Optimal control theory techniques for nitrogen vacancy ensembles in single crystal diamond
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2023-09-27 |
| Journal | Quantum Information Processing |
| Authors | Madelaine S. Z. Liddy, Troy W. Borneman, Peter Sprenger, David G. Cory |
| Institutions | University of Waterloo |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research presents a controls-based solution for achieving orientation-selective quantum control of Nitrogen Vacancy (NV) center ensembles in single crystal diamond, optimized for high-sensitivity quantum sensing applications.
- Core Achievement: Demonstrated collective, orientation-selective quantum control of NV ensembles in (100) diamond using Optimal Control Theory (OCT) and circularly polarized microwaves (CPW).
- Zero-Field Control: Achieved arbitrary simultaneous control over all four Principal Axis Systems (P.A.S.) without requiring an external static magnetic field, simplifying hardware design.
- Control Mechanism: CPW fields are generated by dual parallel microstrip resonators, enabling the use of a single central control frequency (2.87 GHz).
- Optimization: OCT, specifically the GRAPE algorithm, was used to design robust, transition-selective pulses (identity and π-type operations) optimized over the incoherent distribution of Hamiltonians.
- Performance Metrics: Measured Rabi drive strengths were up to 2.64 MHz for the high-frequency sub-ensemble, requiring 10 µs pulses for state-to-state transfer.
- Engineering Value: The methodology offers a controls-based alternative to complex optical polarization methods for suppressing or studying individual NV orientation signals, crucial for integrating high-sensitivity NV-based sensors.
Technical Specifications
Section titled “Technical Specifications”| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Crystal Orientation | (100) | N/A | Single crystal DNV-B1 sample (Element Six). |
| Diamond Thickness | 500 | µm | Used to keep focal volume away from microstrips. |
| Estimated NV Centers (Focal Volume) | 16,000 | N/A | Within 0.59 µm beam diameter. |
| Zero Field Splitting (Δ) | ≈ 2.87 | GHz | Quantization of the effective spin-1 particle. |
| Central Control Frequency (ωτ) | 2.87 | GHz | Used for IQ mixing in the RF system. |
| High-Frequency Rabi Drive (ΩNVA) | 2.64 | MHz | Measured strength for sub-ensemble A. |
| Low-Frequency Rabi Drive (ΩNVB) | 1.03 | MHz | Measured strength for sub-ensemble B. |
| Experimental Field Orthogonality (η) | 115 | ° | Measured phase value used in the phenomenological Hamiltonian. |
| OCT Pulse Length (State-to-State) | 10 | µs | Achieved in 250 steps of 40 ns. |
| Identity Pulse Performance (Ideal 100%) | 40 ± 1.5 | % | Population of the |
| Pi Pulse Performance (Ideal 0%) | 17 ± 1.5 | % | Population of the |
| Microstrip Length | 7.5 | mm | Dual parallel microstrip resonators. |
| Microstrip Width | 127 | µm | N/A |
| Microstrip Spacing | 150 | µm | Used to avoid optical interference. |
| Objective Working Distance (WD) | 160 | µm | Distance from objective to diamond surface. |
| Focal Volume Distance from Microstrips | ≈ 70 | µm | Minimizes reflected green light signal. |
Key Methodologies
Section titled “Key Methodologies”The experimental procedure combined optical characterization, RF system engineering, and quantum optimal control theory:
- Sample and RF Integration: A 500 µm-thick DNV-B1 (100) diamond was mounted atop a dual-channel PCB featuring two parallel microstrips (150 µm spacing) designed to deliver sufficient microwave power to the focal volume.
- Optical Equalization: The NV ensemble was excited with off-resonant green light (532 nm). A half-wave plate (HWP) was rotated (optimal value 42°) to align the light electric field with the NV electric dipole, ensuring equal fluorescence from all four NV orientations.
- Microwave Control Generation: A 2.87 GHz central frequency signal was split into two channels. Each channel was mixed via an IQ mixer with independent amplitude and phase envelopes (I1/2, Q1/2) generated by a four-channel AWG, creating two independently controllable microwave fields.
- System Characterization: Dual-channel Rabi experiments were performed to measure the Rabi drive strengths (ΩNVA = 2.64 MHz, ΩNVB = 1.03 MHz) and the experimental orthogonality phase (η = 115°) for the two degenerate NV sub-ensembles.
- Spin-Locking Demonstration: Preliminary control was shown using a single microwave channel spin-locking experiment, which selectively suppressed the evolution of one NV sub-ensemble while allowing the other to evolve freely.
- Optimal Control Pulse Design: The GRAPE algorithm was used to optimize amplitude-only control envelopes (Ω1/2) based on the measured phenomenological Hamiltonian parameters. Pulses were optimized for state-to-state targets (identity: |0> → |0>; selective π-type: |0> → |+1>).
- Pulse Implementation: Optimized 10 µs pulses were implemented experimentally, demonstrating distinguishable control between the identity and π-type operations across the two sub-ensembles.
Commercial Applications
Section titled “Commercial Applications”The demonstrated control techniques and hardware integration are critical for advancing quantum sensing technology:
- Vector Magnetometry: Enables simultaneous and selective manipulation of all four NV orientations, allowing for richer vector measurements of magnetic fields (DC and AC) and temperature within a single crystal.
- Compact Quantum Sensors: Provides a pathway for realizing high-sensitivity NV-based quantum sensing devices that are deployable at room temperature, eliminating the need for bulky external static magnetic field coils.
- Chemical and Biological Sensing: Applicable to imaging small magnetic fields, including those generated by nearby bacteria and molecules, enhancing capabilities in single-cell magnetic imaging.
- Robust Pulse Engineering: OCT-designed pulses, especially those optimized for robustness against zero-field splitting variations and hyperfine interactions, are essential for reliable operation in noisy, real-world environments.
- Diamond Material Characterization: The techniques can be used for high-precision sensing of crystal strain in the diamond lattice, relevant for quality control in diamond synthesis.
- RF Hardware Optimization: The use of dual microstrip resonators and CPW fields provides a scalable, low-complexity solution for delivering control signals to quantum ensembles.
View Original Abstract
Abstract Nitrogen vacancy centre ensembles are excellent candidates for quantum sensors due to their vector magnetometry capabilities, deployability at room temperature and simple optical initialization and readout. This work describes the engineering and characterization methods required to control all four principle axis systems (P.A.S.) of NV ensembles in a single crystal diamond without an applied static magnetic field. Circularly polarized microwaves enable arbitrary simultaneous control with spin-locking experiments and collective control using optimal control theory (OCT) in a (100) diamond. These techniques may be further improved and integrated to realize high-sensitivity NV-based quantum sensing devices using all four P.A.S. systems.