Continuous real-time sensing with a nitrogen-vacancy center via coherent population trapping

At a Glance

Metadata	Details
Publication Date	2021-04-12
Journal	Physical review. A/Physical review, A
Authors	Shu-Hao Wu, Ethan Turner, Hailin Wang
Institutions	University of Oregon
Citations	15
Analysis	Full AI Review Included

Continuous Real-Time Quantum Sensing via Coherent Population Trapping in Diamond NV Centers

6CCVD Technical Analysis and Sales Documentation

This document analyzes the research demonstrating continuous real-time magnetic field sensing using a single Nitrogen Vacancy (NV) center in diamond via Coherent Population Trapping (CPT). This application is highly relevant to engineers and scientists developing next-generation quantum sensors, leveraging the unique material properties of MPCVD Single Crystal Diamond (SCD) supplied by 6CCVD.

Executive Summary

Application Breakthrough: Theoretical demonstration of continuous, real-time magnetic field sensing using a single NV center, overcoming limitations of pulsed interferometry (e.g., Ramsey).
Mechanism: Utilizes Coherent Population Trapping (CPT) in a $\Lambda$-type three-level system, where fluctuating magnetic fields kick the NV center out of the dark state, generating single-photon emissions.
Low Count Efficiency: Achieves effective magnetic field estimation even when the average photon count per update time interval ($\tau = 10$ µs) is much smaller than 1.
Estimation Technique: Employs an advanced Ornstein-Uhlenbeck (OU) Bayesian estimator, leveraging known statistical properties of the fluctuating environment (nuclear spin bath).
Performance Metric: The estimation variance obtained with the OU Bayesian estimator nearly approaches the classical Cramer-Rao Lower Bound (CRLB), demonstrating maximum information extraction from detected photons.
Time Resolution: Provides dynamical information on a timescale comparable to the inverse of the average photon counting rate (10,000 counts/second).
Material Requirement: Requires ultra-high purity Single Crystal Diamond (SCD) to ensure long spin coherence times ($T_2^*$) and stable, isolated NV centers.

Technical Specifications

The following parameters were extracted from the theoretical analysis and numerical simulations, highlighting the stringent requirements for the diamond material and experimental setup.

Parameter	Value	Unit	Context
Quantum Sensor System	NV Center (A-type three-level)	N/A	Solid-state quantum sensing platform
Model Fluctuating Environment	¹³C Nuclear Spin Bath	N/A	Modeled as Ornstein-Uhlenbeck (OU) process
Spin Bath Memory Time ($\tau_N$)	1	ms	Used for numerical simulations
Fluctuation Variance ($\sigma/2\pi$)	0.13	MHz	Corresponds to Dephasing Time $T_2^*$ = 1.7 µs
NV Radiative Lifetime ($\Gamma/2\pi$)	13	MHz	Spontaneous emission rate [34]
Simulation Rabi Frequency ($\Omega/2\pi$)	2.8	MHz	Used in Stochastic Schrödinger Equation (SSE) simulation
Simulation Raman Detuning/Bias ($\Delta_0/2\pi$)	0.25	MHz	Used in numerical simulation
Optimal Rabi Frequency ($\Omega/2\pi$)	2.5	MHz	Optimal CPT parameter for minimum variance
Optimal Bias ($\Delta_0/2\pi$)	0.2	MHz	Optimal CPT parameter for minimum variance
Update Time Interval ($\tau$)	10	µs	Used for real-time Bayesian estimation
Overall Collection Efficiency ($\eta$)	1.6	%	Realistic experimental condition for detected photons
Average Photon Count Rate	10,000	counts/second	Achieved under $\eta=1.6%$

Key Methodologies

The research relies on advanced quantum optics and statistical estimation techniques applied to the NV center system:

