Exploring 2D Synthetic Quantum Hall Physics with a Quasiperiodically Driven Qubit

At a Glance

Metadata	Details
Publication Date	2020-10-16
Journal	Physical Review Letters
Authors	Eric Boyers, Philip J. D. Crowley, Anushya Chandran, Alexander O. Sushkov
Institutions	Boston University
Citations	50
Analysis	Full AI Review Included

Technical Documentation & Analysis: Exploring 2D Synthetic Quantum Hall Physics in Diamond

This document analyzes the research paper “Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit” to highlight the critical material requirements and demonstrate how 6CCVD’s advanced MPCVD diamond solutions meet and exceed the needs of solid-state quantum research.

Executive Summary

The research successfully demonstrated a synthetic 2D quantum Hall effect using a single Nitrogen-Vacancy (NV) center in diamond, validating the use of driven solid-state qubits for exploring complex topological physics.

Core Achievement: Experimental realization of the half-Bernevig-Hughes-Zhang (half-BHZ) model using the electronic spin of an NV center driven by two incommensurate radiofrequency (RF) tones.
Topological Signature: Quantized Chern numbers were extracted by measuring the frequency of quantum state overlap oscillations (fidelity) between two distinct spin trajectories.
Quantified Results: Measured Chern numbers were $C \approx 1$ (Topological regime) and $C \approx 0.5$ (Critical Dirac point), consistent with theoretical predictions.
Coherence Management: A spin-echo protocol was implemented to extend the topological evolution lifetime, achieving spin coherence times ($T_2$) up to $125 \pm 7$ µs.
Material Requirement: The experiment relies fundamentally on high-purity, isotopically enriched diamond (C¹²) to maintain the long coherence times necessary for observing quasi-periodic dynamics.
6CCVD Value: 6CCVD specializes in the high-purity Single Crystal Diamond (SCD) required for next-generation NV-based quantum devices, offering custom dimensions, isotopic control, and integrated metalization.

Technical Specifications

The following hard data points were extracted from the experimental implementation of the synthetic half-BHZ Hamiltonian using the NV center.

Parameter	Value	Unit	Context
Qubit Host Material	C¹² enriched Diamond	N/A	Grown by CVD, N¹⁵ implanted NV centers
Static Magnetic Field ($B_s$)	$\approx 500$	G	Tuned to Excited State Level Anti-Crossing (LAC)
Carrier Frequency ($\omega_0$)	$\approx 1.46$	GHz	Resonant frequency for $
Drive Rabi Frequency ($\gamma B_0$)	$2\pi \times 0.25$	MHz	Amplitude of RF magnetic field
Drive Frequencies ($\Omega_1, \Omega_2$)	$2\pi \times (0.5, 0.5\phi)$	MHz	Incommensurate, $\phi$ is the golden ratio
Spin Coherence Time ($T_2$)	$125 \pm 7$	µs	Achieved using spin-echo protocol
Measured Chern Number ($C$) (Topological, $m=1$)	$0.97 \pm 0.03$	N/A	Extracted from overlap oscillation frequency
Measured Chern Number ($C$) (Critical, $m=2$)	$0.50 \pm 0.02$	N/A	Demonstrates half-quantization at Dirac point
Polishing Requirement	Ultra-smooth	N/A	Necessary for high-quality optical interface (532nm laser)

Key Methodologies

The experiment required precise control over material properties, spin manipulation, and complex RF driving protocols.

