrid quantum system

Engineering strong single-photon optomechanical couplings is crucial for optomechanical systems. Here, we propose a hybrid quantum system consisting of a nanobeam (phonons) coupled to a spin ensemble and a cavity (photons) to overcome it. Utilizing the critical property of the lower-branch polariton (LBP) formed by the ensemble-phonon interaction, the LBP-cavity coupling can be greatly enhanced by three orders magnitude of the original one, while the upper-branch polariton (UBP)-cavity coupling is fully suppressed. Our proposal breaks through the condition of the coupling strength less than the critical value in previous schemes using two harmonic oscillators. Also, strong Kerr effect can be induced in our proposal. This shows our proposed approach can be used to study quantum nonlinear and nonclassical effects in weakly coupled optomechanical systems.

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.

Inducing micromechanical motion by optical excitation of a single quantum dot

Hybrid quantum optomechanical systems¹ interface a macroscopic mechanical degree of freedom with a single two-level system such as a single spin^2-4, a superconducting qubit^5-7 or a single optical emitter^8-12. Recently, hybrid systems operating in the microwave domain have witnessed impressive progress^13,14. Concurrently, only a few experimental approaches have successfully addressed hybrid systems in the optical domain, demonstrating that macroscopic motion can modulate the two-level system transition energy^9,10,15. However, the reciprocal effect, corresponding to the backaction of a single quantum system on a macroscopic mechanical resonator, has remained elusive. In contrast to an optical cavity, a two-level system operates with no more than a single energy quantum. Hence, it requires a much stronger hybrid coupling rate compared to cavity optomechanical systems^1,16. Here, we build on the large strain coupling between an oscillating microwire and a single embedded quantum dot⁹. We resonantly drive the quantum dot's exciton using a laser modulated at the mechanical frequency. State-dependent strain then results in a time-dependent mechanical force that actuates microwire motion. This force is almost three orders of magnitude larger than the radiation pressure produced by the photon flux interacting with the quantum dot. In principle, the state-dependent force could constitute a strategy to coherently encode the quantum dot quantum state onto a mechanical degree of freedom¹.

Superconducting Nanoelectromechanical Transducer Resilient to Magnetic Fields

Nanoscale electromechanical coupling provides a unique route toward control of mechanical motions and microwave fields in superconducting cavity electromechanical devices. However, conventional devices composed of aluminum have presented severe constraints on their operating conditions due to the low superconducting critical temperature (1.2 K) and magnetic field (0.01 T) of aluminum. To enhance their potential in device applications, we fabricate a superconducting electromechanical device employing niobium and demonstrate a set of cavity electromechanical dynamics, including back-action cooling and amplification, and electromechanically induced reflection at 4.2 K and in strong magnetic fields up to 0.8 T. Niobium-based electromechanical transducers operating at this temperature could potentially be employed to realize compact, nonreciprocal microwave devices in place of conventional isolators and cryogenic amplifiers. Moreover, with their resilience to magnetic fields, niobium devices utilizing the electromechanical back-action effects could be used to study spin-phonon interactions for nanomechanical spin-sensing.

Optomechanical atomic force microscope

In the scanning probe microscope system, the weak signal detection of cantilever vibration is one of the important factors affecting the sensor sensitivity. In our current work, we present a novel design concept for an atomic force microscope (AFM) combined with optomechanics with an ultra-high quality factor and a low thermal noise. The detection system consists of a fixed mirror placed on the cantilever of the AFM and pump-probe beams that is equivalent to a Fabry-Perot cavity. We realize that the AFM combined with an optical cavity can achieve ultra-sensitive detection of force gradients of 10^-12 N m^-1 in the case of high-vacuum and low effective temperature of 1 mK, which may open up new avenues for super-high resolution imaging and super-high precision force spectroscopy.

Coupling of light and mechanics in a photonic crystal waveguide

High-Q mechanical modes of transverse oscillation at a few megahertz are characterized for a photonic crystal waveguide (PCW) consisting of parallel dielectric nanobeams. The transduction of thermally excited motion of 33 pm at 300 K results in phase modulation with high signal-to-noise ratio for light propagating in a guided mode of the PCW. Numerical modeling gives good agreement with experiment. With these measurements in hand, the system is assessed for possible applications in quantum information science and technology involving strong coupling of single phonons of vibration to single atoms and photons trapped within the PCW.

