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Magnetometry via spin-mechanical coupling in levitated optomechanics

MetadataDetails
Publication Date2017-08-04
JournalOptics Express
AuthorsPardeep Kumar, M. Bhattacharya
Citations24
AnalysisFull AI Review Included

Technical Analysis & Product Documentation: MPCVD Diamond for Levitated Optomechanics and Ultra-Sensitive Magnetometry

Section titled “Technical Analysis & Product Documentation: MPCVD Diamond for Levitated Optomechanics and Ultra-Sensitive Magnetometry”

This paper presents a novel hybrid nanomechanical magnetometer utilizing a single Nitrogen-Vacancy ($\text{NV}^-$) center spin coupled to the mechanical oscillation of an optically levitated nanodiamond via a Magnetic Field Gradient (MFG). This research validates diamond as a superior platform for quantum sensing and metrology.

  • Core Achievement: Demonstrated ultra-sensitive MFG detection using levitated optomechanics, achieving a sensitivity of 1 $\mu$Tm-1/$\sqrt{\text{Hz}}$ under optimal cooling and ultrahigh vacuum conditions.
  • Dual Sensing Modalities: Sensitivity was characterized using two distinct methods: analyzing the position spectrum of the mechanical oscillator, and manipulating the spin degrees of freedom using Ramsey interferometry.
  • Material Requirement: Relies on the high quality and robust coherence of the $\text{NV}^-$ center embedded within a single crystal diamond lattice, emphasizing the need for high-purity CVD diamond.
  • Versatility: The proposed magnetometer architecture functions effectively under both feedback-cooled (T$_{eff}$ = 4 K) and less stringent ambient (room temperature, atmospheric pressure) conditions, confirming its suitability for portable applications.
  • Future Applications: The system provides a platform for fundamental physics tests, including the generation of macroscopic quantum superposition states and the investigation of quantum gravity.
  • 6CCVD Relevance: Replication and advancement of this research require precision-engineered, optical-grade Single Crystal Diamond (SCD) material, a core specialization of 6CCVD.

The following hard parameters define the operating regime and core achievements of the proposed levitated nanomechanical magnetometer:

ParameterValueUnitContext
Optimal MFG Sensitivity (Mechanical)1 $\mu$Tm-1/$\sqrt{\text{Hz}}$Magnetic Field Gradient / FrequencyUltrahigh vacuum (< 10-5 mbar) and optimal cooling (T$_{eff}$ = 4 K).
Optimal MFG Sensitivity (Spin)100 $\mu$Tm-1/$\sqrt{\text{Hz}}$Magnetic Field Gradient / FrequencyPhoton-shot noise and spin-projection noise limited using Ramsey sequence.
Room Temp/High Pressure Sensitivity$\approx$ 100 mTm-1/$\sqrt{\text{Hz}}$Magnetic Field Gradient / FrequencyDemonstrates robust operation under ambient conditions.
Nanodiamond Radius (R)50nmMechanical oscillator dimension.
Diamond Density ($\rho$)2200kg/m3Standard CVD Diamond density.
Mechanical Frequency ($\omega_{m}$)38kHzOscillation frequency of the levitated particle (z-axis).
NV Defect StateNegatively Charged ($\text{NV}^-$)N/APreferred state due to existence of spin triplet ground state for magnetometry.
Excitation Laser Wavelength532nmGreen laser source for spin initialization ($\text{3A}_2 \rightarrow \text{3E}_2$ transition).
Photoluminescence Readout637nmZero-Phonon Line (ZPL) detection.
Optimal Effective Temperature ($T_{eff}$)4KTemperature achieved through feedback cooling in ultrahigh vacuum.

