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arXiv:2104.09638 · Journal of Applied Physics

Using silicon-vacancy centers in diamond to probe the full strain tensor

Kelsey M. Bates, Matthew W. Day, Christopher L. Smallwood, Rachel Owen, Tim Schröder, Edward Bielejec, Ronald Ulbricht, Steven T. Cundiff

Published Jul 9, 2021• 24 citations
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Abstract

An ensemble of silicon vacancy (SiV−) centers in diamond is probed using two-pulse correlation spectroscopy and multidimensional coherent spectroscopy. Two main distinct families of SiV− centers are identified, and these families are paired with two orientation groups by comparing spectra from different linear polarizations of the incident laser. By tracking the peak centers in the measured spectra, the full diamond strain tensor is calculated local to the laser spot. Measurements are made at multiple points on the sample surface, and variations in the strain tensor are observed.

DOI
10.1063/5.0052613

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Multidimensional Coherent Spectroscopy: Probing the Strain Tensor in Diamond and the Effects of Correlated Dephasing

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This work covers two main results united by multidimensional coherent spectroscopy (MDCS): one experimental and one theoretical. MDCS is a nonlinear optical technique in which a sample is probed using a series of ultrashort pulses. Measurements are made while varying the relative time delays between the pulses, and the resulting spectra yield a much richer set of information compared to traditional linear spectroscopies. The experimental work concerns the negatively charged silicon-vacancy (SiV) center in diamond. We use two-pulse correlation (TPC) spectroscopy and rephasing MDCS to probe a diamond sample with a high density of implanted SiV centers. These spectra reveal a large number of spectral peaks, which can be grouped into two families of SiV centers using the MDCS spectra. By comparing spectra from two polarizations of the incident light, we associate the two families with two orientation groups within the diamond. We link the differences in the frequencies of the spectral peaks to strain intrinsic to our sample, and use the peak locations from both families to solve for the full strain tensor local to the laser spot. By measuring TPC spectra at multiple points on the sample, we track changes in the measured strain. We observe non-zero strain on the order or 1e-5 at every measured location, and observe variation in both the normal and shear strain in the sample. We interpret the strain as likely to be due to the high implantation density of silicon in the diamond. These results could be useful when using SiV centers as a strain gauge. The theoretical work uses simulations to calculate spectra. The simulations developed here begin by recursively generating a list of Feynman diagrams for a given signal pathway and system. The contributions due to each Feynman diagram are calculated and combined to find the complete spectrum. The code is designed to be very flexible, and can be used to simulate arbitrary types of MDCS spectra and energy level diagrams. We then apply the simulations to investigate the effects of correlated dephasing due to scattering events in the Markovian limit on MDCS of interacting systems. We derive a mathematical expression to represent the dephasing rate of a coherence in terms of the dephasing rates of the coherences from the constituent energy transitions and the correlation matrix of these transitions. This expression is applied to simulate double-quantum and higher-order n-quantum spectra of multiple interacting systems. For double-quantum spectra, correlated dephasing results in a higher double-quantum dephasing rate, and anticorrelated dephasing results in a lower double-quantum dephasing rate. Similar results are found for the n-quantum dephasing rate. Generally, for certain configurations, the many-body dephasing rate can be arbitrarily low, and the n-quantum linewidth can be arbitrarily narrow, although this requires some form of anticorrelation. These results could be useful in creating quantum sensors with higher sensitivities, since one limit of the sensitivity is the decoherence time of the system.

