State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2021-02-09 |
| Journal | Physical Review Research |
| Authors | Matthew Carl Cambria, Aedan Gardill, Y. Li, Ariel Norambuena, J. R. Maze |
| Institutions | University of WisconsināMadison, Universidad Mayor |
| Citations | 16 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive Summaryā- Ultimate Coherence Limit Established: The maximum theoretically achievable NV electronic spin coherence time (T2,max) in high-purity bulk diamond at room temperature (295 K) is limited by spin-phonon interactions to 6.8(2) ms in the standard single-quantum basis.
- State-Dependent Relaxation: Relaxation rates are state-dependent. The qutrit transition rate (Ī³, |ms = -1> ā |ms = +1>) is approximately twice as fast as the qubit transition rate (Ī©, |ms = 0> ā |ms = Ā±1>).
- Phonon-Limited Dynamics: Relaxation rates (Ī© and Ī³) were found to be independent of native NV concentration across four orders of magnitude (10-5 ppb to 10 ppb), confirming that spin-phonon interactions are the dominant limiting mechanism.
- Theoretical Model Failure: The standard theoretical model for NV spin-lattice relaxationāthe two-acoustic-phonon Raman processāpredicts a rate of zero for the qutrit transition (Ī³) due to time-reversal symmetry constraints.
- Dominant Qutrit Mechanism: The observed fast qutrit relaxation (Ī³) is attributed to either Orbach-like processes involving two quasilocalized phonons or contributions from higher-order terms in the spin-phonon Hamiltonian.
- Double-Quantum Limitation: The faster qutrit decay limits the T2,max for the noise-immune double-quantum basis to 5.7(2) ms, approximately 1 ms shorter than the single-quantum basis limit.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operating Temperature | 295 Ā± 1 | K | Ambient conditions for all measurements. |
| Maximum T2 (Single-Quantum Basis) | 6.8(2) | ms | Ultimate phonon-limited coherence time (T2,max = 2/(3Ī©)). |
| Maximum T2 (Double-Quantum Basis) | 5.7(2) | ms | Coherence limit set by T2,max = 1/(Ī© + Ī³). |
| Qubit Relaxation Rate (Ī©) Range | 50 to 70 | s-1 | Measured rate for |
| Qutrit Relaxation Rate (Ī³) Range | 100 to 250 | s-1 | Measured rate for |
| NV Concentration Range | 10-5 to 10 | ppb | Range across high-purity CVD bulk diamond samples (A, B, C). |
| Ground State Zero-Field Splitting (Dgs) | 2.87 | GHz | NV Hamiltonian parameter. |
| NV Electronic Spin Gyromagnetic Ratio (gĀµB) | 2.8 | MHz/G | NV Hamiltonian parameter. |
| Empirical Activation Energy (Ī) | 73(4) | meV | Associated with the exponential (Orbach-like) term in T1 relaxation. |
| Quasilocalized Phonon Energy (ħĻloc) | 65 | meV | Center of the vibrational resonance band implicated in relaxation. |
| Magnetic Field Magnitude (B) | < 100 | G | Typical applied field magnitude. |
Key Methodologies
Section titled āKey Methodologiesā- Sample Selection: Experiments utilized native NV centers in three distinct high-purity Chemical Vapor Deposition (CVD) grown bulk diamond samples from different growers, covering a wide range of native NV concentrations (10-5 ppb to 10 ppb).
- Microscopy and Environment: Measurements were conducted using a homebuilt confocal microscope maintained at a temperature stable to 295 K (Ā±1 K).
- Spin Initialization and Readout: Spin polarization and readout were achieved using approximately 1 mW of 532-nm green laser light.
- Magnetic Field Control: Applied magnetic fields (typically < 100 G) were characterized by on-axis (B||) and off-axis (Bā„) components relative to the NVās spatial axis of symmetry.
- State-Selective Measurement: State-selective Ļ-pulses were employed to measure the population decay into and out of each spin state (|0>, |+1>, |-1>) individually.
- Rate Extraction via Subtraction: Relaxation rates (Ī© and Ī³) were extracted from the population decay curves using a classical three-level population model. The rates were isolated by subtracting specific population curves (e.g., FĪ©(Ļ) = P0,0(Ļ) - P0,+1(Ļ)) to yield single-exponential decays.
- Theoretical Modeling: Relaxation rates were analyzed using Fermiās golden rule applied to second order, considering two-phonon Raman processes involving both acoustic and quasilocalized phonons, and incorporating time-reversal symmetry arguments.
Commercial Applications
Section titled āCommercial Applicationsā- Quantum Computing and Memory: The established T2,max of 6.8 ms sets the fundamental upper limit on the coherence time for NV-based qubits operating at room temperature, directly impacting the maximum achievable fidelity and duration of quantum gate operations and memory storage.
- High-Performance Magnetometry: For magnetic field sensing applications, the T2 limit defines the maximum integration time and thus the ultimate sensitivity (Ī“Bmin). Engineers must account for the faster qutrit relaxation (Ī³) when designing sensors utilizing the double-quantum basis, which, despite its noise immunity, is limited to a shorter T2,max of 5.7 ms.
- Solid-State Defect Engineering: The finding that quasilocalized phonons (Orbach-like processes) are likely dominant in qutrit relaxation provides a clear target for material science efforts. Future diamond growth recipes could focus on engineering the lattice to shift or suppress the 65 meV quasilocalized vibrational modes, potentially extending T2 beyond 6.8 ms.
- Thermal and Strain Sensing Calibration: Since spin relaxation is highly dependent on phonon interactions, precise knowledge of the underlying mechanisms (Raman T5 scaling vs. Orbach exponential scaling) is crucial for accurate calibration and noise mitigation in NV-based thermal and strain sensors.
- Advanced Spin-Lattice Hamiltonian Development: The experimental results necessitate the refinement of spin-lattice Hamiltonian models to include second-order atomic displacements or other terms that correctly predict a non-zero relaxation rate for the qutrit transition, improving the predictive power of simulations for NV systems.
View Original Abstract
Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system. We show that relaxation on the |m<sub>s</sub> = -1> ā|m<sub>s</sub> = +1> transition occurs approximately twice as fast as relaxation on the |m<sub>s</sub> = 0> ā|m<sub>s</sub> = Ā±1> transitions under ambient conditions in native NVs in high-purity bulk diamond. The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions. We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms. Lastly, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind |m<sub>s</sub> = -1> ā|m<sub>s</sub> = +1> relaxation, motivating future measurements of the temperature dependence of this relaxation rate.