Nonlinear dynamics of a two-level system of a single spin driven beyond the rotating-wave approximation
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-05-01 |
| Journal | Physical review. A/Physical review, A |
| Authors | âKâ. âRâ. âKâ. âRao, Dieter Suter |
| Institutions | TU Dortmund University |
| Citations | 19 |
| Analysis | Full AI Review Included |
Technical Documentation and Analysis: Strong-Driving Dynamics in NV Diamond
Section titled âTechnical Documentation and Analysis: Strong-Driving Dynamics in NV DiamondâResearch Paper Analyzed: Nonlinear dynamics of a two-level system of a single spin driven beyond the rotating-wave approximation (arXiv:1610.04512v2)
Executive Summary
Section titled âExecutive SummaryâThe analyzed research details the experimental study of nonlinear quantum dynamics in a single Nitrogen-Vacancy (NV) center in diamond, specifically focusing on the strong-driving regime crucial for advanced quantum computing applications.
- Core Achievement: Observation and analysis of anharmonic Rabi oscillations when the driving field amplitude ($\omega_1$) is comparable to or greater than the transition frequency ($\omega_0 = 1.7$ MHz), demonstrating the breakdown of the Rotating-Wave Approximation (RWA).
- Physical System: A two-level electron spin subsystem of an NV center coupled to a first-shell $^{13}$C nuclear spin in diamond, operating near a Level Anti-Crossing (LAC).
- Material Requirements: The experiment necessitates ultra-high-purity diamond (nitrogen concentration < 5 ppb) to maintain necessary spin coherence and isolate the target spin system.
- Strong Driving Regime: Achieved electron spin Rabi frequencies ($\omega_1$) up to 3.62 MHz in a static magnetic field (28.9 G), creating a platform for studying ultrafast quantum gates.
- Observed Dynamics: System dynamics are highly nonlinear, oscillating with multiple frequencies, which is relevant for developing optimal control theory and ultra-fast qubit protocols.
- 6CCVD Value Proposition: 6CCVD provides the necessary Electronic Grade Single Crystal Diamond (SCD) material, which can be isotopically purified to further minimize decoherence, supporting both fundamental research and quantum device development.
Technical Specifications
Section titled âTechnical SpecificationsâThe core parameters and material requirements extracted from the experimental methodology are summarized below:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Material Purity (N) | < 5 | ppb | Required nitrogen impurity concentration |
| Crystal Type | Natural $^{13}$C Abundance | N/A | Used for $^{13}$C nuclear spin coupling |
| NV Zero-Field Splitting (D) | 2870.2 | MHz | Intrinsic energy splitting |
| Static Magnetic Field (B) | 28.9 | G | Applied field magnitude |
| LAC Orientation Angle ($\theta$) | 38.4 | ° | Angle relative to the NV symmetry axis |
| Two-Level System $\omega_0$ | 1.7 | MHz | Electron spin transition frequency at LAC |
| Maximum Applied Rabi Frequency ($\omega_1$) | 3.62 | MHz | Strong-driving regime amplitude |
| MW Preparation Pulse Frequency | 2876.6 | MHz | Used for $m_s = 0 \leftrightarrow m_s = \pm 1$ selective transitions |
| Averaging Repetitions | 200,000 | N/A | Required repetitions for time-domain data |
Key Methodologies
Section titled âKey MethodologiesâThe experimental study relied on precise material selection, strict magnetic field control, and a multi-step quantum pulse sequence:
- Crystal Preparation: Utilized an ultra-high purity diamond crystal (N < 5 ppb) with natural $^{13}$C concentration to realize the NV-$^{13}$C coupled spin system.
- Magnetic Field Alignment: A home-built setup with a rotating permanent magnet was used to orient the magnetic field (B=28.9 G) accurately to $\theta = 38.4^{\circ}$ relative to the NV axis, achieving the critical Level Anti-Crossing (LAC) condition.
- State Initialization (Polarization): Optical excitation followed by a selective Microwave (MW) $\pi$ pulse (2873.9 MHz) was applied to polarize the electron spin, creating a population difference between the target two-level states ($m_s = \pm 1$ manifold).