Material Synthesis and Doping: Diamond was grown via C¹² enriched Carbon Vapor Deposition (CVD). NV centers were created by N¹⁵ ion bombardment followed by annealing.
Qubit Initialization and Readout: The NV electronic spin was initialized and read out using a 532nm laser in a scanning confocal microscope setup, detecting fluorescence counts via an Avalanche Photodiode (APD).
Magnetic Field Alignment: A static external magnetic field ($B_s$) was aligned with the NV symmetry axis and tuned to the Excited State Level Anti-Crossing (LAC) ($\approx 500$ G) to create an effective two-level qubit system.
Quasi-Periodic Driving: RF magnetic fields ($B_x, B_y, B_z$) were generated using a Signal Generator (SG) and an Arbitrary Waveform Generator (AWG) to implement the two-tone, incommensurate drive frequencies ($\Omega_1, \Omega_2$).
Diabatic Suppression: A calculated counter-diabatic potential ($V_{CD}$) was applied via the RF fields to suppress Landau-Zener transitions, ensuring the qubit followed the instantaneous eigenstates outside the adiabatic limit.
Coherence Protocol: A spin-echo sequence (interleaved $\pi_x$ pulses) was used during the evolution time to mitigate low-frequency noise and extend the spin coherence time ($T_2$).
Topological Measurement: The topological phase was probed by measuring the quantum state overlap (fidelity $F(t)$) between two trajectories starting at slightly perturbed initial drive phases ($\delta\theta_0$).

6CCVD Solutions & Capabilities

This research underscores the critical need for high-quality, specialized diamond materials for advancing solid-state quantum technologies. 6CCVD is uniquely positioned to supply the necessary materials and fabrication services to replicate and extend this work into scalable quantum devices.

Applicable Materials

To achieve the long coherence times ($T_2 = 125 \pm 7$ µs) required for quasi-periodic dynamics, the researchers utilized C¹² enriched diamond. 6CCVD offers materials optimized for this application:

Material	Specification	Application Relevance
Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen content (< 5 ppb N) and high isotopic purity (e.g., > 99.999% C¹² enrichment available).	Essential for NV Qubits: Minimizes decoherence caused by paramagnetic impurities and nuclear spin bath noise, enabling long $T_2$ times.
Boron-Doped Diamond (BDD)	SCD or PCD films with controlled boron doping levels.	Future Integration: Required for advanced device architectures involving integrated electronics, charge state control, or p-n junctions near the NV layer.

Customization Potential

The experimental setup requires precise integration of RF waveguides and optical components. 6CCVD provides comprehensive customization capabilities:

Custom Dimensions and Substrates: We supply SCD plates and wafers up to 125mm (PCD) in custom sizes and orientations (e.g., [100], [111]) necessary for mounting in complex magnetic resonance and optical systems.
Precision Thickness and Polishing: SCD films are available from $0.1$ µm to $500$ µm thick, with substrates up to $10$ mm. Our SCD polishing achieves an atomic-scale finish (Ra < 1nm), crucial for minimizing surface noise and ensuring high-efficiency optical coupling for 532nm laser readout.
Integrated Metalization Services: To facilitate the generation of the complex RF magnetic fields ($B_x, B_y, B_z$) used in the experiment, 6CCVD offers in-house metal deposition (Au, Pt, Pd, Ti, W, Cu) for creating integrated on-chip waveguides and contacts directly on the diamond surface.

Engineering Support

The implementation of advanced protocols like the counter-diabatic potential ($V_{CD}$) and spin-echo sequences requires deep knowledge of solid-state physics and material-qubit interactions.

Expert Consultation: 6CCVD’s in-house PhD team provides authoritative engineering support for projects involving NV Center Qubits and Topological Quantum Computing. We assist researchers in selecting the optimal diamond grade, isotopic purity, and surface preparation to maximize qubit performance and coherence lifetime.
Global Supply Chain: We ensure reliable, global shipping (DDU default, DDP available) of highly sensitive diamond materials to research facilities worldwide.

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

View Original Abstract

Quasiperiodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which characterizes the topological phases of the system. We further observe half-quantization of the Chern number at the transition between the synthetic Hall regime and the trivial regime, and the associated concentration of local Berry curvature in synthetic phase space. Our Letter opens up the possibility of using driven qubits to design and study higher-dimensional topological insulators and semimetals in synthetic dimensions.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevlett.125.160505