Holonomic Quantum Control by Coherent Optical Excitation in Diamond

At a Glance

Metadata	Details
Publication Date	2017-10-02
Journal	Physical Review Letters
Authors	Brian B. Zhou, Paul C. Jerger, V. O. Shkolnikov, F. Joseph Heremans, Guido Burkard
Institutions	University of Konstanz, University of Chicago
Citations	159
Analysis	Full AI Review Included

Holonomic Quantum Control in Diamond: Leveraging High-Purity MPCVD Substrates

Analysis of “Holonomic Quantum Control by Coherent Optical Excitation in Diamond” (arXiv:1705.00654v2)

This technical analysis details the realization of single-loop, non-adiabatic holonomic quantum gates utilizing the nitrogen-vacancy (NV) center in diamond. The research validates detuned optical driving as a robust method for high-fidelity quantum control, offering significant advantages over multi-cycle resonant approaches by reducing exposure to excited-state decoherence. 6CCVD identifies this work as critical validation for high-purity Single Crystal Diamond (SCD) material solutions in quantum computing architecture.

Executive Summary

Core Achievement: Demonstration of arbitrary, single-qubit holonomic gates in a diamond NV center using a single cycle of non-adiabatic optical excitation.
Methodology: Control is achieved by varying the amplitude, phase, and detuning of a two-tone optical field driving $\Lambda$ system transitions in the NV triplet ground and excited states.
Fidelity Enhancement: Off-resonant (detuned) gates achieved superior fidelities (up to F = 0.83(2)) compared to resonant gates by minimizing excitation to the lossy intermediate excited state ($A_2$).
Speed Advantage: The single-cycle, non-adiabatic approach eliminates the need for concatenating two separate cycles, enabling fast gate operation (pulse durations 5-10 ns) critical for outrunning decoherence.
Material Requirement: The experiment required high-quality, electronic-grade Type IIa bulk diamond with low strain (0.97 GHz) to resolve narrow optical transitions at 5 K.
Limiting Factors: Gate fidelity was primarily limited by short excited-state lifetime ($T_1 \approx 11.1$ ns), dephasing time ($T_{\phi} \approx 18$ ns), and spectral hopping (Gaussian standard deviation $\sigma_{\Delta} \approx 15$ MHz).

Technical Specifications

The following parameters define the experimental configuration and performance metrics:

Parameter	Value	Unit	Context
Material Used	Type IIa, Electronic-Grade	N/A	(100)-oriented bulk diamond
Operating Temperature	5	K	Closed-cycle cryostat for resolving narrow lines
NV Depth (below surface)	2	µm	Confocal microscopy setup
Static Magnetic Field (B)	261	G	Aligned to NV axis; splits ground states by 1.461 GHz
Excitation/Interaction Laser	637	nm	Two tunable diode lasers used for holonomic gate
Initialization Laser	532	nm	Diode laser for initial spin state preparation
Microwave Frequency	1.461	GHz	Matches ground state splitting for sideband generation
Excited State Splitting (2$\delta_{s}$)	1.94	GHz	Strain splitting of $E_{x}$ and $E_{y}$ excited state levels
Optimal Rabi Frequency ($\Omega/2\pi$)	150 - 252	MHz	Range optimized for high fidelity
Pulse Duration	5 to 10	ns	Short pulse time for fast gate operation
Pulse Rise/Fall Time (Trapezoid)	1.2 ± 0.1	ns	Limiting factor for fidelity above $\Omega/2\pi$ > 600 MHz
Excited State Lifetime ($T_1$)	11.1	ns	Primary decoherence limit
Excited State Dephasing ($T_{\phi}$)	18	ns	Secondary decoherence limit
Spectral Hopping ($\sigma_{\Delta}/2\pi$)	15	MHz	Gaussian standard deviation used in simulation
Highest Fidelity Achieved (X($\pi/2$))	0.83(2)	N/A	Off-resonant gate at $\Delta/\Omega = 1/\sqrt{3}$
Hadamard (H) Gate Fidelity	0.74(2)	N/A	Resonant gate at $\Omega/2\pi = 168$ MHz

Key Methodologies

The experiment utilized a complex setup involving precise material specification, cryogenic conditions, and coordinated laser/microwave control to implement single-loop holonomic gates.

