Second-order Stark shifts exceeding 10$\,$GHz in electrically contacted SiV$^-$ centers in diamond

TL;DR

This work tackles the challenge of inhomogeneous optical transition frequencies among SiV- centers in diamond by implementing in-plane interdigitated electrodes to apply local electric fields and induce Stark shifts. The authors observe a predominantly second-order Stark effect, with shifts exceeding 10 GHz arising from large polarizabilities, and they reveal emitter-to-emitter variations in polarizability linked to local strain and charge environments. Density-functional theory provides a physical picture: the SiV- e_u state is resonant with valence-band states, leading to delocalization and enhanced polarizability, in contrast to SnV- or NiV centers. The results indicate a viable path toward scalable, electrically tunable SiV-–based quantum technologies (e.g., quantum repeaters) by overcoming inhomogeneous broadening, while outlining routes to higher fields and full Stark-tensor characterization.

Abstract

Negatively charged silicon vacancy centers (SiV$^-$) in diamond exhibit excellent spin coherence and optical properties, making them promising candidates for quantum technologies. However, the strain-induced inhomogeneous distribution of optical transition frequencies poses a challenge for scalability. We demonstrate electrical tuning of the SiV$^-$ center zero-phonon lines using in-plane contacts to apply moderate electric fields up to 45$\,$MV/m. The second-order Stark shift exceeds 10$\,$GHz, which is of the same order of magnitude as the 15$\,$GHz inhomogeneous distribution of SiV$^-$ observed in emitters embedded in optical nanostructures such as photonic crystal nanocavities. Analysis of individual SiV$^-$ centers shows significant variation in polarizabilities between defects indicating that the polarizability strongly depends on local parameters like strain. The observed polarizabilities are 3-25 times larger than those of tin vacancy centers, which we attribute to valence band resonances that delocalize the $e_u$ wavefunctions. Photoluminescence excitation measurements reveal that optical linewidths increase moderately with applied electric field strength. Our results demonstrate that large electrical Stark shifts can overcome the inhomogeneous distribution of transition frequencies, representing a significant step toward scalable SiV$^-$-based quantum technologies such as quantum repeaters.

Figures (7)

• Figure 1: SiV$^-$ energy level diagram, sample schematic and photoluminescence excitation spectra for a varying applied local electric fields. a) Energy level diagram of SiV$^-$ centers. The ground states $|E_{g\text{1/2}} \rangle$ and $|E_{g\text{,3/2}}\rangle$, that have a hole in the $e_g$ states, are split by approximately 50GHz due to spin-orbit coupling and the Jahn-Teller effect. Strain can increase this splitting. The excited states $|E_{u\text{1/2}}\rangle$ and $|E_{u\text{3/2}}\rangle$, that both have a hole in the $e_u$ orbitals are lying close to the valence band maximum and split by at least 250GHz. The red arrows define the optical transitions A to D that can be observed in photoluminescence (PL) and PL excitation. b) Top-view schematic of the relevant parts of the sample showing two thin Ti/Au electrodes on flat bulk diamond. The electrode distance is 7.6µm and we ground one of the electrodes and apply a voltage to the other. We focus the excitation and detection spot at approximately a quarter of the electrode distance from one of the electrodes. This breaks the symmetry in voltage because the photocurrent is stronger when the electrode closer to the excitation spot is positively biased. The small black spots E1, E2, E3 and E4 schematically mark different studied single SiV$^-$ positions along the electrode edges. The grey spots mark other single SiV$^-$, which we did not select. c) Photoluminescence excitation spectra of the emitter labelled E4, transition C (denoted E4-C), for different applied electric fields show that the optical emission frequency of SiV$^-$ changes with the field. The solid lines represent Lorentzian peak fits of the data, individually performed for each voltage.
• Figure 2:
• Figure 3: Stark tuning of different individual emitters and statistics on analyzed parameters. The emitters are labelled from E1 to E9 and the measured transition is indicated with a letter from A to D as specified in Figure \ref{['fig:Fig1']} a). a) Center frequencies of various emitters as a function of the applied electric field. Here, we show only the data that we measured for transition C. b) Same as in a) but for transitions D. c) Correlation plot of fitted polarizability versus offset electric field $E_0$. The data indicate that high polarizabilities are accompanied by high local electric field offsets. Tin vacancy polarizabilities are shown for comparison Aghaeimeibodi2021_Vuckovic_TinVac2021DeSantis2021_Englund_StarkTun_TinVac_2021.
• Figure S1: Photoluminescence spectrum of SiV$^-$, which used a 564THz (532nm) laser for excitation and an $f=500mm$ spectrometer with a grating that has $1200$ lines per millimeter for detection. We assign lines A, B, C and D to one of the emitting SiV$^-$. The fact that there are more emission lines indicates that multiple SiV$^-$ with varying degrees of strain contribute.
• Figure S2: COMSOL simulation of the static electric field. The field is calculated in the diamond 100nm (resembling SiV$^-$ implantation depth) below the surface along a line that runs perpendicular to the edges of the electrode fingers. In the simulation, we applied 10V to the right gold electrode and grounded the left one. The electrode separation is 7.6µm. The x-direction runs parallel to the diamond surface between the electrodes. Positive y-direction is from the diamond surface upwards into the vacuum. The dashed line indicates the approximate position of the SiV$^-$ that we studied.