Enhancing the Robustness of Dynamical Decoupling Sequences with Correlated Random Phases

At a Glance

Metadata	Details
Publication Date	2020-05-05
Journal	Symmetry
Authors	Zhenyu Wang, J. Casanova, Martin B. Plenio
Institutions	Ikerbasque, Universität Ulm
Citations	12
Analysis	Full AI Review Included

Executive Summary

Core Value Proposition: Introduction of a Correlated Random Phase (CRP) protocol that significantly enhances the robustness and selectivity of Dynamical Decoupling (DD) sequences used in quantum sensing, particularly for Nitrogen-Vacancy (NV) centers in diamond.
Error Elimination: The CRP method imposes constraints on the random phases (Φ_r,m) applied to basic DD pulse units, ensuring the sum of their phase factors vanishes (Z_r,M = 0). This effectively eliminates the leading-order static error term (linear in the perturbative parameter ε).
Robustness Enhancement: The CRP protocol demonstrates superior fidelity against static control imperfections, including frequency detuning (up to 50%) and Rabi frequency amplitude errors (up to 30%), compared to both standard (coherent) and uncorrelated randomization protocols.
Small M Advantage: The improvement is most pronounced when the total DD sequence length is short (small number of repetitions, M=6), which is crucial for achieving longer detection times without accumulating high-order errors.
Spurious Response Suppression: The technique effectively suppresses spurious harmonic responses generated by finite-width pi pulses and coupling to unwanted nuclear spins (e.g., ¹³C), thereby improving the reliability and selectivity of the quantum sensor for target spins (e.g., ¹H).
Implementation: The method is compatible with widely used DD sequences, including Carr-Purcell (CP), XY8, and YY8 protocols.

Technical Specifications

Parameter	Value	Unit	Context
DD Sequence Repetitions (M)	6, 24	N/A	Number of times the basic unit (e.g., XY8) is repeated.
Total Pi Pulses (M=6)	48	N/A	Total pulses for XY8/YY8 sequences in small M test.
Pi Pulse Duration (t_p)	15, 100	ns	Control pulse width used in simulations.
Inter Pulse Spacing (τ)	200	ns	Time between pi pulses (Figure 2 context).
Max Detuning Error Tested	Up to 50	%	Percentage deviation from ideal Rabi frequency (Ω_ideal).
Max Amplitude Error Tested	Up to 30	%	Percentage deviation from ideal Rabi frequency (Ω_ideal).
Correlated Elimination Size (G)	2, 3	N/A	Number of subsequent DD units constrained for phase factor cancellation.
Target Spin (¹H) Coupling	2π x (2, 4)	kHz	Hyperfine field components (A_parallel, A_perp).
Noise Spin (¹³C) Coupling	2π x (10, 200)	kHz	Hyperfine field components (A_parallel, A_perp).
Applied Magnetic Field (B_z)	400	G	Applied along the NV center symmetry axis.
Spurious Resonance Frequency	~1740	kHz	Frequency of false signal generated by ¹³C noise.

Key Methodologies

Basic DD Unit Selection: Employed established robust DD sequences (XY8, YY8, Carr-Purcell) as the fundamental pulse unit (Û_unit) for periodic repetition.
Control Error Modeling: Simulated the non-ideal evolution matrix (Û_π) of the pi pulses, incorporating static errors due to frequency detuning (Δ) and Rabi frequency amplitude fluctuations (Ω), which are the dominant sources of pulse error.
Correlated Random Phase (CRP) Protocol: A global phase shift (Φ_r,m) was applied to all pi pulses within the m^th DD unit. The constraint was imposed that the sum of the phase factors (exp(-iΦ_r,m)) for a defined elimination size G (typically G=2 or G=3) must equal zero.
Error Accumulation Analysis: The overall sequence evolution (Û) was analyzed perturbatively. The CRP constraint (Z_r,M = 0) ensures that the leading-order static error term (proportional to Mε) is completely eliminated, regardless of the total number of repetitions M.
Fidelity Simulation: Sequence robustness was numerically evaluated by calculating the survival probability (P_ψ) of the qubit, defined as the fidelity of the final state relative to the initial state (eigenstate of σ_x), in the absence of external signals.
Quantum Sensing Simulation: Modeled an NV electron spin coupled to a target ¹H spin and a noise ¹³C spin under DD control to test the suppression of spurious harmonic peaks caused by finite pulse width and noise coupling.
Statistical Averaging: All results for protocols utilizing random phases (both uncorrelated and correlated) were averaged over 100 random sequences to ensure statistically reliable performance metrics.

Commercial Applications

Quantum Sensing and Metrology: Direct application for enhancing the sensitivity and reliability of quantum sensors, particularly those based on solid-state defects like NV centers in diamond, used for AC magnetic field detection.
Nanoscale NMR and ESR: Improving the spectral resolution and selectivity required for detecting and identifying individual nuclear spins (e.g., ¹H, ¹³C) in extremely small volumes, crucial for analyzing complex molecules or biological samples.
Solid-State Quantum Computing: Utilizing the enhanced robustness of DD sequences to extend qubit coherence times (T₂) and suppress environmental noise and control errors in diamond-based quantum registers.
Materials Science Characterization: High-resolution probing of local magnetic and electric fields within novel materials, enabling the study of spin clusters and defects with atomic precision.
Bioimaging and Medical Diagnostics: Developing highly robust diamond probes for sensing and imaging biological processes at the nanoscale, where control errors and environmental noise are significant challenges.

View Original Abstract

We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to π pulse imperfections and spurious responses due to finite-width π pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond.

Tech Support

Original Source

DOI: https://doi.org/10.3390/sym12050730

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