Experimental characterization of spin-$\frac{3}{2}$ silicon vacancy centers in $6H$-SiC

Silicon carbide (SiC) hosts many interesting defects that can potentially serve as qubits for a range of advanced quantum technologies. Some of them have very interesting properties, making them potentially useful, e.g., as interfaces between stationary and flying qubits. Here we present a detailed overview of the relevant properties of the spins in silicon vacancies of the $6H$-SiC polytype. This includes the temperature-dependent photoluminescence, optically detected magnetic resonance, and the relaxation times of the longitudinal and transverse components of the spins during free precession as well as under the influence of different refocusing schemes.

Figure 1

Structure of a negatively charged spin 3/2 silicon-vacancy (${\mathrm{V}}_{\mathrm{Si}}^{-}$). The blue spheres with labels C represent the carbon atoms. The white circle with the dashed boundary represents the ${\mathrm{V}}_{\mathrm{Si}}^{-}$.

Figure 2

Experimental setup for photoluminescence measurements. The red line from the laser represents the laser beam and C denotes the mechanical chopper. The gray rectangle labeled S is the SiC sample. Ellipsoids labeled M, L, and F represent reflecting mirrors, convex lenses, and a long-pass filter, respectively. The rectangle labeled APD represents the avalanche photodiode module.

Figure 3

PL spectra measured at different temperatures. The sample is excited with a 790-nm laser. Peaks labeled ${\mathrm{V}}_1$, ${\mathrm{V}}_2$, and ${\mathrm{V}}_3$ correspond to the zero-phonon lines of ${\mathrm{V}}_{\mathrm{Si}}^{-}$ at the lattice sites $k_1$, $h$, and $k{}_2$, respectively.

Figure 4

Energy-level diagram of the $6H$-SiC ${\mathrm{V}}_{\mathrm{Si}}^{-}$ showing the ground, excited, and shelving states. Radiative transitions with rates $k_{31}$ and $k_{20}$ are marked by red arrows. The laser beam excitation is shown with thick orange arrows. Spin-dependent nonradiative transitions generating the ground-state spin polarization are shown as black arrows. States $|0\rangle$ and $|1\rangle$ represent the $\mathrm{degenerate}|\pm \frac{3}{2}\rangle$ ($|\pm \frac{1}{2}\rangle$) and $|\pm \frac{1}{2}\rangle$ ($|\pm \frac{3}{2}\rangle$) ground states of the ${\mathrm{V}}_1/{\mathrm{V}}_3$ (${\mathrm{V}}_2$) type $V_{\mathrm{Si}}^{-}$. The states $|2\rangle$ and $|3\rangle$ represent the doubly degenerate excited states and $|4\rangle$ the shelving states.

Figure 5

(a) ODMR signal vs frequency recorded with different RF powers in zero magnetic field. The horizontal axis is the frequency in MHz and the vertical axis the relative change of the PL, recorded by the lock-in amplifier. (b) ODMR signal vs RF power and (c) linewidth vs RF power.

Figure 6

Experimental setup for measuring the ODMR of silicon vacancies. The red line from the laser represents the path of the laser beam. Ellipsoids labeled M, L, and F represent mirrors, convex lenses, and long-pass filter, receptively. The gray rectangle labeled with S is the SiC sample. The RF is applied using straight a $50\mu \mathrm{m}$ diameter copper wire placed over the sample, in series with a 50-$\mathrm{\Omega }$ resistor which is represented by a rectangle labeled with R. The tree orthogonal ring-pairs Cx, Cy, and Cz represent Helmholtz coils. They allows us to apply magnetic fields in an arbitrary direction. Rounded rectangles labeled PFG, APD, and DDS represent a programmable function generator, an avalanche photodetector module and a direct digital synthesizer, respectively.

Figure 7

Energy levels of (a) the ${\mathrm{V}}_1/{\mathrm{V}}_3$ vacancy and (b) ${\mathrm{V}}_2$ vacancy in a magnetic field $B\parallel c$ axis. (c) Experimental ODMR and (d) simulated ODMR showing resonances from ${\mathrm{V}}_1/{\mathrm{V}}_3$ and ${\mathrm{V}}_2$ for a range of magnetic fields $B\parallel c$ axis. The color scale in (c) and (d) is in units of $\mathrm{\Delta }\mathrm{PL}/\mathrm{PL}\%$.

Figure 8

Experimental setup used for measuring the relaxation rates. The acousto-optical modulator (AOM) generates the laser pulses. The red line from the laser represents the path of the laser beam. Ellipsoids labeled with M, L, and F represent reflecting mirrors, convex lenses, and long-pass filter, receptively. DWG is a digital word generator (TTL pulse generator). The gray rectangle labeled with S is the SiC sample. AWG is an arbitrary waveform generator. The RF is applied to the sample by a resonant LC circuit.

Figure 9

(a) Pulse sequence for measuring Rabi oscillations. The red and blue rectangles represent the laser and RF pulses and the pulse duration is written above the pulse. (b) Experimental Rabi oscillations for ${\mathrm{V}}_1$/${\mathrm{V}}_3$ and ${\mathrm{V}}_2$. The $y$ axis represents the normalized change of the PL signal and the $x$ axis the RF pulse duration ${\tau }_R$.

Figure 10

(a) Pulse sequence used to measure the $T_1$ relaxation. The red and blues rectangles represent the laser and RF pulses. The length of the pulse is written above the pulse. (b) Resulting signal (normalized) as a function of the delay ${\tau }_1$, measured at room temperature.

Figure 11

(a) Pulse sequences for measuring the free-induction decay. The red and blues rectangles represent the laser pulses and RF pulses, respectively. The pulse duration is written above the pulse. (b) FID signals measured for ${\mathrm{V}}_1/{\mathrm{V}}_3$ and ${\mathrm{V}}_2$.

Figure 12

(a) Pulse sequence used to measure dephasing of the transverse spin components. The red and blue rectangles represent the laser and RF pulses, respectively. The length of the pulses is written above them. (b) Signals measured for ${\mathrm{V}}_1/{\mathrm{V}}_3$ and ${\mathrm{V}}_2$ as a function of the delay ${\tau }_2$.

Figure 13

(a) Pulse sequence for measuring the spin coherence time under multiple refocusing pulses. The red and blues rectangles represent the laser and RF pulses, respectively. (b) Decay of the spin coherence during the multiple echo sequence. The experimental data (circles) are fitted to function (4).