Measurable quantum geometric phase from a rotating single spin

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.

Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.

Characterizing Temperature and Strain Variations with Qubit Ensembles for Their Robust Coherence Protection

Solid-state spin defects, especially nuclear spins with potentially achievable long coherence times, are compelling candidates for quantum memories and sensors. However, their current performances are still limited by dephasing due to variations of their intrinsic quadrupole and hyperfine interactions. We propose an unbalanced echo to overcome this challenge by using a second spin to refocus variations of these interactions while preserving the quantum information stored in the nuclear spin free evolution. The unbalanced echo can be used to probe the temperature and strain distribution in materials. We develop first-principles methods to predict variations of these interactions and reveal their correlation over large temperature and strain ranges. Experiments performed in an ensemble of ∼10^{10} nuclear spins in diamond demonstrate a 20-fold dephasing time increase, limited by other noise sources. We further numerically show that our method can refocus even stronger noise variations than present in our experiments.

Temperature Sensitivity of 14N-V and 15N-V Ground-State Manifolds

We measure electron- and nuclear-spin transition frequencies in the ground state of nitrogen-vacancy (N-V) centers in diamond for two nitrogen isotopes (14N-V and 15N-V) over temperatures ranging from 77 to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters Q (for 14N-V), D, A‖, A⊥, and γ e / γ n , and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the m s = 0 spin manifold near room temperature are found to be 0.52(1) ppm/K for 14N-V(|mI = -1⟩ ↔ |mI = +1⟩) and -1.1(1) ppm/K for 15N-V(|mI = -1/2⟩ ↔ |mI = +1/2⟩). An isotopic shift in the zero-field splitting parameter D between 14N-V and 15N-V is measured to be ~ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear-spin transition frequencies, especially for 15N-V. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.

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.

Enhancing Spin-Based Sensor Sensitivity by Avoiding Microwave Field Inhomogeneity of NV Defect Ensemble

The behavior of the magnetic field sensitivity of nitrogen-vacancy (NV) centers as a function of microwave power and the inhomogeneous distribution of MW fields was systematically studied. An optimal structure for exciting spin structures by MW signals was designed using two parallel loop antennas. The volume of the homogeneous regions was approximately 42 mm³, and the associated diameter of the diamond reached up to 5.2 mm with 10¹⁶ NV sensors. Based on this structure, the detection contrast and voltage fluctuation of an optically detected magnetic resonance (ODMR) signal were optimized, and the sensitivity was improved to 5 nT/√Hz. In addition, a pulse sequence was presented to fully eliminate the MW broadening. The magnetic field sensitivity was improved by approximately one order of magnitude as the π-pulse duration was increased to its coherence time. This offers a useful way to improve the sensitivity of spin-based sensors.

Nuclear Spin Gyroscope based on the Nitrogen Vacancy Center in Diamond

A rotation sensor is one of the key elements of inertial navigation systems and compliments most cell phone sensor sets used for various applications. Currently, inexpensive and efficient solutions are mechanoelectronic devices, which nevertheless lack long-term stability. Realization of rotation sensors based on spins of fundamental particles may become a drift-free alternative to such devices. Here, we carry out a proof-of-concept experiment, demonstrating rotation measurements on a rotating setup utilizing nuclear spins of an ensemble of nitrogen vacancy centers as a sensing element with no stationary reference. The measurement is verified by a commercially available microelectromechanical system gyroscope.

NV center pumped and enhanced by nanowire ring resonator laser to integrate a 10 μm-scale spin-based sensor structure

In this work, we propose a 10 μm-scale spin-based sensor structure, which mainly consists of a nanowire (NW) ring resonator laser, nitrogen-vacancy (NV) defects in a nanodiamond (ND) and a microwave (MW) antenna. The NW laser was bent into a ring with a gap to pump the NV defects in the ND which was assembled in the gap with the diameter of ∼8 μm. And the fluorescent light of NV defects was enhanced by the NW ring resonator about 8 times. Furthermore, the NW laser pulse was produced by the optical switch and a simple plus-sequences was designed to get the Rabi oscillation signal. Based on the Rabi oscillation, a Ramsey-type sequence was used to detect the magnetic field with the sensitivity of 83 nT √Hz^-1 for our 10 μm-scale spin-based sensor structure. It proves the spin state in our structure allows for coherent spin manipulation for more complex quantum control schemes. And our structure fulfills the fundamental requirements to develop chip-scale spin-based sensors.