The experiment utilizes levitated optomechanics combined with quantum spin manipulation techniques to measure the Magnetic Field Gradient (MFG):

  1. Optomechanical Levitation: A nanodiamond containing a single $\text{NV}^-$ center is trapped in ultrahigh vacuum using a focused Gaussian beam (optical dipole trap), allowing mechanical oscillations along the z-axis at $\omega_{m} \approx 38$ kHz.
  2. Spin Initialization and Readout: The $\text{NV}^-$ center spin is initialized into the $m_s = 0$ ground state via optical illumination (532 nm) and subsequent spin-selective intersystem crossing. Readout is achieved by monitoring the $637$ nm photoluminescence intensity.
  3. Mechanical Ground State Preparation: Interferometric monitoring of particle position is used for feedback cooling, driving the mechanical oscillator into the quantum ground state (mean phonon number $\langle N \rangle < 1$) under optimal conditions ($T_{eff} = 4$ K, pressure $\le 10^{-5}$ mbar).
  4. Spin-Mechanical Coupling: A homogeneous MFG is applied along the z-direction, creating a coupling Hamiltonian ($H_{int}$) proportional to the spin operator ($S_z$) and the mechanical creation/annihilation operators ($a^{\dagger}, a$), mediating the energy exchange.
  5. Ramsey Interferometry Sequence: For the most sensitive measurements, a $\pi/2 - T - \pi/2$ microwave pulse sequence is applied to the $\text{NV}^-$ spin. The spin-mechanical interaction during the free evolution time ($T$) induces a mechanical phase shift conditioned on the spin state, which is then read out optically.

6CCVD provides the specialized MPCVD diamond materials and precision engineering required to replicate, scale, and industrialize quantum metrology platforms utilizing $\text{NV}$-center diamond.

Replication and scaling of this research demand high-purity Single Crystal Diamond (SCD) optimized for quantum coherence and mechanical stability.

  • Optical Grade Single Crystal Diamond (SCD): Required for maximizing NV coherence time ($\text{T}_2^*$) and minimizing spurious optical loss/heating that degrades cooling efficiency. 6CCVD supplies SCD wafers up to 125 mm in dimension.
  • Low-Strain SCD Substrates: The performance of the spin-mechanical coupling depends critically on lattice strain control. Our MPCVD growth process is optimized to minimize internal strain, ensuring stable NV spectral properties.
  • Custom NV Doping/Implantation: While the paper uses a single NV center, scaling requires reliable NV formation. 6CCVD supports customers through custom recipes focusing on controlled nitrogen incorporation during growth or providing substrates suitable for post-growth ion implantation and annealing.

The future integration of levitated nanodiamond sensors or the development of on-chip optomechanical resonators requires precision fabrication beyond bulk material.

Requirement6CCVD Service & SpecificationEngineering Advantage
Precision GeometryCustom Dimensions and Laser Cutting. We supply SCD plates/wafers in custom shapes and sizes, or thin membranes (thickness down to 0.1 $\mu$m) for integration into micro-cavities and resonators.Enables the fabrication of specific geometries required for advanced optomechanical coupling structures (e.g., cantilevers or micro-disk resonators).
Surface QualityUltra-Smooth Polishing (Ra &lt; 1 nm for SCD). Essential for minimizing photon scattering and parasitic absorption critical for achieving T$_{eff}$ = 4 K feedback cooling.Guarantees the necessary optical quality and low mechanical damping needed for quantum ground state preparation.
Hybrid IntegrationCustom Metalization Services (Au, Pt, Ti, W, Cu). Necessary for creating integrated microwave coils (MW Coils, Fig. 1) directly on the diamond surface used for spin manipulation (Ramsey sequence).Provides a full material-to-device solution, accelerating development cycles for hybrid quantum systems.
Material ThicknessSCD/PCD Thickness Control (0.1 $\mu$m to 500 $\mu$m). Provides flexibility in designing the mass ($m$) and mechanical frequency ($\omega_m$) of the diamond oscillator, crucial parameters identified in the paper (Eq. 7).Fine-tune mechanical parameters for optimal signal response and isolation in specific sensing environments.

6CCVD’s in-house PhD team specializes in CVD diamond material science and quantum applications. We can assist researchers and engineers in selecting optimal diamond specifications (e.g., crystal orientation, surface termination, and nitrogen content) required to achieve superior coherence times necessary for photon-shot noise limited Magnetic Field Gradient sensing projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

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 1ÎźTm<sup>-1</sup>/Hz. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100mTm<sup>-1</sup>/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 100ÎźTm<sup>-1</sup>/Hz. We conclude that this hybrid levitated nanomechanical magnetometer provides a favorable and versatile platform for sensing applications.