Observations of thermally driven transverse vibration of a photonic crystal waveguide (PCW) are reported. The PCW consists of two parallel nanobeams whose width is modulated symmetrically with a spatial period of 370 nm about a 240-nm vacuum gap between the beams. The resulting dielectric structure has a band gap (i.e., a photonic crystal stop band) with band edges in the near infrared that provide a regime for transduction of nanobeam motion to phase and amplitude modulation of an optical guided mode. This regime is in contrast to more conventional optomechanical coupling by way of moving end mirrors in resonant optical cavities. Models are developed and validated for this optomechanical mechanism in a PCW for probe frequencies far from and near to the dielectric band edge (i.e., stop band edge). The large optomechanical coupling strength predicted should make possible measurements with an imprecision below that at the standard quantum limit and well into the backaction-dominated regime. Since our PCW has been designed for near-field atom trapping, this research provides a foundation for evaluating possible deleterious effects of thermal motion on optical atomic traps near the surfaces of PCWs. Longer-term goals are to achieve strong atom-mediated links between individual phonons of vibration and single photons propagating in the guided modes (GMs) of the PCW, thereby enabling optomechanics at the quantum level with atoms, photons, and phonons. The experiments and models reported here provide a basis for assessing such goals.

Dynamically-enhanced strain in atomically thin resonators

Graphene and related two-dimensional (2D) materials associate remarkable mechanical, electronic, optical and phononic properties. As such, 2D materials are promising for hybrid systems that couple their elementary excitations (excitons, phonons) to their macroscopic mechanical modes. These built-in systems may yield enhanced strain-mediated coupling compared to bulkier architectures, e.g., comprising a single quantum emitter coupled to a nano-mechanical resonator. Here, using micro-Raman spectroscopy on pristine monolayer graphene drums, we demonstrate that the macroscopic flexural vibrations of graphene induce dynamical optical phonon softening. This softening is an unambiguous fingerprint of dynamically-induced tensile strain that reaches values up to ≈4 × 10⁻⁴ under strong non-linear driving. Such non-linearly enhanced strain exceeds the values predicted for harmonic vibrations with the same root mean square (RMS) amplitude by more than one order of magnitude. Our work holds promise for dynamical strain engineering and dynamical strain-mediated control of light-matter interactions in 2D materials and related heterostructures.

Here, the authors use Raman spectroscopy on circular graphene drums to demonstrate dynamical softening of optical phonons induced by the macroscopic flexural motion of graphene, and find evidence that the strain in graphene is enhanced under non-linear driving.

Enhancing Spin-Phonon and Spin-Spin Interactions Using Linear Resources in a Hybrid Quantum System

Hybrid spin-mechanical setups offer a versatile platform for quantum science and technology, but improving the spin-phonon as well as the spin-spin couplings of such systems remains a crucial challenge. Here, we propose and analyze an experimentally feasible and simple method for exponentially enhancing the spin-phonon and the phonon-mediated spin-spin interactions in a hybrid spin-mechanical setup, using only linear resources. Through modulating the spring constant of the mechanical cantilever with a time-dependent pump, we can acquire a tunable and nonlinear (two-phonon) drive to the mechanical mode, thus amplifying the mechanical zero-point fluctuations and directly enhancing the spin-phonon coupling. This method allows the spin-mechanical system to be driven from the weak-coupling regime to the strong-coupling regime, and even the ultrastrong coupling regime. In the dispersive regime, this method gives rise to a large enhancement of the phonon-mediated spin-spin interactions between distant solid-state spins, typically two orders of magnitude larger than that without modulation. As an example, we show that the proposed scheme can apply to generating entangled states of multiple spins with high fidelities even in the presence of large dissipations.

