Observation of Non-Hermitian Topology with Nonunitary Dynamics of Solid-State Spins

At a Glance

Metadata	Details
Publication Date	2021-08-23
Journal	Physical Review Letters
Authors	Wengang Zhang, Xiaolong Ouyang, Xianzhi Huang, Xin Wang, Huili Zhang
Institutions	ShangHai JiAi Genetics & IVF Institute, Tsinghua University
Citations	82
Analysis	Full AI Review Included

Technical Documentation & Analysis: Non-Hermitian Topology in Solid-State Spins

This document analyzes the research paper “Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins” (arXiv:2012.09191v1) to extract critical material requirements and align them with 6CCVD’s advanced MPCVD diamond capabilities.

Executive Summary

This research marks a significant step in quantum simulation, demonstrating the first direct observation of non-Hermitian topological invariants in a solid-state system. The core findings and material implications are summarized below:

Pioneering Simulation: Achieved the first experimental demonstration of simulating non-Hermitian topological phases (specifically the Su-Schrieffer-Heeger model) using a solid-state quantum simulator.
Platform: Utilized a Nitrogen-Vacancy (NV) center in high-purity diamond, leveraging the coupled electron spin (target qubit) and a nearby $^{13}$C nuclear spin (ancilla qubit).
Methodology: Successfully implemented non-unitary dynamics via a dilation method, overcoming challenges associated with complex eigenenergies in non-Hermitian systems.
Key Result: Directly measured the topological winding number ($w$) corresponding to three distinct topological regions ($w = 0, 1/2, 1$), matching theoretical predictions with high precision.
Material Requirement: The experiment relies critically on electronic grade diamond with long spin coherence times ($T_2^* = 3.3$ µs) and precise control over the $^{13}$C isotopic environment (natural abundance 1.1%).
6CCVD Value Proposition: Replication and extension of this work require ultra-high purity Single Crystal Diamond (SCD) substrates, which 6CCVD provides with industry-leading control over isotopic purity and surface quality (Ra < 1 nm).

Technical Specifications

The following hard data points were extracted from the experimental setup and results, highlighting the stringent requirements for the diamond material and control systems.

Parameter	Value	Unit	Context
Electron Spin Dephasing Time ($T_2^*$)	3.3	µs	Measured via Ramsey experiment
Hyperfine Coupling Strength ($A_{zz}$)	$2\pi \times 13.7$	MHz	Coupling between electron spin and $^{13}$C nuclear spin
External Magnetic Field	480	Gauss	Applied along the NV axis for spin polarization
Laser Excitation Wavelength	532	nm	Used for off-resonance optical pumping
$^{13}$C Isotopic Abundance	1.1	%	Natural abundance in the electronic grade diamond
Electron Spin Zero-Field Splitting ($D$)	$2 \times 2.87$	GHz	NV center ground state
Maximum Evolution Time	1.8	µs	Duration of the non-unitary dynamics simulation
Observed Winding Numbers ($w$)	0, 1/2, 1	Dimensionless	Topological invariant confirmed experimentally

Key Methodologies

The experiment required precise control over the diamond material and complex microwave/RF pulse sequences to implement the non-Hermitian Hamiltonian.

Material Selection: Used electronic grade Single Crystal Diamond (SCD) with natural $^{13}$C abundance (1.1%) to provide the necessary coupled electron ($e^-$) and nuclear ($^{13}$C) spin system.
Spin Initialization: Employed a 532 nm green laser for optical pumping to initialize the electron spin to $|m_s=0\rangle$. A 480 Gauss magnetic field was applied to utilize the Excited-State Level Anti-Crossing (ESLAC) for simultaneous nuclear spin polarization.
Hamiltonian Simulation: Implemented the non-Hermitian SSH Hamiltonian $H(k)$ using a dilation method, mapping the non-unitary dynamics of the target electron spin ($H_e$) onto the unitary dynamics of a dilated system ($H_{e,n}$) involving the ancillary nuclear spin.
Pulse Control: Microwave (MW) and Radio Frequency (RF) signals were generated by an Arbitrary Waveform Generator (AWG) and controlled via an IQ-mixer to apply time-dependent amplitude, frequency, and phase pulses.
Spin Readout: Spin states were read out using spin-dependent photoluminescence (PL) rate measurement. Final state populations were reconstructed using maximum likelihood estimation.
Topological Invariant Measurement: The winding number ($w$) was determined by measuring the expectation values of the Pauli operators $\langle \sigma_x \rangle$ and $\langle \sigma_z \rangle$ as the momentum $k$ was swept across the Brillouin zone.

