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Modified coherence of quantum spins in a damped pure-dephasing model

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2022-03-21
JournalPhysical review. B./Physical review. B
AuthorsMattias Johnsson, Ben Q. Baragiola, Thomas Volz, Gavin K. Brennen
InstitutionsCentre for Quantum Computation and Communication Technology, ARC Centre of Excellence for Engineered Quantum Systems
AnalysisFull AI Review Included

Technical Documentation & Analysis: Modified Coherence of Quantum Spins in Damped Pure-Dephasing Models

Section titled “Technical Documentation & Analysis: Modified Coherence of Quantum Spins in Damped Pure-Dephasing Models”

This document analyzes the theoretical findings regarding spin coherence protection in solid-state defects, specifically NV centers in diamond, and maps the material requirements directly to 6CCVD’s advanced MPCVD diamond capabilities.

Executive Summary

Section titled “Executive Summary”

The research provides an exact analytic solution for non-Markovian spin dynamics in a large-spin pure-dephasing model coupled to dissipative bosonic modes, with direct application to solid-state quantum systems.

  • Quantum Zeno Effect (QZE): Identifies the Overdamped Regime ($\Gamma \gg \omega$) where high vibrational mode decay rates ($\Gamma_k$) are inversely proportional to the spin coherence decay rate, effectively preserving coherence via the QZE.
  • Solid-State Relevance: The model is explicitly shown to apply to NV centers in diamond, suggesting that large vibrational decay rates (often considered detrimental) can be leveraged for coherence protection.
  • Dissipative Protection: Demonstrates that coupling between bosonic modes ($\kappa$) can create a privileged symmetric mode, enabling dissipative protection of the collective spin subspace.
  • Quantum Control Handle: The spectral gap created by inter-mode coupling provides a mechanism to selectively address the symmetric mode for quantum control protocols, such as engineering spin squeezing.
  • Process Fidelity: Achieves high theoretical process fidelity ($F_{pro} \approx 0.97$) for a target spin squeezing unitary in the underdamped regime, validating the model’s utility for quantum information processing.
  • Material Implication: The findings underscore the critical need for host materials (like diamond) where the phonon environment and defect coupling parameters ($\eta_k, \omega_k, \Gamma_k$) can be precisely controlled and characterized.

Technical Specifications

Section titled “Technical Specifications”

The following hard data and critical parameters were extracted from the theoretical analysis:

ParameterValueUnitContext
Spin Size (j)$j \ge 1/2$N/AModel applies to two-level systems ($j=1/2$) and large spins ($j > 1/2$).
Maximum Process Fidelity ($F_{pro}$)0.9703N/AAchieved for a $J=5$ spin squeezing unitary (Fig. 6).
Critical Damping Ratio$\Gamma / \omega = 1$N/ADefines the transition between underdamped and overdamped regimes.
Overdamped Coherence Decay Rate$\propto \Gamma_k^{-1}$N/ADecay rate is inversely proportional to the mode decay rate (QZE regime).
Long-Time Limit Condition$\Gamma_k t \gg 1$N/ATime scale required for the oscillating transients to die off.
Thermal State Characterization$\beta = 1/k_B T$N/AInverse temperature of the local thermal baths.
Symmetric Mode Energy Gap$O(N)$N/AExpected spectral gap for N randomly coupled bosonic modes (Sec. IV).
Spin-Mode Coupling Strength$\eta / \omega_s = 0.1$N/AParameter used in the high-fidelity example (Fig. 6).