Anisotropic Spin-Acoustic Resonance in Silicon Carbide at Room Temperature

We report on acoustically driven spin resonances in atomic-scale centers in silicon carbide at room temperature. Specifically, we use a surface acoustic wave cavity to selectively address spin transitions with magnetic quantum number differences of ±1 and ±2 in the absence of external microwave electromagnetic fields. These spin-acoustic resonances reveal a nontrivial dependence on the static magnetic field orientation, which is attributed to the intrinsic symmetry of the acoustic fields combined with the peculiar properties of a half-integer spin system. We develop a microscopic model of the spin-acoustic interaction, which describes our experimental data without fitting parameters. Furthermore, we predict that traveling surface waves lead to a chiral spin-acoustic resonance that changes upon magnetic field inversion. These results establish silicon carbide as a highly promising hybrid platform for on-chip spin-optomechanical quantum control enabling engineered interactions at room temperature.

Laser-Synthesis of NV-Centers-Enriched Nanodiamonds: Effect of Different Nitrogen Sources

Due to the large number of possible applications in quantum technology fields—especially regarding quantum sensing—of nitrogen-vacancy (NV) centers in nanodiamonds (NDs), research on a cheap, scalable and effective NDs synthesis technique has acquired an increasing interest. Standard production methods, such as detonation and grinding, require multistep post-synthesis processes and do not allow precise control in the size and fluorescence intensity of NDs. For this reason, a different approach consisting of pulsed laser ablation of carbon precursors has recently been proposed. In this work, we demonstrate the synthesis of NV-fluorescent NDs through pulsed laser ablation of an N-doped graphite target. The obtained NDs are fully characterized in the morphological and optical properties, in particular with optically detected magnetic resonance spectroscopy to unequivocally prove the NV origin of the NDs photoluminescence. Moreover, to compare the different fluorescent NDs laser-ablation-based synthesis techniques recently developed, we report an analysis of the effect of the medium in which laser ablation of graphite is performed. Along with it, thermodynamic aspects of the physical processes occurring during laser irradiation are analyzed. Finally, we show that the use of properly N-doped graphite as a target for laser ablation can lead to precise control in the number of NV centers in the produced NDs.

Optomechanical probe of an axial-vector mediated interaction in the quantum regime

We present an atomic, molecular, and optical physics based method to search for axial-vector mediated dipole-dipole interaction between electrons. In our optomechanical scheme, applying a static magnetic field and a pump beam and a probe beam to a hybrid mechanical system composed of a nitrogen-vacancy center and a cantilever resonator, we could obtain a probe absorption spectrum. Based on the study of the relationship between this spectrum and the exotic dipole-dipole interaction, we put forward our detection principle and then provide a prospective constraint most stringent at a rough interaction range from 4 × 10^-8 to 2 × 10^-7m. Our results indicate that this scheme could be put into consideration in relevant experimental searches.

Acoustic field induced nonlinear magneto-optical rotation in a diamond mechanical resonator

We study the nonlinear magneto-optical rotation (MOR) of a linearly polarized microwave probe field passing through many nitrogen-vacancy (NV) centers embedded in a high-Q single-crystal diamond mechanical resonator. On the basis of the strain-mediated coupling mechanism, we establish a three-level closed-loop system in the ground states of the NV center in the presence of a static magnetic field. It is shown that by applying an acoustic field, the birefringence is induced in the system through the cross-Kerr effect, so that the probe field is transmitted with a high intensity and rotated polarization plane by 90 degrees. In addition, we demonstrate that the acoustic field has a major role in enhancing the MOR angle to 90 degrees. Moreover, it is shown that the MOR angle of the polarization plane after passing through the presented system is sensitive to the relative phase of the applied fields. The physical mechanism of the MOR enhancement is explained using the analytical expressions which are in good agreement with the numerical results. The presented scheme can be used as a polarization converter for efficient switching TE/TM modes in optical communication, the depolarization backscattering lidar, polarization spectroscopy and precision measurements.

