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6CCVD Research

Quantifying phonon-induced non-Markovianity in color centers in diamond

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2020-02-20
JournalPhysical review. A/Physical review, A
AuthorsAriel Norambuena, J. R. Maze, Peter Rabl, Raúl Coto
InstitutionsVienna Center for Quantum Science and Technology, Universidad Mayor
Citations16
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research introduces a novel, experimentally practical method for quantifying Non-Markovianity (NM) in solid-state quantum systems, crucial for advancing quantum technology platforms.

  • Simple NM Measure: The study proposes NC(T), a measure of Non-Markovianity derived directly from the system’s coherence C(t), which is readily accessible via standard Ramsey spectroscopy.
  • Solid-State Validation: The measure is applied to characterize the complex phonon environments of Silicon-Vacancy (SiV-) and Nitrogen-Vacancy (NV-) color centers in diamond.
  • Structured Environment Analysis: The dynamics are shown to be governed by a competition between low-frequency bulk acoustic phonons and high-frequency quasi-localized phonon modes.
  • Temperature Dependence: NM is dominated by the strong coupling to quasi-localized modes at low temperatures (T < 100 K). Conversely, NM is suppressed at high temperatures (T ≈ 300 K) due to the influence of super-Ohmic bulk acoustic phonons.
  • Coherent Map Extension: The measure is successfully extended to coherent dynamical maps (systems with external Rabi driving) by introducing a filtering function (S-1/2) to eliminate false NM signals caused by coherent population oscillations.
  • Critical Temperature Identified: For strong coupling regimes, a critical temperature of approximately 120 K (Tloc) is found, above which the coherent driving term has a negligible effect on the open system dynamics.

Technical Specifications

Section titled “Technical Specifications”

The following parameters characterize the phonon environment and the operational regimes for diamond color centers:

ParameterValueUnitContext
SiV- Localized Phonon Frequency (ωloc)15.19THzFrequency of the quasi-localized mode responsible for strong electron-phonon coupling.
NV- Main Phonon Frequency15.7THzFrequency corresponding to the main peak in the NV- spectral density function.
SiV- Acoustic Phonon Cutoff (ωc)~1THzCutoff frequency for low-energy bulk acoustic phonons (J(ω) ~ ω3 scaling).
SiV- Lorentzian Width (Γ)0.8414THzPhenomenological decay rate (width) associated with the quasi-localized mode.
Low Temperature RegimeT < 20KRegime where phonon occupancy is low (coth(ω/2kBT) ≈ 1).
High Temperature RegimeT > 286KRegime where thermal activation of the strong localized phonon mode occurs.
Critical Temperature (Tloc)T ≈ 116KTemperature associated with the quasi-localized phonon mode (ħωloc/kB).
Coherent Oscillation NegligibilityT ≈ 120KTemperature above which Rabi-induced coherence oscillations are negligible in the strong coupling regime.

Key Methodologies

Section titled “Key Methodologies”

The quantification of Non-Markovianity relies on a combination of theoretical modeling and simulation of standard experimental techniques.

  1. System Hamiltonian Definition: The color center is modeled as a two-level system (TLS) coupled to the phonon bath using the generalized Spin-Boson Hamiltonian. The analysis focuses on the optical coherence between the ground (|g>) and excited (|e>) orbital states.
  2. Spectral Density Function (SDF) Construction: The SDF, J(ω), characterizing the phonon environment, is defined as a sum of three components: Jbulk (acoustic phonons, scaling as ω3), Jloc1 (Lorentzian quasi-localized mode), and Jloc2 (Gaussian vibrational modes).
  3. Dephasing Rate Calculation: The time-dependent dephasing rate γ(t) is calculated exactly using the integral formulation involving the SDF and the thermal occupancy factor (coth(ħω/2kBT)). Negative values of γ(t) are used as a witness for NM.
  4. Coherence Measurement Simulation (Ramsey Spectroscopy): The coherence C(t) is simulated, corresponding to the measurement of the Pauli operator expectation values (<σx> and <σy>) achievable via standard Ramsey pulse sequences (two π/2 pulses separated by time t).
  5. Non-Markovianity Quantification (NC): The NM measure NC is calculated by integrating the positive values of the time derivative of coherence (Ċ(t)) over the evolution time T, capturing the back-flow of quantum information from the bath to the system.
  6. Coherent Map Filtering: For systems under external driving (Rabi frequency Ω), a renormalized coherence C̃(t) = C(t) × S-1/2 is used. The filtering factor S is derived from the population dynamics (<σz>) measured under specific initial conditions, effectively isolating the dephasing dynamics from coherent oscillations.
  7. Strong Coupling Analysis: The Generalized Polaron Transformation (FPT/VPT) is employed to analyze the system dynamics when electron-phonon coupling is strong, allowing for the calculation of the renormalized Rabi frequency (ΩR = BΩ).

Commercial Applications

Section titled “Commercial Applications”

This research provides fundamental tools for engineering and optimizing solid-state quantum devices, particularly those based on diamond color centers.

Industry/ApplicationRelevance to Technology
Quantum Computing HardwareEssential for designing robust qubits (SiV-, NV-) where coherence time is limited by phonon interactions. The NC measure allows for rapid characterization of material quality and reservoir structure.
Quantum Metrology and SensingNM quantification is critical for optimizing the sensitivity and operational bandwidth of diamond-based sensors (e.g., magnetometers, thermometers) that rely on long coherence times.
Phononic Crystal and Waveguide DesignProvides a metric for evaluating the effectiveness of structured reservoirs (e.g., cantilevers, phononic crystals) engineered to suppress detrimental phonon modes and enhance quantum control.
Quantum Control and Error MitigationA precise understanding of NM dynamics is necessary to implement efficient active error correction and decoupling pulse sequences (like dynamical decoupling) tailored to the specific non-Markovian noise profile.
Solid-State Emitter OptimizationApplicable to other solid-state emitters where optical coherence is limited by lattice vibrations, guiding material scientists in selecting optimal host materials and defect structures.
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 “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2000 - Quantum Computation and Quantum Information
  2. 2002 - The Theory of Open Quantum Systems

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