A single optically detectable tumbling spin in silicon

TL;DR

The paper addresses single-spin dynamics of a silicon G center whose spin tumbles between inequivalent crystal orientations. It employs high-resolution pulse ODMR with a G center integrated in circular Bragg cavities to enhance emission and resolve a fine spin structure arising from spin principal axes reorientation. The authors extract ZFS parameters $|D|=1205$ MHz and $E=516$ MHz and observe Ramsey beatings indicating multiple detuned transitions, confirming spin tumbling; they demonstrate orientation-dependent Rabi frequencies, with a measured ratio $\Omega/\Omega' \approx 2.2$. A geometric, site-based model connects MW coupling to the six possible Si$_i$ positions, enabling quantitative insight into the atomic configuration and reorientation dynamics. Overall, the work establishes G centers as a platform for integrated optical–spin–rotation physics in silicon and opens avenues for probing lattice strain and reorientation with high sensitivity.

Abstract

Electron spin resonance spectroscopy is a widely used technique for analyzing the microscopic structure, local environment and reorientation of atomic and molecular systems. Conventional inductive detection methods typically require to probe more than a billion of electron spins such that single atom motion is hidden through ensemble averaging. While several single spin spectroscopy methods are currently available, they have been so far limited to static systems. Here we demonstrate single spin spectroscopy of a fluorescent tumbling defect in silicon called the G center, behaving as a pseudo-molecule randomly reorienting itself in the crystalline matrix. Using high-resolution spin spectroscopy, we reveal a fine magnetic structure resulting from the spin principal axes jumping between discrete orientations in the crystal. By modeling the atomic reorientation of the defect, we demonstrate that spin tumbling induces variations in the coupling to the microwave magnetic field, enabling position-dependent Rabi frequencies to be detected in coherent spin control experiments. By virtue of its pseudo-molecule configuration, the G center in silicon is a unique quantum system to investigate the mutual interaction between optical, spin and rotation properties in a highly versatile material.

Figures (4)

• Figure 1: A single G center integrated in a micro-cavity.a, Scanning electron micrograph of a circular Bragg grating cavity positioned close to the microwave microstrip. Scale bar is 1 . b, PL spectrum of an individual G center inside a cavity. Inset, PL map around the cavity. Scale bar is 1 . c, Corresponding raw (uncorrected) autocorrelation function, giving $g^{(2)}(0) = 0.02 \pm 0.01$. Solid line is data fitting inferred from a rate equation model of a 3-level system redjem_single_2020. d, Evolution of the PL count rate with optical pumping power. Dashed lines represent a fit to the data with a standard saturation function.
• Figure 2: ODMR on a single G center in silicon.a, Energy level structure of the G center. The thicker dashed line indicates a faster decay from the metastable (MS) level $|0\rangle$ to the ground-state (GS) level udvarhelyi_identification_2021. ES: excited state. b, Atomic structure of the G center in silicon, where carbon atoms are displayed in black and the interstitial silicon atom in purple. G center spin principal axes $\{\mathbf{x},\mathbf{y},\mathbf{z}\}$ are represented by the arrows. For this orientation, spin axes are along $[\bar{1}10]$, $[\bar{1}\bar{1}2]$ and $[111]$, respectively lee_optical_1982. c, PL variation of a single G center versus MW excitation frequency, measured with the pulse sequence indicated on top. Laser and MW pulse durations: $1$ and $15$ ns, respectively. To assess the ODMR contrast, the defect PL signal integrated over the first 50 ns of the readout pulse is normalized with the signal when the MW is off-resonant. Solid line is data fitting with two Lorentzian functions. Error bars represent photon shot noise at one standard deviation.
• Figure 3: Spin coherence properties and fine spin structure of a single G center.a, Rabi oscillations performed on the $|+\rangle \leftrightarrow |0\rangle$ transition, fitted with a sine function (solid line). b, Left, Ramsey fringes measured on the 2 spin transitions. Data are PL signal difference recorded between pulse sequences applying $-\pi/2$ and $+\pi/2$ for the second MW pulse, respectively. Solid lines represent data fitting with a sum of 4 (top) and 5 (bottom) cosine functions with an exponential decay envelope, providing $T_{2_{\nu_+}}^* = 0.8 \pm 0.2$ and $T_{2_{\nu_-}}^* = 1.1 \pm 0.3$. Right, corresponding Fourier-transform power spectra of the data (markers) and of the fit results (solid lines). The frequency detuning values between the spin transitions and the MW magnetic field are reported in the following plot (color arrows). c, High-resolution ODMR spectra recorded with the same sequence as in Figure \ref{['fig:odmr']}c but with a MW $\pi$-pulse duration about 300 ns. Solid curves are fits with Lorentzian functions. The MW frequency $\nu_{_{\mathrm{MW}}}$ used for the Ramsey signals in b is indicated by the dash-dot line. Color arrows show the frequencies extracted from data fitting.
• Figure 4: A reorienting spin.a-b, Frequency selective Rabi oscillations recorded by adjusting the MW excitation frequency at the maximum of the ESR lines, except for the $(4^-,5^-)$ lines that partially overlap and for which the MW frequency was set at the center frequency. MW power used in b is +6dBm compared to a. Solid lines are data fitting with a sine function, allowing to extract the following Rabi frequencies: $\Omega_{\mathrm{det}}= 3.8 \pm 0.1$ MHz for the MW addressing the $(4^-,5^-)$ transitions, and $\Omega' = 1.6 \pm 0.1$ MHz for the other spin transitions. The former Rabi frequency can be corrected from the frequency detuning $\delta = 1.9 \pm 0.1$ MHz, according to $\Omega = \sqrt{\Omega_{\mathrm{det}}^2-\delta^2} = 3.4 \pm 0.1$ MHz cohen-tannoudji_quantum_2019. The ratio between the Rabi frequencies measured on $(4^-,5^-)$ and $(2^-,3^-)$ is then $2.2 \pm 0.2$. c, Representation of MW magnetic field lines generated by the MW microstrip. At the location of the defect spin, the MW magnetic field $\mathbf{B}_{\scaleto{\mathrm{MW}}{4pt}}$ is parallel to the $[001]$ crystal direction. d, Microscopic structure of the G center showing the 6 possible sites of the Si$_{\mathrm{i}}$ atom (purple) and the corresponding x and y spin axes (red and green arrows, resp.). e, Scheme representing, for each Si$_{\mathrm{i}}$ position, the spin principal axes $\textbf{x}$ and $\textbf{y}$ compared to the MW magnetic field projection $\mathbf{B}^{\perp}_{\scaleto{\mathrm{MW}}{4pt}}$ in the $(111)$-plan (pink arrow), and the azimuthal angle $\varphi$ values. f, Non-frequency selective Rabi oscillations performed on the two ESR branches recorded with short MW $\pi$ pulses. On the right axis, simulated evolution of the population $P_0$ in $|0\rangle$ when the Si$_{\mathrm{i}}$ is either in position 0 or 3 (red dashes) or in one of the 4 positions $\{\mathbf{1},\mathbf{2},\mathbf{4},\mathbf{5}\}$ (black dots). Solid lines represent the average population in $|0\rangle$ while assuming an average occupancy per site of $1/6$ and a MW input power constant over the full ODMR range for each ESR branch in Figure \ref{['fig:rabi']}c. Simulation x axes have been adjusted to match data and compensate from different MW power attenuation at 0.7 and 1.7 GHz (see text).