Quantifying phonon-induced non-Markovianity in color centers in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-02-20 |
| Journal | Physical review. A/Physical review, A |
| Authors | Ariel Norambuena, J. R. Maze, Peter Rabl, RaĂșl Coto |
| Institutions | TU Wien, Vienna Center for Quantum Science and Technology |
| Citations | 16 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Coherence as a Measure for Non-Markovianity in Diamond Color Centers
Section titled âTechnical Documentation & Analysis: Coherence as a Measure for Non-Markovianity in Diamond Color CentersâThis document analyzes the research paper âCoherence as a measure for non-Markovianity and its applications to color centers in diamondâ (arXiv:1904.12332v1). The findings are critical for engineers developing robust quantum systems based on diamond color centers (SiV$^{-}$, NV$^{-}$) and highlight the necessity of ultra-high purity MPCVD diamond substrates for controlling system-environment interactions.
Executive Summary
Section titled âExecutive SummaryâThe following points summarize the core technical achievements and the value proposition of the research:
- Novel NM Quantification: Introduces $N_C(T)$, a simple, experimentally accessible measure for quantifying Non-Markovianity (NM) based on the systemâs quantum coherence $C(t)$, measurable via standard Ramsey spectroscopy.
- Diamond Quantum Systems: Applies $N_C(T)$ to critical solid-state qubits, specifically the Silicon-Vacancy (SiV$^{-}$) and Nitrogen-Vacancy (NV$^{-}$) color centers in diamond.
- Phonon Dynamics Dominance: Demonstrates that NM behavior in diamond is driven by the complex competition between bulk acoustic phonons ($\sim\omega^3$ scaling) and distinct quasi-localized phonon modes ($\omega_{loc} \approx 15.19$ THz for SiV$^{-}$).
- Thermal Sensitivity: Reveals a strong temperature dependence, with NM being constant at cryogenic temperatures (T < 100 K) but exhibiting significant, application-specific changes at higher temperatures (T $\approx$ 300 K).
- Coherent Map Extension: Proposes an experimental filtering sequence to extend the $N_C$ measure to coherent dynamical maps (systems with non-zero Rabi frequency $\Omega$), eliminating false positive signs of NM.
- Material Purity Requirement: The observed NM dynamics underscore the critical need for high-ppurity diamond hosts to minimize unwanted defect-phonon interactions and maximize coherence time.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the analysis of the SiV$^{-}$ and NV$^{-}$ systems interacting with the phononic bath:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Localized Phonon Frequency ($\omega_{loc}$) | 15.19 | THz | SiV$^{-}$ center, strong electron-phonon coupling |
| Localized Phonon Width ($\Gamma$) | 0.8414 | THz | Characteristic width of the Lorentzian Spectral Density Function (SDF) |
| Gaussian SDF Center ($\omega_0$) | 9.35 | THz | Captures intermediate vibrational modes (1 THz to 14 THz) |
| Low Temperature Regime | 1 or 10 mK | K | NM measures are constant; dynamics ruled by localized phonons |
| High Temperature Regime | 300 or 286 | K | Thermal activation of localized phonon modes |
| Critical Temperature (NM Transition) | 100 | K | Temperature where $N_Y(T)$ starts increasing linearly |
| Renormalization Factor Negligible Temp | 120 | K | Above this temperature, the $\sigma_x$-term contribution is negligible in strong coupling |
| Optical Rabi Frequency ($\Omega$) | 0.6 | GHz | Used for Variational Polaron Transformation (VPT) analysis |
| Dephasing Oscillation Period | 0.41 | ps | Approximate period ($2\pi/\omega_{loc}$) of coherence oscillations |
Key Methodologies
Section titled âKey MethodologiesâThe research utilized a combination of theoretical modeling and experimental measurement techniques focused on characterizing the system-bath interaction:
- System Modeling: The color center (SiV$^{-}$/NV$^{-}$) is modeled as a two-level system (TLS) coupled to the diamond lattice phonon reservoir via the generalized spin-boson Hamiltonian.
- Phonon Spectral Density Function (SDF): The environment is characterized by a phenomenological SDF, $J(\omega)$, which combines three components: bulk acoustic phonons ($J_{bulk}$), a strong quasi-localized mode ($J_{loc1}$ - Lorentzian), and intermediate vibrational modes ($J_{loc2}$ - Gaussian).