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling

Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

Spin-Phonon Interfaces in Coupled Nanomechanical Cantilevers

Coupled micro- and nanomechanical oscillators are of fundamental and technical interest for emerging quantum technologies. Upon interfacing with long-lived solid-state spins, the coherent manipulation of the quantum hybrid system becomes possible even at ambient conditions. Although the ability of these systems to act as a quantum bus inducing long-range spin-spin interactions has been known, the possibility to coherently couple electron/nuclear spins to the common modes of multiple oscillators and map their mechanical motion to spin-polarization has not been experimentally demonstrated. We here report experiments on interfacing spins to the common modes of a coupled cantilever system and show their correlation by translating ultralow forces induced by radiation from one oscillator to a distant spin. Further, we analyze the coherent spin-spin coupling induced by the common modes and estimate the entanglement generation among distant spins.

Magnetic measurements on micrometer-sized samples under high pressure using designed NV centers

Pressure can be used to tune the interplay among structural, electronic, and magnetic interactions in materials. High pressures are usually applied in the diamond anvil cell, making it difficult to study the magnetic properties of a micrometer-sized sample. We report a method for spatially resolved optical magnetometry based on imaging a layer of nitrogen-vacancy (NV) centers created at the surface of a diamond anvil. We illustrate the method using two sets of measurements realized at room temperature and low temperature, respectively: the pressure evolution of the magnetization of an iron bead up to 30 gigapascals showing the iron ferromagnetic collapse and the detection of the superconducting transition of magnesium dibromide at 7 gigapascals.

Electrically driven optical interferometry with spins in silicon carbide

Interfacing solid-state defect electron spins to other quantum systems is an ongoing challenge. The ground-state spin's weak coupling to its environment not only bestows excellent coherence properties but also limits desired drive fields. The excited-state orbitals of these electrons, however, can exhibit stronger coupling to phononic and electric fields. Here, we demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently drive the divacancy's excited-state orbitals and induce Landau-Zener-Stückelberg interference fringes in the resonant optical absorption spectrum. In addition, we find remarkably coherent optical and spin subsystems enabled by the basal divacancy's symmetry. These properties establish divacancies as strong candidates for quantum communication and hybrid system applications, where simultaneous control over optical and spin degrees of freedom is paramount.

Reliable Nanofabrication of Single-Crystal Diamond Photonic Nanostructures for Nanoscale Sensing

In this manuscript, we outline a reliable procedure to manufacture photonic nanostructures from single-crystal diamond (SCD). Photonic nanostructures, in our case SCD nanopillars on thin (<1 μm) platforms, are highly relevant for nanoscale sensing. The presented top-down procedure includes electron beam lithography (EBL) as well as reactive ion etching (RIE). Our method introduces a novel type of inter-layer, namely silicon, that significantly enhances the adhesion of hydrogen silsesquioxane (HSQ) electron beam resist to SCD and avoids sample charging during EBL. In contrast to previously used adhesion layers, our silicon layer can be removed using a highly-selective RIE step, which is not damaging HSQ mask structures. We thus refine published nanofabrication processes to ease a higher process reliability especially in the light of the advancing commercialization of SCD sensor devices.

Engineering Electron-Phonon Coupling of Quantum Defects to a Semiconfocal Acoustic Resonator

Diamond-based microelectromechanical systems (MEMS) enable direct coupling between the quantum states of nitrogen-vacancy (NV) centers and the phonon modes of a mechanical resonator. One example, a diamond high-overtone bulk acoustic resonator (HBAR), features an integrated piezoelectric transducer and supports high-quality factor resonance modes into the gigahertz frequency range. The acoustic modes allow mechanical manipulation of deeply embedded NV centers with long spin and orbital coherence times. Unfortunately, the spin-phonon coupling rate is limited by the large resonator size, >100 μm, and thus strongly coupled NV electron-phonon interactions remain out of reach in current diamond BAR devices. Here, we report the design and fabrication of a semiconfocal HBAR (SCHBAR) device on diamond (silicon carbide) with f × Q > 10¹² (>10¹³). The semiconfocal geometry confines the phonon mode laterally below 10 μm. This drastic reduction in modal volume enhances defect center coupling to a mechanical mode by 1000 times compared to prior HBAR devices. For the native NV centers inside the diamond device, we demonstrate mechanically driven spin transitions and show a high strain-driving efficiency with a Rabi frequency of (2π)2.19(14) MHz/V_p, which is comparable to a typical microwave antenna at the same microwave power, making SCHBAR a power-efficient device useful for fast spin control, dressed state coherence protection, and quantum circuit integration.