Key Methodologies

Section titled “Key Methodologies”

The theoretical framework relies on advanced quantum dynamics techniques applied to a structured spin-boson model:

  1. Hamiltonian Construction: Utilized the large-spin spin-boson Hamiltonian (Eq. 1), describing a spin-j particle coupled to a collection of discrete vibrational modes in a crystal lattice setting.
  2. Open System Generalization: Incorporated thermal dissipation by coupling each vibrational mode to a local Markovian thermal bath, described by a Lindblad master equation (Eq. 27, 28).
  3. Analytic Solution via Magnus Expansion: Derived an exact analytic solution for the reduced spin density matrix (Eq. 30) by employing the Magnus expansion to remove time ordering in the interaction picture propagator.
  4. Correlation Function Analysis: The reduced dynamics were expressed entirely in terms of the real ($C_{Re}$) and imaginary ($C_{Im}$) parts of the mode quadrature correlation function, including the effects of thermal occupation.
  5. Inter-Mode Coupling Analysis: Extended the model to two and N spins, introducing coupling ($\kappa$) between local vibrational modes to analyze the formation of symmetric and antisymmetric eigenmodes and their impact on collective spin coherence.
  6. Solid-State Mapping: Mapped the general spin-boson model to the specific vibronic Hamiltonian governing two-level emitter defects (e.g., NV centers) in a crystal lattice, including optical decay ($\Gamma_{opt}$) and additional pure dephasing ($\Gamma_{dp}$).

6CCVD Solutions & Capabilities

Section titled “6CCVD Solutions & Capabilities”

The research confirms that defects in solid-state systems, particularly NV centers in diamond, are a prime platform for leveraging these non-Markovian dynamics. Achieving the required material purity, structural integrity, and integration capabilities is essential for replicating and extending this work. 6CCVD is uniquely positioned to supply the necessary diamond materials and customization services.

Research Requirement (NV Centers/Solid State)6CCVD Solution & CapabilityTechnical Advantage
High-Purity Host Material (NV Centers)Electronic Grade SCD (Single Crystal Diamond)Ultra-low nitrogen content (< 1 ppb) minimizes background defects, ensuring long spin coherence times ($T_2$) necessary for observing QZE effects.
Precise Defect Layer ControlSCD thickness control from 0.1”m up to 500”m.Enables precise placement of NV centers relative to the surface for coupling to external systems (e.g., photonic resonators) or for bulk studies.
Scaling and Array IntegrationPolycrystalline Diamond (PCD) plates up to 125mm diameter.Supports the development of large-scale quantum sensor arrays and integrated quantum devices.
Surface Quality (Minimizing unwanted $\Gamma_k$)SCD polishing to Ra < 1nm. Inch-size PCD polishing to Ra < 5nm.Minimizes surface roughness, which can introduce unwanted surface phonon coupling and decoherence, allowing precise control over the engineered $\Gamma_k$ environment.
Custom Electrical/Optical IntegrationIn-house Custom Metalization (Au, Pt, Pd, Ti, W, Cu).Allows researchers to integrate necessary electrodes for microwave control or electrical readout, crucial for manipulating spin states and observing dissipative protection.
Specialized Material NeedsBoron-Doped Diamond (BDD) substrates and films.Available for applications requiring specific charge state control or electrochemical sensing capabilities, extending the utility of the diamond platform.

Engineering Support

Section titled “Engineering Support”

The paper highlights the critical role of the vibrational environment (characterized by $\omega_k$ and $\Gamma_k$) in determining spin coherence dynamics. 6CCVD’s expertise in MPCVD growth allows for precise control over the diamond material properties, which directly influence the phonon environment. Our in-house PhD engineering team can assist researchers in selecting and specifying diamond substrates (SCD or PCD) optimized to either minimize unwanted decoherence or, conversely, to engineer the environment to maximize the desired Quantum Zeno Effect protection, as demonstrated in this theoretical work.

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

View Original Abstract

We consider a spin-j particle coupled to a structured bath of bosonic modes that decay into thermal baths. We obtain an analytic expression for the reduced spin state and use it to investigate non-Markovian spin dynamics. In the heavily overdamped regime, spin coherences are preserved due to a quantum Zeno affect. We extend the solution to two spins and include coupling between the modes, which can be leveraged for preservation of the symmetric spin subspace. For many spins, we find that intermode coupling gives rise to a privileged symmetric mode gapped from the other modes. This provides a handle to selectively address that privileged mode for quantum control of the collective spin. Finally, we show that our solution applies to defects in solid-state systems, such as negatively charged nitrogen vacancy centers in diamond.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2007 - The Theory of Open Quantum Systems [Crossref]

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