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6CCVD Research

Direct Measurement of Topological Numbers with Spins in Diamond

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2016-08-04
JournalPhysical Review Letters
AuthorsFei Kong, Chenyong Ju, Ying Liu, Chao Lei, Mengqi Wang
InstitutionsYale University, University of Science and Technology of China
Citations41
AnalysisFull AI Review Included

Direct Measurement of Topological Numbers with Spins in Diamond: A 6CCVD Analysis

Section titled “Direct Measurement of Topological Numbers with Spins in Diamond: A 6CCVD Analysis”

This technical documentation analyzes the quantum simulation of topological phase transitions utilizing Nitrogen-Vacancy (NV) centers in diamond, emphasizing the material requirements necessary for advancing this research into scalable quantum computing platforms.

Executive Summary

Section titled “Executive Summary”

The research successfully demonstrates a robust method for characterizing topological phase transitions, critical for investigating phenomena like Majorana bound states, using a solid-state diamond platform at room temperature.

  • Core Achievement: Direct quantum simulation and measurement of the topological number ($\nu$) associated with a semiconductor quantum wire (QW) phase transition.
  • Platform: A highly controllable two-qubit system based on a single Nitrogen-Vacancy (NV) center in diamond.
  • Methodology: Deployment of a quantum algorithm for finding eigenvalues, allowing simultaneous extraction of dispersion relations and the topological number.
  • Key Advantage: The method proves robust against magnetic field fluctuations and noise that typically smear the energy gap, providing clear, discretized topological values.
  • Material Limitation: Experimental measurement of the critical energy gap was hindered by fluctuating magnetic fields arising from the surrounding natural 13C spin bath in the diamond matrix.
  • Path to Improvement (6CCVD Solution): The authors recommend adopting isotopically purified diamond to significantly extend electron spin coherence time, enabling higher fidelity measurements and scalability for future quantum simulators.

Technical Specifications

Section titled “Technical Specifications”

The following hard parameters define the simulated system and the physical NV center properties utilized in the experiment.

ParameterValueUnitContext
Simulated SystemQuantum Wire (QW)N/ASemiconductor QW coupled to s-wave superconductor and magnetic field.
Critical Chemical Potential ($\mu$) (Theory)-1.29N/ABoundary between Superconductivity (SC) phase ($\nu=1$) and Topological Superconductivity (TP) phase ($\nu=-1$).
Measured Critical $\mu$~-1.3N/AExperimental phase transition point.
Simulated Pairing Amplitude ($\Delta$)0.165N/AFixed parameter used in phase diagram determination.
Simulated Zeeman Energy ($B_x$)1.3N/AFixed parameter used in phase diagram determination.
Operating TemperatureRoom°C/KSolid-state simulation environment.
External Magnetic Field ($B_{0}$)~50mTApplied along the N-V axis for 14N nuclear spin polarization.
Electron Gyromagnetic Ratio ($\gamma_{e}/2\pi$)-28.03GHz/TNV Electron Spin (S=1).
Nuclear Gyromagnetic Ratio ($\gamma_{n}/2\pi$)3.077MHz/T14N Nuclear Spin (I=1).
Axial Zero-Field Splitting ($D/2\pi$)2.87GHzIntrinsic electron spin parameter.
Hyperfine Coupling ($A/2\pi$)-2.16MHzCoupling between electron and 14N nuclear spin.
Quadrupole Splitting ($Q/2\pi$)-4.945MHzIntrinsic 14N nuclear spin parameter.

Key Methodologies

Section titled “Key Methodologies”

The experiment uses the NV center’s electron and nuclear spins to map the complex QW Hamiltonian, deploying pulsed quantum control techniques for simulation and measurement.

