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arXiv:2409.14856

Coherent population trapping and spin relaxation of a silicon vacancy center in diamond at mK temperatures

Shuhao Wu, Xinzhu Li, Ian Gallagher, Benjamin J. Lawrie, Hailin Wang

Published Sep 23, 2024• 0 citations
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Abstract

We report experimental studies of coherent population trapping and spin relaxation in a temperature range between 4 K and 100 mK in a silicon vacancy (SiV) center subject to a transverse magnetic field. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV ground states.

DOI
10.48550/arxiv.2409.14856

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We report experimental studies of coherent population trapping and spin relaxation in a temperature range between 4 K and 100 mK in a silicon vacancy (SiV) center subject to a transverse magnetic field. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV ground states.
We report experimental studies of coherent population trapping (CPT) and spin relaxation in a temperature range 4 K--100 mK in a silicon vacancy (SiV\text{Si}VSiV) center subject to a transverse magnetic field. The spin linewidth, which is determined by spin dephasing, is extracted from power dependent CPT linewidths. Near and below 1 K, phonon-induced spin dephasing becomes negligible compared with that induced by the spin bath of naturally abundant 13C^{13}\mathrm{C}13C atoms. The temperature dependence of the spin dephasing rates agrees with the theoretical expectation that phonon-induced spin dephasing arises primarily from orbital relaxation induced by first order electron-phonon interactions. A nearly 100-fold increase in spin lifetime is observed when the temperature is lowered from 4 K to slightly below 1 K, indicating that two-phonon spin-flip transitions play an essential role in the spin relaxation of SiV\text{Si}VSiV ground states.
The negatively charged silicon-vacancy (SiV^{-}) color center in diamond has recently emerged as a promising system for quantum photonics. Its symmetry-protected optical transitions enable the creation of indistinguishable emitter arrays and deterministic coupling to nanophotonic devices. Despite this, the longest coherence time associated with its electronic spin achieved to date (∼250 ns) has been limited by coupling to acoustic phonons. We demonstrate coherent control and suppression of phonon-induced dephasing of the SiV^{-} electronic spin coherence by 5 orders of magnitude by operating at temperatures below 500 mK. By aligning the magnetic field along the SiV^{-} symmetry axis, we demonstrate spin-conserving optical transitions and single-shot readout of the SiV^{-} spin with 89% fidelity. Coherent control of the SiV^{-} spin with microwave fields is used to demonstrate a spin coherence time T_{2} of 13 ms and a spin relaxation time T_{1} exceeding 1 s at 100 mK. These results establish the SiV^{-} as a promising solid-state candidate for the realization of quantum networks.
Coherent quantum systems are a key resource for emerging quantum technology. Solid-state spin systems are of particular importance for compact and scalable devices. However, interaction with the solid-state host degrades the coherence properties. The negatively charged silicon vacancy center in diamond is such an example. While spectral properties are outstanding, with optical coherence protected by the defects symmetry, the spin coherence is susceptible to rapid orbital relaxation limiting the spin dephasing time. A prolongation of the orbital relaxation time is therefore of utmost urgency and has been tackled by operating at very low temperatures or by introducing large strain. However, both methods have significant drawbacks: the former requires use of dilution refrigerators and the latter affects intrinsic symmetries. Here, a novel method is presented to prolong the orbital relaxation with a locally modified phonon density of states in the relevant frequency range, by restricting the diamond host to below 100 nm. Subsequently measured coherent population trapping shows an extended spin dephasing time compared to the phonon-limited time in a pure bulk diamond. The method works at liquid helium temperatures of few Kelvin and in the low-strain regime.
The silicon-vacancy center in diamond offers attractive opportunities in quantum photonics due to its favorable optical properties and optically addressable electronic spin. Here, we combine both to achieve all-optical coherent control of its spin states. We utilize this method to explore spin dephasing effects in an impurity-rich sample beyond the limit of phonon-induced decoherence: Employing Ramsey and Hahn-echo techniques at temperatures down to 40 mK we identify resonant coupling to a substitutional nitrogen spin bath as limiting decoherence source for the electron spin.
The properties of the negatively charged silicon-vacancy (SiV) centre in diamond were investigated in this thesis. Polarisation measurements revealed transition dipoles and the symmetry groups of the centre. In a diamond grown by chemical vapour deposition, a high spectral overlap of SiV centres with nearly transform limited optical line widths was found pointing to a low sensitivity of SiV centres to both strain and local electric fields. This low inhomogeneous distribution allowed for a quantum interference leading to a contrast of over 70 % in a Hong-Ou-Mandel experiment. Additionally, an isotopic shift at single site level could be confirmed and than used to identify the 64meV peak in the phonon sideband as a local vibrational mode. A low temperature investigation of optical line width and orbital relaxation time indicated a direct single-phonon process between the orbital states while at higher temperatures a two-phonon dephasing was found to be the main electron-phonon process. The results were consistently described by the microscopic model developed and additional strength was added by consistent studies of spin-orbit splitting and optical lifetime. By applying a magnetic field the spin degeneracy in the ground state was lifted allowing for spin initialisation with over 95 % fidelity with a spin relaxation time of over 2 milliseconds. Two resonant lasers were used to demonstrate coherent population trapping leading to a coherence time in the order of the orbital relaxation time. The coherence was concluded to be limited by orbital dephasing processes and we propose techniques to overcome them. One of them is to use nanodiamonds with a size smaller than half the phonon wavelength to suppress the dephasing process. Investigating the spectral properties at cryogenic temperatures, nearly lifetime limited line widths have been found, making these nanodiamonds good candidates for further spin applications with SiV centres.
We investigate phonon induced electronic dynamics in the ground and excited states of the negatively charged silicon-vacancy ( ) centre in diamond. Optical transition line widths, transition wavelength and excited state lifetimes are measured for the temperature range 4 K–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 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 qubits in the ground states and propose methods to extend coherence times of qubits.