- Driving Sequence (Strong Field): An on-resonance Radio-Frequency (RF) pulse ($\omega = \omega_0 = 1.7$ MHz) of variable amplitude ($\omega_1$) and duration was applied parallel to the NV z-axis to drive the system dynamics.
- Readout: A second selective MW $\pi$ pulse and the final read-out laser pulse were used to measure the dynamics by quantifying the total population of the $m_s = 0$ state (Fluorescence monitoring).
- Analysis: Experimental time-domain data was processed via Fourier transforms to characterize the frequency components of the nonlinear oscillations, confirming multiple frequencies indicative of strong-driving dynamics.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the critical dependence of advanced quantum experiments on materials science, particularly the ultra-high purity and crystalline quality of the diamond substrate. 6CCVD is uniquely positioned to supply and enhance the materials required to replicate and scale this research into robust quantum devices.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the ultra-long coherence times and spin stability required for the strong-driving regime, the following 6CCVD materials are recommended:
-
Electronic Grade Single Crystal Diamond (SCD):
- Requirement: The paper used diamond with N < 5 ppb. 6CCVD offers Electronic Grade SCD with residual nitrogen concentrations consistently < 1 ppb, minimizing paramagnetic defects and maximizing NV coherence time (T2).
- Extension (Isotopic Control): While the paper utilized natural $^{13}$C abundance (1.1%) for the coupled spin, future high-fidelity quantum experiments often require reducing background $^{13}$C. 6CCVD offers isotopically pure $^{12}$C diamond substrates (up to 99.999% $^{12}$C) to eliminate unwanted nuclear spin noise.
-
Custom Substrates:
- 6CCVD can provide SCD wafers with thicknesses matching experimental needs, ranging from 0.1 ”m up to 500 ”m, allowing for specific NV depth engineering.
Customization Potential
Section titled âCustomization PotentialâFor transition from fundamental research to integrated quantum hardware, 6CCVD provides comprehensive manufacturing services:
| Service | 6CCVD Capability | Research Application Link |
|---|---|---|
| High-Precision Polishing | Ra < 1 nm (SCD) | Essential for minimizing surface defects, which can negatively impact NV charge state stability and coherence during optical readout. |
| Custom Dimensions | Plates/wafers up to 125 mm (PCD/SCD upon request) | Provides scalable platforms for arrays of NV sensors or integrated quantum circuits. |
| Metalization Services | Au, Pt, Pd, Ti, W, Cu layers | Crucial for integrating on-chip RF and MW antennas, necessary for delivering the precise, high-amplitude driving fields ($\omega_1$) required in the strong-driving regime. |
| Laser Cutting/Structuring | High-precision laser modification | Enables custom-shaped substrates and the fabrication of micro-antennas or resonators used in microwave delivery setups. |
Engineering Support
Section titled âEngineering SupportâThe challenges encountered in the strong-driving regime, particularly the high sensitivity to RF pulse phase and shape, underscore the need for optimized material selection. 6CCVDâs in-house PhD team specializes in defect engineering and material characterization.
We can assist researchers with similar quantum information processing or optimal control theory projects by:
- Selecting the optimal diamond grade (N, B, and $^{12}$C content) to achieve targeted T1 and T2 coherence limits.
- Consulting on surface treatment and polishing to ensure stable NV charge states for robust optical initialization and readout.
- Designing custom metalization stacks for high-power, high-frequency RF and MW delivery systems.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single Nitrogen-Vacancy center coupled to a first-shell $^{13}$C nuclear spin in diamond at a level anti-crossing point that occurs in the $m_{s}=\pm1$ manifold when the energy level splitting between the $m_{s}$ = $+1$ and $-1$ spin states due to the static magnetic field is $\approx$ 127 MHz, which is roughly equal to the spectral splitting due to the $^{13}$C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the $z$-component of the RF field. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is much smaller than the transition frequency become complex when the driving field strength is comparable or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 1990 - Principles of Magnetic Resonance [Crossref]
- 1987 - Optical Resonance and Two-Level atoms
- 2000 - Quantum Computation and Quantum Information