Experimental violation of the Leggett-Garg inequality with a single-spin system

At a Glance

Metadata	Details
Publication Date	2022-04-22
Journal	Physical review. A/Physical review, A
Authors	Maimaitiyiming Tusun, Wei Cheng, Zihua Chai, Yang Wu, Ya Wang
Institutions	Xinjiang Normal University, University of Science and Technology of China
Citations	7
Analysis	Full AI Review Included

Technical Documentation & Analysis: Violation of the Leggett-Garg Inequality using NV Centers

This document analyzes the research paper “Experimental violation of the Leggett-Garg inequality with a single-spin system” and outlines how 6CCVD’s advanced MPCVD diamond materials and customization capabilities are essential for replicating, extending, and scaling this critical quantum information research.

Executive Summary

The research successfully demonstrated a violation of the Leggett-Garg inequality (LGI) in a three-level quantum system, a key step in testing the boundaries between quantum mechanics and classical realism.

Core Achievement: Experimental violation of the LGI, achieving K₃^exp = 1.625 ± 0.022, which significantly exceeds the classical Lüders bound (1.5).
System Used: A single Nitrogen-Vacancy (NV) center in diamond, utilizing the ¹⁴N nuclear spin as the three-level system and the electron spin as the ancilla qubit.
Critical Material Requirement: The experiment relied on ultra-high purity, isotopically enriched diamond ([¹²C] = 99.999%) to suppress environmental dephasing noise.
Coherence Metric: The high-purity material enabled an electron spin dephasing time (T₂*) of 62 ± 7 µs, crucial for maintaining coherence during the multi-time measurement sequence.
Methodology: The Ideal Negative Result Measurement (INRM) scheme was implemented using controlled gates (CG) and postselection to ensure non-invasive measurement, satisfying a key requirement for LGI testing.
Future Impact: The results validate the use of three-level systems (qutrits) in diamond for fundamental quantum tests and pave the way for high-dimensional quantum computing and sensing applications.

Technical Specifications

The following hard data points were extracted from the experimental results and setup parameters:

Parameter	Value	Unit	Context
Maximum LGI Violation (K₃^exp)	1.625 ± 0.022	Dimensionless	Experimental result, exceeding the Lüders bound (1.5)
Theoretical Maximum LGI (K₃^theo)	1.756	Dimensionless	Ideal prediction for a three-level system
Electron Spin Dephasing Time (T₂*)	62 ± 7	µs	Measured in the isotopically purified NV center
Diamond Isotopic Purity	99.999	%	[¹²C] concentration used to minimize dephasing noise
NV Electron Spin Zero-Field Splitting (D)	2.87	GHz	Intrinsic property of the NV center
¹⁴N Nuclear Quadrupolar Interaction (Q)	-4.95	MHz	Defines the three-level system energy levels
Hyperfine Interaction (A)	-2.16	MHz	Coupling between electron and nuclear spin
Applied Magnetic Field (B)	512	G	Applied along the NV symmetry axis ([111])
Optimal Evolution Time (τ)	14.71	µs	Time corresponding to the optimal rotation angle (θ = 0.416π)
Rabi Frequency (f_rabi)	20	kHz	Set strength for nuclear spin radio frequency pulses

Key Methodologies

The experiment utilized advanced quantum control techniques on a single NV center in diamond:

Material Foundation: The experiment was conducted on an isotopically purified Single Crystal Diamond (SCD) sample ([¹²C] = 99.999%) to maximize coherence time by reducing the magnetic noise from ¹³C nuclear spins.
System Definition: The three-level system (qutrit) was encoded in the ¹⁴N nuclear spin states (|1>_n, |0>_n, |-1>_n). The NV electron spin states (|1>_e, |0>_e) were used as the ancilla qubit for readout and control.
Quantum Control: Three-level Rabi rotation U(θ) on the nuclear spin was achieved by simultaneously applying two radio frequency (RF) pulses (RF1 and RF2) in a rotating frame.
Non-Invasive Measurement (INRM): The core measurement protocol involved implementing controlled gates (CG) via selective microwave pulses. The non-invasiveness was guaranteed by postselecting the final state populations where the ancilla qubit had not flipped (negative result).
LGI Calculation: The correlation functions (Q(t_i)Q(t_j)) required for the LGI test (K₃) were derived from the measured final state populations (P_i^j) after the INRM sequence.
Setup: The experiment utilized an Optically Detected Magnetic Resonance (ODMR) setup, applying a 512 G magnetic field along the [111] crystal axis to define the NV quantization axis.

6CCVD Solutions & Capabilities

This research highlights the absolute necessity of ultra-high-quality, isotope-enriched Single Crystal Diamond (SCD) for advanced quantum experiments. 6CCVD is uniquely positioned to supply the materials and engineering services required to replicate and scale this work.

Applicable Materials

To replicate or extend this research, engineers require diamond substrates optimized for NV center coherence and stability.

Material Requirement	6CCVD Material Recommendation	Technical Rationale
*High Coherence Time (T₂)**	High-Purity Isotope-Enriched SCD	Guaranteed [¹²C] purity > 99.999% to suppress nuclear spin bath noise, essential for achieving T₂* > 60 µs.
Optical Readout & Low Strain	Optical Grade SCD	Low birefringence and minimal internal strain, ensuring stable NV energy levels and high-fidelity optical initialization/readout.
Scaling to Integrated Devices	Thin SCD Wafers (0.1 µm - 500 µm)	Provides the necessary thickness control for integration into photonic structures (e.g., waveguides, resonators) while maintaining crystal quality.

Customization Potential

Scaling this research from a single NV center to integrated quantum circuits requires precise material engineering and fabrication capabilities, all available in-house at 6CCVD.

Custom Dimensions: While the paper used a small sample, 6CCVD offers custom SCD plates up to inch-size and PCD wafers up to 125mm, supporting large-scale device fabrication.
Surface Preparation: Achieving non-invasive measurement and minimizing surface noise requires exceptional surface quality. 6CCVD guarantees ultra-low surface roughness (Ra < 1nm for SCD, Ra < 5nm for inch-size PCD).
Metalization Services: For future integration of microwave control lines (required for the RF and MW pulses used in this experiment), 6CCVD provides internal metalization capabilities, including standard quantum stacks (Ti/Pt/Au, W, Cu, Pd).
Precision Fabrication: We offer custom laser cutting and shaping services to meet specific device geometries required for mounting and integration into ODMR setups.

Engineering Support

The complexity of NV center physics, including defect creation, polarization, and noise mitigation (as discussed in Appendix C), necessitates expert material consultation.

6CCVD’s in-house PhD team specializes in defect engineering and can assist researchers with material selection, surface termination, and post-growth processing to optimize NV center creation yield and maximize coherence for similar Quantum Information and Sensing projects.
We provide global shipping (DDU default, DDP available) and comprehensive technical support to ensure materials meet the stringent requirements of high-fidelity quantum experiments.

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

View Original Abstract

Investigation the boundary between quantum mechanical description and\nclassical realistic view is of fundamental importance. The Leggett-Garg\ninequality provides a criterion to distinguish between quantum systems and\nclassical systems, and can be used to prove the macroscopic superposition\nstate. A larger upper bound of the LG function can be obtained in a multi-level\nsystem. Here, we present an experimental violation of the Leggett-Garg\ninequality in a three-level system using nitrogen-vacancy center in diamond by\nideal negative result measurement. The experimental maximum value of\nLeggett-Garg function is $K_{3}^{exp}=1.625\pm0.022$ which exceeds the L\“uders\nbound with a $5\sigma$ level of confidence.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.105.042613