All-Optical Quantum Sensing of Rotational Brownian Motion of Magnetic Molecules

Sensing the local environment through the motional response of small molecules lays the foundation of many fundamental technologies. The information on local viscosity, for example, is contained in the random rotational Brownian motions of molecules. However, detection of the motions is challenging for molecules with sub-nanometer scale or high motional rates. Here we propose and experimentally demonstrate a novel method of detecting fast rotational Brownian motions of small magnetic molecules. With electronic spins as sensors, we are able to detect changes in motional rates, which yield different noise spectra and therefore different relaxation signals of the sensors. As a proof-of-principle demonstration, we experimentally implemented this method to detect the motions of gadolinium (Gd) complex molecules with nitrogen-vacancy (NV) centers in nanodiamonds. With all-optical measurements of the NV centers' longitudinal relaxation, we distinguished binary solutions with varying viscosities. Our method paves a new way for detecting fast motions of sub-nanometer sized magnetic molecules with better spatial resolution than conventional optical methods. It also provides a new tool in designing better contrast agents in magnetic resonance imaging.

Tunable Coupling of a Double Quantum Dot Spin System to a Mechanical Resonator

The interaction of quantum systems with mechanical resonators is of practical interest for applications in quantum information and sensing and also of fundamental interest as hybrid quantum systems. Achieving a large and tunable interaction strength is of great importance in this field as it enables controlled access to the quantum limit of motion and coherent interactions between different quantum systems. This has been challenging with solid state spins, where typically the coupling is weak and cannot be tuned. Here we use pairs of coupled quantum dots embedded within cantilevers to achieve a high coupling strength of the singlet-triplet spin system to mechanical motion through strain. Two methods of achieving strong, tunable coupling are demonstrated. The first is through different strain-induced energy shifts for the two QDs when the cantilever vibrates, resulting in changes to the exchange interaction. The second is through a laser-driven AC Stark shift that is sensitive to strain-induced shifts of the optical transitions. Both of these mechanisms can be tuned to zero with electrical bias or laser power, respectively, and give large spin-mechanical coupling strengths.

Microscopic Imaging of the Stress Tensor in Diamond Using in Situ Quantum Sensors

The precise measurement of mechanical stress at the nanoscale is of fundamental and technological importance. In principle, all six independent variables of the stress tensor, which describe the direction and magnitude of compression/tension and shear stress in a solid, can be exploited to tune or enhance the properties of materials and devices. However, existing techniques to probe the local stress are generally incapable of measuring the entire stress tensor. Here, we make use of an ensemble of atomic-sized in situ strain sensors in diamond (nitrogen-vacancy defects) to achieve spatial mapping of the full stress tensor, with a submicrometer spatial resolution and a sensitivity of the order of 1 MPa (10 MPa) for the shear (axial) stress components. To illustrate the effectiveness and versatility of the technique, we apply it to a broad range of experimental situations, including mapping the stress induced by localized implantation damage, nanoindents, and scratches. In addition, we observe surprisingly large stress contributions from functional electronic devices fabricated on the diamond and also demonstrate sensitivity to deformations of materials in contact with the diamond. Our technique could enable in situ measurements of the mechanical response of diamond nanostructures under various stimuli, with potential applications in strain engineering for diamond-based quantum technologies and in nanomechanical sensing for on-chip mass spectroscopy.

Nanoscale Vector dc Magnetometry via Ancilla-Assisted Frequency Up-Conversion

Sensing static magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging, and materials science. Even more beneficial would be full vector magnetometry with nanoscale spatial resolution. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with nitrogen vacancy (NV) centers in diamond. Achieving vector magnetometry has, however, often required using an ensemble of sensors or degrading the sensitivity. Here we introduce a hybrid magnetometry platform, consisting of a sensor and an ancillary qubit, that allows vector magnetometry of static fields. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear spin qubit. In particular, sensing transverse fields relies on frequency up-conversion of the dc fields through the ancillary qubit, allowing quantum lock-in detection with low-frequency noise rejection. In combination with the Ramsey detection of longitudinal fields, our frequency up-conversion scheme delivers a sensitive technique for vector dc magnetometry at the nanoscale.

