Electron-phonon processes of the silicon-vacancy centre in diamond

Abstract: We investigate phonon induced electronic dynamics in the ground and excited states of the negatively charged silicon-vacancy ($\mathrm{SiV}^-$) centre in diamond. Optical transition line widths, transition wavelength and excited state lifetimes are measured for the temperature range 4-350 K. The ground state orbital relaxation rates are measured using time-resolved fluorescence techniques. A microscopic model of the thermal broadening in the excited and ground states of the $\mathrm{SiV}^-$ centre is developed. A vibronic process involving single-phonon transitions is found to determine orbital relaxation rates for both the ground and the excited states at cryogenic temperatures. We discuss the implications of our findings for coherence of qubit states in the ground states and propose methods to extend coherence times of $\mathrm{SiV}^-$ qubits.

• The paper identifies a key vibronic process via single-phonon transitions that predominantly governs orbital relaxation in SiV centers at cryogenic temperatures.
• It employs time-resolved fluorescence techniques to measure temperature-dependent optical transition line widths, excited state lifetimes, and ground state relaxation rates.
• The findings inform strategies to enhance qubit coherence, including suppressing phonon effects and engineering phononic bandgap structures.

An Analysis of Electron-Phonon Processes in the Silicon-Vacancy Center in Diamond

The study presented in this paper investigates the phonon-induced electronic dynamics in both the ground and excited states of the negatively charged silicon-vacancy ($SiV$) center in diamond. Through a systematic analysis, the researchers measured several critical parameters of the $SiV$ center, including optical transition line widths, transition wavelengths, and excited state lifetimes at various temperatures ranging from 4 K to 350 K. Using time-resolved fluorescence techniques, the paper scrutinizes the ground state orbital relaxation rates and further develops a microscopic model to explain the observed thermal broadening phenomena in both the excited and ground states.

A central finding of this study is the role of a vibronic process involving single-phonon transitions, which prominently dictate the orbital relaxation rates for both ground and excited states at cryogenic temperatures. These findings have profound implications for the coherence of qubit states residing in the ground state of $SiV$ centers, a subject that the researchers address by proposing methods to extend the coherence times of $SiV$ qubits.

Numerical Results and Observations

The research presented several quantitative observations:

1. Optical Transition and Line Widths: The team discovered that the line width of the optical transition exhibits a $T^3$ temperature dependence at higher temperatures, shifting to an approximate linear temperature dependence below 20 K. This indicates the significance of second-order transitions due to electron-phonon interactions involving $E$-symmetric phonon modes.
2. Ground State Relaxation: The ground state orbital relaxation rate showed a linear dependence on temperature, predominantly below 20 K, with the longest measured relaxation time at 5 K being $T_1$ = 39 ± 1 ns. These observations are attributed to a single-phonon resonant absorption process.
3. Excited States Lifetime: An increase in the excited state lifetime was measured with decreasing temperature, thereby suggesting a significant non-radiative decay component at room temperature, effectively described by a Mott-Seitz model with an activation energy of 55 ± 2 meV.
4. Thermal Effects on Energy Splitting: Both the excited and ground state splittings decreased with rising temperature, displaying a $T^2$ dependency, likely due to the Jahn-Teller effect quantified by linear electron-phonon interactions involving $E$ phonon modes.

Implications and Theoretical Contributions

This study provides a comprehensive microscopic model based on the Jahn-Teller effect that aligns well with experimental observations, effectively advancing the understanding of electron-phonon processes within the $SiV$ center. Notably, the consistent application of linear electron-phonon interactions in explaining the thermal and non-radiative behavior of $SiV$ centers paves a pathway for engineering these centers to optimize qubit coherence times.

Future Directions

The findings suggest several avenues for future research and practical developments:

• Suppressing Phonon Effects: Investigation into methods capable of significantly suppressing phonon occupation, such as working at sub-Kelvin temperatures or leveraging strain to increase the energy splitting between states, holds promise for enhancing the coherence times of $SiV$ centers.
• Phononic Bandgap Structures: Exploring nanostructures that could provide a phononic bandgap for acoustic phonons around the $SiV$ spin-orbit splittings at 50 GHz offers the potential to inhibit orbital relaxation processes rigorously.

In conclusion, the research elucidates that coherence times for $SiV$ ground states are limited by phonon-driven orbital relaxation processes, thus directing future efforts toward reducing these rates to realize improved quantum coherence in practical applications. This paper not only advances the theoretical understanding of electron-phonon interactions but also provides insights crucial for the development of quantum technologies involving silicon-vacancy centers in diamond.