Fast Relaxation on Qutrit Transitions of Nitrogen-Vacancy Centers in Nanodiamonds
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2020-03-04 |
| Journal | Physical Review Applied |
| Authors | Aedan Gardill, Matthew Carl Cambria, Shimon Kolkowitz |
| Institutions | University of Wisconsin–Madison |
| Citations | 15 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”- Dominant Decoherence Mechanism: Fast spin relaxation (rate γ) on the qutrit transition (ms = |±1> states) is the primary source of decoherence in 40 nm commercial nanodiamond (ND) NV centers.
- Performance Limit: At low axial magnetic fields, the qutrit relaxation rate (γ) can exceed 100 kHz, limiting the maximum theoretical coherence time (T2,max) to tens of microseconds.
- Noise Attribution: The fast relaxation is strongly attributed to resonant surface electric field noise (charge noise) incoherently driving transitions between the |±1> states, rather than magnetic noise.
- Noise Scaling: The relaxation rate (γ) exhibits a strong falloff (scaling as 1/Δ±2) with increasing frequency splitting (Δ±) between the |±1> states, consistent with a 1/f2 noise power spectral density.
- Engineering Recommendation: To maximize T2,max, coherent measurements in ND NVs should be performed at moderate axial magnetic fields (Bz > 60 G) to increase the splitting and reduce charge noise sensitivity.
- Temporal Instability: The relaxation rate (γ) fluctuates significantly over hours to days, providing strong evidence that the noise originates from dynamic charge traps or adsorbates on the nanodiamond surface.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Nanodiamond Mean Diameter | 40 | nm | Commercial Adámas Nano NDs |
| NV Ground State Splitting (Dgs/2π) | 2.87 | GHz | Zero-field splitting ( |
| Qutrit Relaxation Rate (γ) (Max Observed) | 240 | kHz | NV5 at Δ± ≈ 11 MHz (Low Field) |
| Qubit Relaxation Rate (Ω) (Typical) | 0.17 to 1.4 | kHz | Measured on |
| Maximum Theoretical Coherence Time (T2,max) (Low Field) | 8.3 to 18 | µs | Hard limit set by γ, calculated via T2,max = 2(3Ω + γ)-1 |
| Qubit T1 Lifetime (Standard Measurement) | ~330 | µs | Standard |
| Electric Field Noise Scaling | 1/Δ±2 | N/A | Consistent with 1/f2 noise power spectral density |
| Estimated RMS Electric Field Noise (ERMS) | ~107 | V/m | Calculated over 20-1000 MHz range |
| Recommended Axial Magnetic Field (Bz) | > 60 | G | Required to achieve high Δ± and mitigate fast γ relaxation |
| Laser Power for Polarization/Readout | ~0.5 | mW | 532 nm laser used for all primary measurements |
Key Methodologies
Section titled “Key Methodologies”- Sample Preparation: Commercial nanodiamonds (40 nm mean diameter, ~100 ppm substitutional nitrogen) were annealed (850 °C) and oxidized, resulting in a carboxylated surface.
- Substrate Coating: NDs were suspended in deionized water (10 µg/mL) with 0.17% poly-vinyl alcohol (PVA) added for adhesion, then spin-coated onto a gridded glass coverslip (3000 rpm).
- NV Center Selection: Single NV centers were identified via confocal microscopy and confirmed as single photon emitters using g(2)(τ) measurements (g(2)(0) < 0.5). Only NVs exhibiting measurable ODMR contrast at low magnetic fields were selected for relaxation studies (5 out of 110 tested).
- Spin State Control: A combination of 532 nm optical illumination (for polarization and readout) and state-selective resonant microwave π-pulses were used to prepare and read out populations in all three ground states (|0>, |±1>).
- Population Dynamics Measurement: The population decay curves (Pi,j(τ)) were measured for all nine possible preparation (i) and readout (j) combinations over a wait time (τ).
- Rate Isolation: The qubit (Ω) and qutrit (γ) relaxation rates were extracted by fitting the three-level rate equations to subtracted population curves (FΩ and Fγ), isolating the single exponential decay components.
- Noise Source Verification: Measurements were repeated on NVs deposited on a clean silicon wafer without PVA, confirming that the fast relaxation behavior is intrinsic to the nanodiamonds themselves, not the substrate or polymer.
Commercial Applications
Section titled “Commercial Applications”- Nanoscale Quantum Sensing: Improving the sensitivity and operational bandwidth of ND NV sensors used for measuring local magnetic fields, electric fields, strain, and temperature in confined spaces.
- Bio-Sensing and In-Vivo Thermometry: Enhancing the coherence time of ND NVs used as probes inside living cells, where surface interactions and charge noise are prevalent limitations.
- Quantum Device Engineering: Providing critical data on surface-induced decoherence mechanisms (charge noise) relevant for designing and optimizing other solid-state quantum systems, including:
- Superconducting qubits.
- Semiconductor quantum dots.
- Ion traps (where electric field noise causes heating).
- Surface Science and Interface Characterization: Utilizing the qutrit transition relaxation rate (γ) as a spectroscopic probe to quantify and map the power spectral density of electric field noise near material surfaces.
- Advanced Material Processing: Informing surface functionalization and annealing protocols for nanodiamonds to minimize charge traps and stabilize the local electric environment, thereby extending T2.
View Original Abstract
Thanks to their versatility, nitrogen-vacancy (N-V) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-Vs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the m<sub>s</sub> = | ± 1 $\rangle$ states of the N- V<sup>-</sup> electronic ground state in approximately 40-nm nanodiamonds under ambient conditions. For frequency splittings between these states of 20 MHz or less the maximum theoretically achievable coherence time of the N-V spin is approximately 2 orders of magnitude shorter than would be expected if the N-V spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with N-Vs in nanodiamonds should be performed at moderate axial magnetic fields ( > 60 G). We also observe that the qutrit relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for N-V s in nanodiamonds.