Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system

At a Glance

Metadata	Details
Publication Date	2016-11-28
Journal	Nature Physics
Authors	Brian B. Zhou, Alexandre Baksic, Hugo Ribeiro, Christopher G. Yale, F. Joseph Heremans
Institutions	Argonne National Laboratory, University of Konstanz
Citations	251
Analysis	Full AI Review Included

Accelerated Quantum Control in Solid-State Diamond $\Lambda$ Systems

Executive Summary

This documentation analyzes the research paper detailing the use of Superadiabatic Transitionless Driving (SATD) protocols, specifically tailored for the Nitrogen-Vacancy (NV) center in diamond, to significantly accelerate quantum state manipulation.

Core Achievement: Implementation of novel “shortcuts to adiabaticity” (SATD and MOD-SATD) to expedite Stimulated Raman Adiabatic Passage (STIRAP) in a solid-state three-level Lambda ($\Lambda$) system hosted by an NV center in electronic-grade diamond.
Speed Enhancement: The optimized Modified SATD (MOD-SATD) protocol achieved a 2.7-fold speed-up in population transfer time (requiring only 12.6 ns) compared to standard adiabatic STIRAP protocols while maintaining high transfer efficiency (>90%).
Dissipation Mitigation: The MOD-SATD design successfully reduced the intermediate excited state occupation by $\sim$20% compared to standard SATD, significantly decreasing exposure to key decoherence mechanisms (11.1 ns excited state lifetime, 55.5 MHz dephasing).
Robustness Verified: Protocols demonstrated superior robustness against experimental imperfections, including dissipation effects, spectral diffusion ($\sim 31$ MHz standard deviation), and fluctuations in laser intensity or pulse shape determination.
Coherence Preservation: The superadiabatic shortcuts retained superior phase coherence compared to the adiabatic process, achieving a fidelity of $F = 0.93 \pm 0.01$ for the preparation of superposition states using fractional STIRAP.
Material Necessity: High-purity, electronic-grade Single Crystal Diamond (SCD) is confirmed as the essential platform for realizing these fast, robust, and coherent quantum control techniques.

Technical Specifications

The following hard parameters define the operational conditions and observed performance metrics extracted from the study on the single NV center in diamond.

Parameter	Value	Unit	Context
Host Material	Electronic Grade Diamond	Substrate	Naturally-occurring NV center
Operating Temperature ($T$)	5.5	K	Closed-cycle cryostat environment
Magnetic Field ($B$)	252.5	G	Applied along NV axis for Zeeman splitting
Ground State Splitting ($\Delta$)	1.414	GHz	Between $
Protocol Laser Wavelength	637.2	nm	Tunable, used for optical driving
Standard Pulse Duration ($L$)	16.8	ns	Fixed duration for Rabi strength analysis
Shortest Protocol Length ($L_{SA}$)	12.6	ns	MOD-SATD, maintaining >85% efficiency
Quantum Speed Limit ($L_{QSL}$)	5.8	ns	Theoretical minimum limit for state transfer
Max Rabi Frequency ($\Omega$) Tested	$2\pi \cdot 135$	MHz	Used for coherence transfer experiments
Speed-up Factor (vs. Adiabatic)	2.7	Times	For achieving 90% transfer efficiency
Excited State Lifetime ($T_1$)	11.1	ns	Spontaneous emission decay of $
Orbital Dephasing Rate ($\Gamma_{orb}$)	55.5	MHz	Dephasing of excited state $
Spectral Diffusion Std Dev ($\sigma$)	$\sim 2\pi \cdot 31$	MHz	Gaussian detuning fluctuation
Transfer Fidelity ($\mathcal{F}$)	0.93 $\pm$ 0.01	N/A	Highest measured for superposition initialization (SATD)

Key Methodologies

The experimental approach utilized highly specialized optical and microwave infrastructure to implement the sub-nanosecond pulse shapes required for Superadiabatic Transitionless Driving.