- Dephasing Rate Calculation: The time-dependent dephasing rate, $\gamma(t)$, is derived from the SDF and temperature $T$ using the integral expression (Eq. 4), which fully determines the systemâs coherence dynamics during free evolution.
- Non-Markovianity Measure ($N_C$): NM is quantified by integrating the negative rate of change of coherence, $N_C(T) = 1 + \int_0^T \frac{\dot{C}(\tau) d\tau}{\int_0^T |\dot{C}(\tau)| d\tau}$, which detects the back-flow of quantum information.
- Experimental Access: Coherence $C(t)$ is measured experimentally using standard Ramsey spectroscopy (two $\pi/2$-pulses separated by time $t$).
- Coherent Map Filtering: For systems with non-zero Rabi frequency ($\Omega$), a renormalized coherence $\tilde{C}(t) = C(t) \times S^{-1/2}$ is introduced, requiring a specific three-step measurement sequence of the expectation value $\langle \sigma_z \rangle$ under different initial conditions.
- Strong Coupling Analysis: The generalized polaron transformation (Full Polaron Transformation, FPT, and Variational Polaron Transformation, VPT) is employed to analyze the system dynamics in the strong electron-phonon coupling regime.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful replication and extension of this researchâparticularly the engineering of stable, high-coherence color centersâis fundamentally dependent on the quality and customization of the diamond host material. 6CCVD is uniquely positioned to supply the necessary materials and processing services.
| Requirement from Research Paper | 6CCVD Solution & Capability | Technical Advantage |
|---|---|---|
| Ultra-High Purity Diamond Host (Minimizing bulk defects and unwanted acoustic phonon coupling) | Electronic Grade Single Crystal Diamond (SCD) | Our MPCVD SCD offers extremely low nitrogen (N) and compensating defect concentrations, crucial for maximizing $T_2$ and coherence time $C(t)$ in SiV$^{-}$ and NV$^{-}$ centers by reducing background noise. |
| Integration into Structured Reservoirs (e.g., cantilevers, waveguides, phononic crystals) | Custom Dimensions and Precision Processing | We supply SCD plates up to 10x10mm and PCD wafers up to 125mm. Custom laser cutting and etching services ensure the precise geometries required for engineering specific phononic spectral densities $J(\omega)$. |
| Cryogenic and High-Temperature Stability (Experiments span 1 mK to 300 K) | Thick Substrates for Thermal Management | SCD substrates are available in thicknesses from 0.1 ”m up to 500 ”m, and substrates up to 10mm, providing robust thermal anchoring and mechanical stability essential for stable operation across wide temperature ranges. |
| Coherent Control and Readout (Requires electrodes for Rabi frequency $\Omega$ control and filtering sequences) | In-House Custom Metalization Services | We offer internal deposition of standard metal stacks (Au, Pt, Pd, Ti, W, Cu) directly onto polished diamond surfaces, enabling the integration of microwave or optical control structures necessary for Ramsey spectroscopy and filtering sequences. |
| Surface Quality (Minimizing surface-related dephasing, which can mimic NM effects) | Ultra-Low Roughness Polishing | SCD surfaces are polished to an industry-leading roughness of Ra < 1nm, reducing surface scattering and minimizing additional dephasing sources that complicate the analysis of bulk phonon dynamics. |
| Material Selection and Recipe Tuning (Complex modeling involving SDF, Polaron transformations, and temperature effects) | Expert Engineering Support | 6CCVDâs in-house PhD team specializes in material selection and optimization for quantum applications. We can assist researchers in selecting the optimal SCD purity and orientation to minimize specific phonon coupling constants ($g_k$) for similar SiV$^{-}$ and NV$^{-}$ projects. |
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
The degree of non-Markovianity of a continuous bath can be quantified by means of the coherence. This simple measure is experimentally accessible through Ramsey spectroscopy, but it is limited to incoherent dynamical maps. We propose an extension of this measure and discuss its application to color centers in diamond, where the optical coherence between two orbital states is affected by interactions with a structured phonon bath. By taking realistic phonon spectral density functions into account, we show that this measure is well-behaved at arbitrary temperatures and that it provides additional insights about how non-Markoviantiy is affected by the presence of both bulk and quasi-localized phonon modes. Importantly, with only a little overhead the measure can be adapted to eliminate the false signs of non-Markovianity from coherent dynamical maps and is thus applicable for a large class of systems modeled by the spin-boson Hamiltonian.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 2000 - Quantum Computation and Quantum Information
- 2002 - The Theory of Open Quantum Systems