6CCVD Solutions & Capabilities

The successful execution of this quantum simulation relies entirely on the quality and precise engineering of the diamond substrate. 6CCVD is uniquely positioned to supply the materials required to replicate, optimize, and scale this research.

Applicable Materials

To achieve the long coherence times ($T_2^* = 3.3$ µs) and controlled spin environment necessary for NV center quantum simulation, the following 6CCVD materials are required:

6CCVD Material	Specification	Application in Research
Optical Grade SCD	Ultra-low strain, high purity, low nitrogen concentration (< 1 ppb).	Essential for maximizing $T_2^*$ and minimizing decoherence errors during the 1.8 µs evolution time.
Isotopically Controlled SCD	SCD with high $^{12}$C enrichment (> 99.99%) or controlled $^{13}$C doping.	Optimization: High $^{12}$C enrichment significantly increases $T_2$ and $T_2^*$ for the electron spin, enabling longer simulation times and higher fidelity.
Custom Thickness Wafers	SCD plates from 0.1 µm up to 500 µm thickness.	Allows precise control over NV center depth relative to the surface, crucial for integration with MW/RF structures and minimizing surface noise.

Customization Potential

The experiment utilized a homemade MW coplanar waveguide and required a specific crystal orientation ((100) direction) and magnetic field alignment. 6CCVD offers comprehensive customization services to integrate the diamond material seamlessly into complex quantum setups:

Custom Dimensions: 6CCVD can supply SCD wafers up to 10 mm thick and PCD plates up to 125 mm in diameter, allowing for scaling up of quantum simulation platforms.
Precision Polishing: We guarantee surface roughness of Ra < 1 nm for SCD, critical for high-fidelity optical access (532 nm laser) and minimizing surface defects that contribute to decoherence.
Integrated Metalization: 6CCVD offers in-house deposition of thin-film metals (Au, Pt, Pd, Ti, W, Cu). We can fabricate custom coplanar waveguide (CPW) structures directly onto the diamond surface, eliminating the need for external, homemade components and improving MW delivery efficiency.
Laser Cutting & Shaping: Custom laser cutting services ensure precise geometry for mounting and integration with optical and RF systems.

Engineering Support

Replicating non-Hermitian topological simulations requires deep expertise in both quantum physics and material science.

Coherence Optimization: 6CCVD’s in-house PhD team specializes in optimizing diamond growth recipes to maximize spin coherence times ($T_2$ and $T_2^*$) by controlling defect density and isotopic purity.
NV Center Material Selection: We provide consultation on selecting the optimal diamond grade (e.g., high $^{12}$C purity vs. controlled $^{13}$C doping) based on whether the research requires maximizing coherence or utilizing nuclear spins as ancilla qubits.
Integration Assistance: Our engineers can assist researchers in designing custom metalization layers and substrate geometries for optimal coupling with microwave and radio frequency control systems used in NV center quantum simulation projects.

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

View Original Abstract

Non-Hermitian topological phases exhibit a number of exotic features that have no Hermitian counterparts, including the skin effect and breakdown of the conventional bulk-boundary correspondence. Here, we implement the non-Hermitian Su-Schrieffer-Heeger Hamiltonian, which is a prototypical model for studying non-Hermitian topological phases, with a solid-state quantum simulator consisting of an electron spin and a ^{13}C nuclear spin in a nitrogen-vacancy center in a diamond. By employing a dilation method, we realize the desired nonunitary dynamics for the electron spin and map out its spin texture in the momentum space, from which the corresponding topological invariant can be obtained directly. From the measured spin textures with varying parameters, we observe both integer and fractional winding numbers. The non-Hermitian topological phase with fractional winding number cannot be continuously deformed to any Hermitian topological phase and is intrinsic to non-Hermitian systems. Our result paves the way for further exploiting and understanding the intriguing properties of non-Hermitian topological phases with solid-state spins or other quantum simulation platforms.