Probing the State of a Mechanical Oscillator with an Ultrastrongly Coupled Quantum Emitter

Performing accurate position measurements of a mechanical resonator by coupling it to some optically driven quantum emitter is an important challenge for quantum sensing and metrology. We fully characterize the quantum noise associated with this measurement process, by deriving master equations for the coupled emitter and the resonator valid in the ultrastrong coupling regime. At short timescales, we show that this noise sets a fundamental limit to the readout sensitivity and that the standard quantum limit can be recovered for realistic experimental conditions. At long timescales, the scattering of the mechanical quadratures leads to the decoupling of the emitter from the driving light, switching off the noise source. This method can be used to describe the interaction of any quantum system strongly coupled to a finite size reservoir.

Spin-Mechanical Coupling of an InAs Quantum Dot Embedded in a Mechanical Resonator

We demonstrate strain-induced coupling between a hole spin in a quantum dot and mechanical motion of a cantilever. The optical transitions of quantum dots integrated into GaAs mechanical resonators are measured synchronously with the motion of the driven resonators. In a Voigt magnetic field, both electron and hole spin splittings are measured, showing negligible change for the electron spin but a large change for the hole spin of up to 36%. This large effect is attributed to the stronger spin orbit interaction of holes compared to electrons.

Motion Control and Optical Interrogation of a Levitating Single Nitrogen Vacancy in Vacuum

Levitation optomechanics exploits the unique mechanical properties of trapped nano-objects in vacuum to address some of the limitations of clamped nanomechanical resonators. In particular, its performance is foreseen to contribute to a better understanding of quantum decoherence at the mesoscopic scale as well as to lead to novel ultrasensitive sensing schemes. While most efforts have focused so far on the optical trapping of low-absorption silica particles, further opportunities arise from levitating objects with internal degrees of freedom, such as color centers. Nevertheless, inefficient heat dissipation at low pressures poses a challenge because most nano-objects, even with low-absorption materials, experience photodamage in an optical trap. Here, by using a Paul trap, we demonstrate levitation in vacuum and center-of-mass feedback cooling of a nanodiamond hosting a single nitrogen-vacancy center. The achieved level of motion control enables us to optically interrogate and characterize the emitter response. The developed platform is applicable to a wide range of other nano-objects and represents a promising step toward coupling internal and external degrees of freedom.

Controlling the coherence of a diamond spin qubit through its strain environment

The uncontrolled interaction of a quantum system with its environment is detrimental for quantum coherence. For quantum bits in the solid state, decoherence from thermal vibrations of the surrounding lattice can typically only be suppressed by lowering the temperature of operation. Here, we use a nano-electro-mechanical system to mitigate the effect of thermal phonons on a spin qubit - the silicon-vacancy colour centre in diamond - without changing the system temperature. By controlling the strain environment of the colour centre, we tune its electronic levels to probe, control, and eventually suppress the interaction of its spin with the thermal bath. Strain control provides both large tunability of the optical transitions and significantly improved spin coherence. Finally, our findings indicate the possibility to achieve strong coupling between the silicon-vacancy spin and single phonons, which can lead to the realisation of phonon-mediated quantum gates and nonlinear quantum phononics.

Orbital State Manipulation of a Diamond Nitrogen-Vacancy Center Using a Mechanical Resonator

We study the resonant optical transitions of a single nitrogen-vacancy (NV) center that is coherently dressed by a strong mechanical drive. Using a gigahertz-frequency diamond mechanical resonator that is strain coupled to a NV center's orbital states, we demonstrate coherent Raman sidebands out to the ninth order and orbital-phonon interactions that mix the two excited-state orbital branches. These interactions are spectroscopically revealed through a multiphonon Rabi splitting of the orbital branches which scales as a function of resonator driving amplitude and is successfully reproduced in a quantum model. Finally, we discuss the application of mechanical driving to engineering NV-center orbital states.