  1. System Preparation: A single NV center in natural diamond, comprising a substitutional nitrogen atom and an adjacent vacancy, is used. The electron spin (S=1) and the nearby 14N nuclear spin (I=1) form a two-qubit system.
  2. Qubit Subspace Mapping: The QW system’s Nambu spinor basis is mapped one-to-one onto a four-state subspace of the NV system, spanned by specific combined electron/nuclear spin states (${|4), |5), |7), |8}$).
  3. Hamiltonian Simulation: The QW Hamiltonian ($H_{\text{QW}}$) is replicated in the rotating frame of the NV system ($H_{\text{NV}}^{\text{rot}}$). This is achieved by simultaneous application of two Microwave (MW) pulses (controlling electron spin transitions) and two Radio-Frequency (RF) pulses (controlling nuclear spin transitions).
  4. Parameter Tuning: Simulated QW parameters (momentum $p$, chemical potential $\mu$, pairing amplitude $\Delta$, Zeeman energy $B_x$) are linearly mapped to the physical pulse control parameters ($\Omega_{\text{MW1,2}}$, $\Omega_{\text{RF}}$, and detuning $\delta_{\text{MW}}$).
  5. Eigenvalue Measurement: A quantum algorithm for finding eigenvalues is applied. The system is evolved under $H_{\text{QW}}$ for an adjustable time $m\tau$.
  6. Readout & Analysis: Photoluminescence (PL) is detected after the evolution period. The resulting time-domain signals ($a_{\psi, m}$) are Fourier transformed to yield the energy spectrum (eigenvalues) of the simulated Hamiltonian, whose sign directly determines the topological number $\nu$.

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

This research confirms the crucial role of high-purity Single Crystal Diamond (SCD) in advancing solid-state quantum simulation. 6CCVD provides the next-generation materials and engineering services required to overcome current limitations and enable scalable quantum platforms.

Paper Requirement/Limitation6CCVD SCD Material Solution6CCVD Engineering Capabilities
Primary Limitation: Phase errors and energy gap smearing caused by the fluctuating magnetic field from the native 13C spin bath in natural diamond (p. 10, 12).Material: Ultra-High Purity, Isotopically Purified Single Crystal Diamond (SCD). We offer < 0.01% 13C concentration.Impact: Significantly extends electron spin coherence time ($T_2^*$), stabilizing measurements near the critical phase transition point ($\mu \approx -1.29$) and enabling higher fidelity quantum control required for scalability 29.
Physical Platform: Requirement for stable, optical-grade diamond wafers hosting single NV centers.Material: Optical Grade SCD Wafers.Custom Dimensions: Plates/wafers available up to 125mm (PCD) or custom-cut SCD plates. Thickness capabilities ranging from 0.1”m to 500”m (SCD).
High-Fidelity Optical Access: Experiments depend on high-quality photoluminescence (PL) readout.Requirement: Minimal surface defects and ultra-low roughness.Precision Polishing: Best-in-class polishing achieving surface roughness $R_{a} < 1\text{ nm}$ (SCD) and $R_{a} < 5\text{ nm}$ (Inch-size PCD) for optimal optical coupling.
Integrated Quantum Circuitry: Need for microwave and RF control pulse transmission structures.Material: N/A (Substrate independent).Custom Metalization: In-house capability for depositing thin films (Au, Pt, Pd, Ti, W, Cu) for contact pads, waveguides, and integrated quantum sensing elements.
Future Scalability: Extending simulation capability to multiple coupled spins (p. 12).Material: Precision-engineered SCD with tailored NV implantation or growth processes for controlled defect density and location.Engineering Support: 6CCVD’s in-house PhD team can assist with material selection and specification for projects involving scalable quantum simulation architectures and complex Majorana fermion investigations.

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

View Original Abstract

Topological numbers can characterize the transition between different topological phases, which are not described by Landau’s paradigm of symmetry breaking. Since the discovery of the quantum Hall effect, more topological phases have been theoretically predicted and experimentally verified. However, it is still an experimental challenge to directly measure the topological numbers of various predicted topological phases. In this Letter, we demonstrate quantum simulation of topological phase transition of a quantum wire (QW), by precisely modulating the Hamiltonian of a single nitrogen-vacancy (NV) center in diamond. Deploying a quantum algorithm of finding eigenvalues, we reliably extract both the dispersion relations and topological numbers. This method can be further generalized to simulate more complicated topological systems.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 1998 - Topological Quantum Numbers in Nonrelativistic Physics [Crossref]

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