Coherent Population Trapping (CPT): The NV center is treated as a $\Lambda$-type three-level system (two ground spin states $|0\rangle, |1\rangle$ coupled to an excited state $|e\rangle$). Two external optical fields with equal Rabi frequency ($\Omega$) drive the system into a dark state, preventing spontaneous emission.
Magnetic Field Coupling: Fluctuations in the magnetic environment ($\omega_B$) modulate the frequency separation between the ground states, kicking the NV center out of the dark state and inducing single-photon emissions.
Stochastic Simulation: The time series of single-photon emissions is simulated using the Stochastic Schrödinger Equation (SSE), tracking the system collapse and excited-state population ($\rho_{ee}$).
Ornstein-Uhlenbeck (OU) Modeling: The fluctuating magnetic environment (nuclear spin bath) is modeled as an OU process, characterized by memory time ($\tau_N$) and variance ($\sigma$).
Bayesian Inference: The OU Bayesian estimator is applied to the low-count photon time series ($y_n$). By incorporating the known statistical properties of the OU process, the estimator provides continuous real-time tracking of the fluctuating field ($x_n$).
Performance Validation: Estimation variances are calculated and compared against the classical Cramer-Rao Lower Bound (CRLB), confirming that the Bayesian approach extracts nearly the maximum possible information from the detected photons.

6CCVD Solutions & Capabilities

Replicating and advancing this cutting-edge quantum sensing research requires diamond materials with exceptional purity, precise geometry, and integrated device features. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond solutions.

Research Requirement	6CCVD Solution & Capability	Technical Advantage for Quantum Sensing
Ultra-High Purity Diamond Host	Optical Grade Single Crystal Diamond (SCD): High-purity SCD wafers are essential for minimizing intrinsic defects and maximizing the NV center spin coherence time ($T_2^*$).	Ensures stable, isolated quantum sensors capable of achieving the long coherence times required for high-sensitivity measurements.
Noise Reduction & Coherence Extension	Custom Isotopic Purity: We offer isotopically engineered SCD (e.g., < 0.1% ¹³C concentration).	Directly mitigates the primary source of magnetic fluctuation noise (the ¹³C nuclear spin bath), significantly extending $\tau_N$ and improving the signal-to-noise ratio, allowing the OU Bayesian estimator to operate closer to the CRLB.
Device Integration & Scalability	Custom Dimensions and Thickness: SCD plates available up to 125mm in diameter. Thickness control from 0.1 µm to 500 µm. Substrates up to 10mm thick.	Supports the fabrication of large-area quantum devices and integration into complex optical/microwave setups necessary for CPT control.
Efficient Optical Readout	Precision Polishing (Ra < 1 nm): SCD surfaces are polished to atomic flatness. Inch-size PCD polishing to Ra < 5 nm.	Minimizes optical scatter and surface-related decoherence, maximizing the overall collection/detection efficiency ($\eta = 1.6%$ in the paper) crucial for low-count estimation.
Control Field Delivery	Custom Metalization Services: Internal capability for deposition of Au, Pt, Pd, Ti, W, and Cu.	Enables the integration of microwave strip lines and antennas directly onto the diamond surface for precise control of the Rabi frequency ($\Omega$) and initialization of the NV spin states.

Engineering Support: 6CCVD’s in-house PhD team specializes in MPCVD growth parameters optimized for quantum applications. We provide expert consultation on material selection, NV creation techniques (e.g., implantation/annealing), and surface preparation necessary to replicate or extend this continuous real-time magnetic sensing project.

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

View Original Abstract

We propose and theoretically analyze the use of coherent population trapping\nof a single diamond nitrogen vacancy (NV) center for continuous real-time\nsensing. The formation of the dark state in coherent population trapping\nprevents optical emissions from the NV center. Fluctuating magnetic fields,\nhowever, can kick the NV center out of the dark state, leading to a sequence of\nsingle-photon emissions. A time series of the photon counts detected can be\nused for magnetic field estimations, even when the average photon count per\nupdate time interval is much smaller than 1. For a theoretical demonstration,\nthe nuclear spin bath in a diamond lattice is used as a model fluctuating\nmagnetic environment. For fluctuations with known statistical properties, such\nas an Ornstein-Uhlenbeck process, Bayesian inference-based estimators can lead\nto an estimation variance that approaches the classical Cramer-Rao lower bound\nand can provide dynamical information on a timescale that is comparable to the\ninverse of the average photon counting rate. Real-time sensing using coherent\npopulation trapping adds a new and powerful tool to the emerging technology of\nquantum sensing.\n

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Original Source

DOI: https://doi.org/10.1103/physreva.103.042607