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An ensemble of silicon vacancy (SiV−) centers in diamond is probed using two-pulse correlation spectroscopy and multidimensional coherent spectroscopy. Two main distinct families of SiV− centers are identified, and these families are paired with two orientation groups by comparing spectra from different linear polarizations of the incident laser. By tracking the peak centers in the measured spectra, the full diamond strain tensor is calculated local to the laser spot. Measurements are made at multiple points on the sample surface, and variations in the strain tensor are observed.
This work covers two main results united by multidimensional coherent spectroscopy (MDCS): one experimental and one theoretical. MDCS is a nonlinear optical technique in which a sample is probed using a series of ultrashort pulses. Measurements are made while varying the relative time delays between the pulses, and the resulting spectra yield a much richer set of information compared to traditional linear spectroscopies. The experimental work concerns the negatively charged silicon-vacancy (SiV) center in diamond. We use two-pulse correlation (TPC) spectroscopy and rephasing MDCS to probe a diamond sample with a high density of implanted SiV centers. These spectra reveal a large number of spectral peaks, which can be grouped into two families of SiV centers using the MDCS spectra. By comparing spectra from two polarizations of the incident light, we associate the two families with two orientation groups within the diamond. We link the differences in the frequencies of the spectral peaks to strain intrinsic to our sample, and use the peak locations from both families to solve for the full strain tensor local to the laser spot. By measuring TPC spectra at multiple points on the sample, we track changes in the measured strain. We observe non-zero strain on the order or 1e-5 at every measured location, and observe variation in both the normal and shear strain in the sample. We interpret the strain as likely to be due to the high implantation density of silicon in the diamond. These results could be useful when using SiV centers as a strain gauge. The theoretical work uses simulations to calculate spectra. The simulations developed here begin by recursively generating a list of Feynman diagrams for a given signal pathway and system. The contributions due to each Feynman diagram are calculated and combined to find the complete spectrum. The code is designed to be very flexible, and can be used to simulate arbitrary types of MDCS spectra and energy level diagrams. We then apply the simulations to investigate the effects of correlated dephasing due to scattering events in the Markovian limit on MDCS of interacting systems. We derive a mathematical expression to represent the dephasing rate of a coherence in terms of the dephasing rates of the coherences from the constituent energy transitions and the correlation matrix of these transitions. This expression is applied to simulate double-quantum and higher-order n-quantum spectra of multiple interacting systems. For double-quantum spectra, correlated dephasing results in a higher double-quantum dephasing rate, and anticorrelated dephasing results in a lower double-quantum dephasing rate. Similar results are found for the n-quantum dephasing rate. Generally, for certain configurations, the many-body dephasing rate can be arbitrarily low, and the n-quantum linewidth can be arbitrarily narrow, although this requires some form of anticorrelation. These results could be useful in creating quantum sensors with higher sensitivities, since one limit of the sensitivity is the decoherence time of the system.
Color centers in diamond are point defects within the diamond host lattice that absorb and emit light at optical frequencies. Besides contributing to the striking visual characteristics of "fancy colored" diamonds as gemstones, the centers--particularly the negatively charged nitrogen-vacancy (NV) center and silicon-vacancy (SiV-) center--offer a number of possibilities for quantum computation and quantum information processing. In this talk, I will summarize recent progress made in characterizing negatively charged silicon-vacancy centers in diamond using the technique of optical multidimensional coherent spectroscopy (MDCS). By comparing photoluminescence-based and heterodyne-detection based signal collection schemes in a high-density SiV- center sample, we have selectively identified a population of long-lived and nonradiative silicon-vacancy centers in diamond with more than 40 times as much inhomogeneous spectral broadening as the radiative silicon-vacancy center states that are more commonly observed using photoluminescence. Estimates of the degree of inhomogeneity and overall sample characteristics indicate that strain is likely to play a large role in the formation of these nonradiative states. The findings open possibilities for being able to actively tune the degree of radiative coupling in silicon-vacancy center systems, opening possibilities for new types of quantum-optical devices.
Negatively charged silicon-vacancy (SiV−^-−) centers in diamond offer an attractive platform for the development of many forms of quantum technology. However, questions remain in connection to how large ensembles of SiV−^-− centers behave in concert. Here, we develop a computational model designed to simulate recent experiments where optical multidimensional coherent spectroscopy (MDCS) was used to examine a high-concentration sample of SiV−^-− centers in diamond, revealing significant variations in spectral signature depending on the detection scheme. Simulation results reveal that strain effects are highly random in this system, with a characteristic axial strain of 2.8×10−42.8 \times 10^{-4}2.8×10−4 and a shear strain of 3.5×10−53.5 \times 10^{-5}3.5×10−5. They suggest in addition that highly strained centers (with values exceeding 1.5×10−51.5 \times 10^{-5}1.5×10−5) may become significantly decoupled from optical emission. The results have implications for the use of SiV−^-− centers as quantum sensors.
We characterize a high-density sample of negatively charged silicon-vacancy (SiV^{-}) centers in diamond using collinear optical multidimensional coherent spectroscopy. By comparing the results of complementary signal detection schemes, we identify a hidden population of SiV^{-} centers that is not typically observed in photoluminescence and which exhibits significant spectral inhomogeneity and extended electronic T_{2} times. The phenomenon is likely caused by strain, indicating a potential mechanism for controlling electric coherence in color-center-based quantum devices.