Material and Environment: Experiments used a naturally-occurring NV center within an electronic grade diamond substrate. The sample was held in a closed-cycle cryostat operating at 5.5 K, reducing thermal dephasing. A 252.5 G magnetic field was applied to control Zeeman splitting.
Spin Initialization: A 532 nm laser was used to initialize the NV center spin state, achieving $>90%$ polarization into the $|m_s=0\rangle$ state.
Optical Field Generation and Stabilization: Two actively stabilized 637 nm tunable lasers were used for resonant excitation.
Pulse Shaping (PEOM/AEOM System):
- The single laser beam was passed through a Phase Electro-Optic Modulator (PEOM). The PEOM was driven by a signal generator (SG) at 1.414 GHz (matching the Zeeman splitting) to generate frequency harmonics. This allowed the simultaneous resonant excitation of both $|-1\rangle \rightarrow |A_2\rangle$ and $|+1\rangle \rightarrow |A_2\rangle$ transitions.
- The output was then passed through an Amplitude Electro-Optic Modulator (AEOM), providing sub-nanosecond analog intensity modulation capabilities.
Control Generation (AWG): A 10 GHz clock-speed Arbitrary Waveform Generator (AWG) provided coordinated temporal profiles for the Stokes ($\Omega_S(t)$) and Pump ($\Omega_P(t)$) pulses, implementing the complex SATD and MOD-SATD pulse shapes designed for transitionless driving in a dressed state basis.
Microwave Control: Additional microwave tones (2.171 GHz and 3.585 GHz) were delivered via a coplanar waveguide to manipulate the NV center within its ground state manifold for initialization and tomography.
Modeling and Optimization: The experimental results were compared against a Master Equation Model incorporating measured decoherence parameters ($T_1$, $\Gamma_{orb}$, and Gaussian spectral diffusion $\sigma$) to confirm the deviation of the optimal pulse shape parameter ($A^{opt}_{shape} < A$) under dissipative conditions.

6CCVD Solutions & Capabilities

The findings demonstrate the critical role of ultra-pure, high-quality diamond substrates in enabling sub-nanosecond quantum control techniques. 6CCVD specializes in delivering bespoke MPCVD diamond solutions optimized for these demanding quantum applications.

To replicate or extend the accelerated quantum control demonstrated in this research, 6CCVD recommends the following specific solutions:

Requirement from Research	6CCVD Solution & Specifications	Sales Value Proposition
Ultra-High Purity Substrate	Optical Grade Single Crystal Diamond (SCD): Material with extremely low impurity concentrations (< 1 ppb assumed, 6CCVD can specify high-purity growth). This is essential for minimizing spectral diffusion and maximizing spin coherence times ($T_2$).	Guarantee minimal parasitic interaction and maximize qubit performance stability, enabling protocols that exceed the demonstrated 2.7x speed-up.
Controlled NV Generation	Custom NV Generation via Ion Implantation: While the paper used a naturally-occurring NV center, 6CCVD offers controlled NV generation in SCD via low-energy ion implantation followed by annealing, allowing specific depth and density control.	Provide tailored NV arrays or single-NV devices with controlled placement and properties, crucial for scalable quantum architectures.
Advanced Surface Integration	Ultra-Polished SCD Wafers: Polishing capability to achieve surface roughness Ra < 1 nm for Single Crystal Diamond. Required for high-fidelity coupling of the 637 nm protocol lasers and integration with high-Q optical cavities.	Minimize optical scattering losses and ensure robust, reproducible spin-photon interfaces necessary for the EOM/AWG systems.
Complex Structure Fabrication	Custom Laser Cutting and Etching: 6CCVD provides precision laser services to achieve custom plate dimensions (up to 125mm PCD) and structural features necessary for housing cryostat optical windows and integrated microwave circuitry (coplanar waveguides).	Accelerate prototype fabrication by delivering geometrically complex, quantum-ready substrates directly to specification.
On-Chip Qubit Control	In-House Metalization Services: Capabilities include deposition of contact layers (Ti, Pt, Au, W, Cu). This allows for direct fabrication of integrated microwave lines (coplanar waveguides) on the diamond surface, critical for delivering the necessary 1.414 GHz ground-state splitting fields.	Streamline the manufacturing pipeline for hybrid solid-state systems, ensuring compatibility between the SCD host and high-frequency control electronics.

Engineering Support

The successful implementation of SATD protocols requires precise matching of material properties (low dissipation rates) to pulse shape calculations. 6CCVD’s in-house PhD team can assist with material selection, impurity level specifications, and geometric design considerations for customers working on accelerated quantum state transfer, geometric quantum computation, and advanced solid-state qubit control projects.

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Tech Support

Original Source

DOI: https://doi.org/10.1038/nphys3967