Observation of a Quantum Phase from Classical Rotation of a Single Spin

The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. We report on a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and it can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200 000 rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation, and quantum phase, and they will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.

Hyperpolarized relaxometry based nuclear T1 noise spectroscopy in diamond

The origins of spin lifetimes in quantum systems is a matter of importance in several areas of quantum information. Spectrally mapping spin relaxation processes provides insight into their origin and motivates methods to mitigate them. In this paper, we map nuclear relaxation in a prototypical system of [Formula: see text] nuclei in diamond coupled to Nitrogen Vacancy (NV) centers over a wide field range (1 mT-7 T). Nuclear hyperpolarization through optically pumped NV electrons allows signal measurement savings exceeding million-fold over conventional methods. Through a systematic study with varying substitutional electron (P1 center) and [Formula: see text] concentrations, we identify the operational relaxation channels for the nuclei at different fields as well as the dominant role played by [Formula: see text] coupling to the interacting P1 electronic spin bath. These results motivate quantum control techniques for dissipation engineering to boost spin lifetimes in diamond, with applications including engineered quantum memories and hyperpolarized [Formula: see text] imaging.

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.

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.

Seeing the unseen: Imaging rotation in cells with designer anisotropic particles

Cellular functions are enabled by cascades of transient biological events. Imaging and tracking the dynamics of these events have proven to be a powerful means of understanding the principles of cellular processes. These studies have typically focused on translational dynamics. By contrast, investigations of rotational dynamics have been scarce, despite emerging evidence that rotational dynamics are an inherent feature of many cellular processes and may also provide valuable clues to understanding those cell functions. Such studies have been impeded by the limited availability of suitable rotational imaging probes. This has recently changed thanks to the advances in the development of anisotropic particles for rotational imaging. In this review, we will summarize current techniques for imaging rotation using particle probes that are anisotropic in shape or optical properties. We will highlight two studies that demonstrate how these techniques can be applied to explore important facets of cellular functions.

Single-spin magnetic resonance in the nitrogen-vacancy center of diamond

Magnetic resonance of single spins has flourished mostly because of the unique properties of the NV center in diamond. This review covers the basic physics of this defect center, introduces the techniques for working with single spins and gives an overview of some applications like quantum information and sensing.

A compact, diode laser based excitation system for microscopy of NV centers

We demonstrate that a recently introduced family of direct-emitting green laser diodes is a simple yet efficient light source for excitation of NV centers in diamond. Thanks to their fast (sub-ns) response time, these sources are suitable for a broad variety of measurements, including pulsed optically detected magnetic resonance (ODMR) and fluorescence lifetime imaging. This feature, together with a drastically simplified design, is a significant advantage over the traditional excitation system comprising an Nd: YAG laser switched by an acousto-optic modulator. We introduce a simple design for such a compact laser system and experimentally verify that it enables simultaneous lifetime and ODMR measurements on NV centers. In particular, we find that the NV(-) charge state remains stable in spite of the short excitation wavelength of the new source.

Cavity-enhanced room-temperature magnetometry using absorption by nitrogen-vacancy centers in diamond

We demonstrate a cavity-enhanced room-temperature magnetic field sensor based on nitrogen-vacancy centers in diamond. Magnetic resonance is detected using absorption of light resonant with the 1042 nm spin-singlet transition. The diamond is placed in an external optical cavity to enhance the absorption, and significant absorption is observed even at room temperature. We demonstrate a magnetic field sensitivity of 2.5  nT/Hz, and project a photon shot-noise-limited sensitivity of 70  pT/Hz for a few mW of infrared light, and a quantum projection-noise-limited sensitivity of 250  fT/Hz for the sensing volume of ∼90  μm×90  μm×200  μm.

Electronic properties and metrology applications of the diamond NV- center under pressure

The negatively charged nitrogen-vacancy (NV-) center in diamond has realized new frontiers in quantum technology. Here, the optical and spin resonances of the NV- center are observed under hydrostatic pressures up to 60 GPa. Our results motivate powerful new techniques to measure pressure and image high-pressure magnetic and electric phenomena. Additionally, molecular orbital analysis and semiclassical calculations provide insight into the effects of compression on the electronic orbitals of the NV- center.