Experimental violation of the Leggett-Garg inequality with a single-spin system
At a Glance
Section titled âAt a Glanceâ| 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 | University of Science and Technology of China, Xinjiang Normal University |
| Citations | 7 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research demonstrates a significant experimental violation of the Leggett-Garg inequality (LGI) in a solid-state system, pushing the boundaries between quantum mechanics and classical realism.
- Core Achievement: Experimental violation of the LGI, achieving a maximum value of K3exp = 1.625 ± 0.022.
- Bound Exceeded: This result exceeds the classical LĂŒders bound (1.5) with a high confidence level (5Ï).
- System Used: A single Nitrogen-Vacancy (NV) center in isotopically purified diamond, utilizing the 14N nuclear spin as the three-level quantum system (qutrit).
- Methodology: The Ideal Negative Result Measurement (INRM) scheme was implemented using controlled gates and postselection to ensure the non-invasive measurement required for a valid LGI test.
- Material Quality: The use of isotopically purified diamond ([12C] = 99.999%) resulted in a long electron spin dephasing time (T2* = 62(7) ”s), crucial for maintaining quantum coherence during the complex pulse sequences.
- Implication: The violation confirms that either macroscopic realism or the assumption of non-invasive measurability must be incorrect for this system, validating the applicability of quantum mechanics at higher complexity levels.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum LGI Value (K3exp) | 1.625 ± 0.022 | Dimensionless | Experimental result, exceeding LĂŒders bound (1.5). |
| Theoretical Maximum LGI (K3) | 1.756 | Dimensionless | Ideal prediction for a three-level system. |
| Electron Spin Dephasing Time (T2*) | 62(7) | ”s | Measured in the isotopically purified diamond sample. |
| Diamond Isotopic Purity ([12C]) | 99.999 | % | Used to suppress environmental dephasing noise. |
| Applied Magnetic Field | 512 | G | Applied along the NV symmetry axis ([111]). |
| Electron Spin Polarization | 95 | % | Initial state polarization considered in simulation. |
| Nuclear Spin Polarization | 98 | % | Initial state polarization considered in simulation. |
| Zero-Field Splitting (D) | 2.87 | GHz | NV electron spin Hamiltonian parameter. |
| Nuclear Quadrupole Interaction (Q) | -4.95 | MHz | 14N nuclear spin Hamiltonian parameter. |
| Hyperfine Interaction (A) | -2.16 | MHz | Interaction between electron and nuclear spins. |
| Nuclear Spin Rabi Frequency (frabi) | 20 | kHz | Set frequency for the three-level Rabi rotation U(Ξ). |
| Ancilla Flip Probability (p) | 0.995 ± 0.002 | Dimensionless | Probability of electron spin flip during controlled gate (near ideal fidelity). |
Key Methodologies
Section titled âKey MethodologiesâThe experiment was conducted on a single NV center in diamond using optically detected magnetic resonance (ODMR) techniques, focusing on precise control of the electron and nuclear spins.
- Material Selection: An isotopically purified diamond sample ([12C] = 99.999%) was used to maximize the coherence time (T2*) of the electron spin, mitigating decoherence effects during the pulse sequences.
- System Encoding: 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) served as the ancilla qubit for measurement and readout.
- Initialization: The NV center was initialized to a highly polarized state (effectively |0>e|1>n) using laser pulses and selective microwave pulses.
- Quantum Evolution (U(Ξ)): The time evolution U(Ξ) = e-iΞSxz on the three-level nuclear spin was realized by applying two simultaneous radio frequency (RF) pulses (RF1 and RF2) tuned to the specific nuclear spin resonance frequencies (Ï45 and Ï56).
- Ideal Negative Result Measurement (INRM):
- Controlled Gate (CG): Implemented using selective microwave pulses that couple the electron and nuclear spins. The CG flips the state of the electron spin (ancilla) unless the nuclear spin is in the desired state.
- Non-Invasiveness: Non-invasiveness is ensured by postselecting the final state populations where the ancilla qubit has not flipped (the ânegative resultâ).
- LGI Calculation: The LGI function K3 was calculated by measuring the expectation values (Q(ti)Q(tj)) derived directly from the final state populations (Pji) corresponding to the non-flipped ancilla state after the INRM sequence.
Commercial Applications
Section titled âCommercial ApplicationsâThe successful demonstration of high-fidelity, non-invasive measurement and control over a three-level solid-state system has direct implications for advanced quantum technologies.
- Solid-State Quantum Computing:
- NV centers are leading candidates for robust, room-temperature qubits. This work validates complex, multi-time measurement protocols essential for quantum error correction and state verification.
- Enables the development of qutrit-based (three-level) quantum logic gates, potentially increasing computational density and noise resilience compared to standard qubits.
- Quantum Memory and Repeaters:
- The use of the highly coherent nuclear spin as the storage element (qutrit) provides a stable platform for quantum memory, critical for long-distance quantum communication networks.
- High-Precision Quantum Sensing:
- The use of isotopically purified diamond and the achieved long T2* time enhances the sensitivity of NV-based magnetometers and gyroscopes, enabling applications in navigation, geological surveys, and medical diagnostics (e.g., NMR spectroscopy at the nanoscale).
- Fundamental Physics Platforms:
- Provides a scalable, controllable solid-state system for testing foundational quantum theories, including decoherence mechanisms and the transition from quantum to classical behavior (macrorealism).
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\âuders\nbound with a $5\sigma$ level of confidence.\n