Sample and Environment:
- An electronic-grade, (100)-oriented Type IIa diamond sample (from Element Six) containing a single NV center was used.
- The sample was cooled to $T = 5$ K using a closed-cycle cryostat to resolve narrow optical transitions.
- A static magnetic field (261 G) was aligned to the NV axis to establish the qubit space ($|m_s = \pm 1\rangle$ sublevels).
Quantum State Preparation:
- A 532 nm diode laser initialized the spin state into $|m_s = 0\rangle$.
- Resonant microwave pulses (2.147 GHz and 3.608 GHz) were delivered via a coplanar waveguide to prepare the NV into desired superposition states (e.g., $|m_s = \pm 1\rangle$).
Optical Gate Implementation (Two-Tone Driving):
- The holonomic gate was driven by a tunable 637 nm interaction laser.
- The beam was routed through both a Phase Electro-Optic Modulator (PEOM) and an Amplitude Electro-Optic Modulator (AEOM).
- PEOM Function: Created frequency harmonics (sidebands) at 1.461 GHz, matching the ground state splitting, allowing the carrier and the red-shifted sideband to simultaneously drive the $|-1\rangle \rightarrow |A_2\rangle$ and $|+1\rangle \rightarrow |A_2\rangle$ transitions, respectively, forming the required $\Lambda$ system.
- AEOM Function: Shaped the nanosecond-scale pulses into trapezoidal approximations of square pulses (1.2 ns ramp time) and compensated for PEOM modulation to maintain constant intensity ratio between the two utilized harmonics.
Process and State Tomography:
- The resulting quantum state was read out using appropriate microwave pulses to transfer the state to $|0\rangle$ at a rephasal time.
- Phonon sideband emission was filtered (650 nm to 800 nm) and detected using an avalanche photodiode (APD).
- Quantum Process Tomography was performed on an overcomplete set of states to determine the process matrix $\chi_{exp}$ and calculate gate fidelities, normalized against an identity operation fidelity ($F_{Identity} = 0.97$).

6CCVD Solutions & Capabilities

The successful implementation of fast, high-fidelity holonomic gates relies critically on the underlying diamond material properties—specifically low internal strain, minimal impurities, and excellent surface quality—which 6CCVD specializes in providing via high-quality MPCVD growth.

Applicable Materials

To replicate or extend this research, particularly in scalable quantum systems, a consistent supply of ultra-low strain material is necessary.

Research Requirement	6CCVD MPCVD Solution	Key Advantage
Electronic-Grade Type IIa Bulk	Optical Grade SCD (Single Crystal Diamond)	High purity (low nitrogen/boron) ensures long spin coherence and minimizes spectral hopping ($\sigma_{\Delta}$), enabling clearer resolution of transitions.
Low Strain / High Quality	Ultra-Low Birefringence SCD Substrates	SCD growth minimizes crystal defects and strain, essential for narrow linewidths and repeatable excited-state fine structure splitting.
High Polishing (for shallow NV)	SCD Polishing: Ra < 1 nm	Allows reliable creation and imaging of shallow NV centers ($\sim 2$ µm deep) with minimal surface-induced decoherence effects.
Quantum Sensing/Integration	Engineered PCD/SCD Wafers (up to 125mm)	Scaling potential for future two-qubit architectures leveraging nearby nuclear spins or cavity integration.

Customization Potential

The experiment utilized complex optical systems requiring precise delivery of excitation energy. 6CCVD offers specialized manufacturing services to optimize NV host materials for optical integration:

Custom Dimensions: 6CCVD can supply SCD or PCD wafers in custom dimensions (plates/wafers up to 125 mm PCD) suitable for specialized cryogenic mounting apparatuses used in this type of experiment.
Precision Cutting and Dicing: We offer sub-millimeter precision laser cutting and dicing services to produce small, custom-shaped NV chips, ensuring perfect fit within cryostat sample stages and optimized microwave waveguide integration.
Integrated Metalization Services: While this study used external microwave delivery via a coplanar waveguide, future integration requires on-chip structures. 6CCVD provides in-house metalization (e.g., Ti/Pt/Au, W/Cu) for creating high-Q superconducting resonators or integrated microwave antennas directly on the SCD surface.

Engineering Support

The fidelity limitations observed (spectral hopping $\sigma_{\Delta}$) highlight the challenge of environmental noise, particularly charge noise induced by the initialization laser. 6CCVD’s in-house PhD engineering team can assist researchers in selecting diamond materials optimized for reducing surface charge noise and improving excited-state properties:

Optimized NV Creation: Consultations on material specifications (e.g., specific nitrogen concentration during growth, post-processing techniques) to maximize the yield and spectral stability of NV centers suitable for demanding Holonomic Quantum Computation (HQC) projects.
Surface Termination: Guidance on optimal surface termination techniques to mitigate environmental charge noise, thereby reducing $\sigma_{\Delta}$ and extending effective $T_{\phi}$.

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

View Original Abstract

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.