Electrically driven optical interferometry with spins in silicon carbide

Abstract

Interfacing solid-state defect electron spins to other quantum systems is an ongoing challenge. The ground-state spin's weak coupling to its environment not only bestows excellent coherence properties but also limits desired drive fields. The excited-state orbitals of these electrons, however, can exhibit stronger coupling to phononic and electric fields. Here, we demonstrate electrically driven coherent quantum interference in the optical transition of single, basally oriented divacancies in commercially available 4H silicon carbide. By applying microwave frequency electric fields, we coherently drive the divacancy's excited-state orbitals and induce Landau-Zener-Stückelberg interference fringes in the resonant optical absorption spectrum. In addition, we find remarkably coherent optical and spin subsystems enabled by the basal divacancy's symmetry. These properties establish divacancies as strong candidates for quantum communication and hybrid system applications, where simultaneous control over optical and spin degrees of freedom is paramount.

Fig. 1. Single kh VVs in commercially available 4H-SiC.

(A) Lattice configuration of kh VVs in 4H-SiC. The defect axis is indicated by the green dashed line. Inset (left): Local atomic configuration around the kh VV showing C_1h symmetry. Inset (right): Emission spectrum of a single kh VV. arb. units, arbitrary units. (B) Energy diagram of the kh VV. The spin sublevels mix due to the effect of transverse zero-field splitting E_GS/ES, causing |±1〉 to become |±〉 near-zero external magnetic field. Spin-selective optical transitions (blue, yellow, and red arrows) enable spin-state readout. (C) Optical image of the 4H-SiC sample with a lithographically patterned capacitor and wire. Inset: Scanning confocal image of the marked region between the coplanar capacitor plates using 905-nm excitation. Highlighted emitters are single kh VVs. kcps, kilocounts per second.

Fig. 2. Optical properties of single kh VVs.

(A) PLE spectrum of a single kh VV prepared into |0〉 (blue), |–〉 (yellow), and |+〉 (red) with dc electric field (1 MV/m) applied and spectral diffusion compensated. Optical detuning measured with respect to 277.9337 THz (1078.647 nm). Inset: $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ transition exhibiting a narrow, Lorentzian lineshape with spectral diffusion compensated. (B) Optical coherence of kh VVs. Optical Rabi oscillations between $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ (blue circles) and $\mid +\rangle \leftrightarrow \mid A_{+}^{\prime }\rangle$ (red circles) at 7.6-μW resonant excitation. Both transitions exhibit near–lifetime-limited optical coherence (T₂ ≈ 2 T₁). $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ exhibits no detectable spin relaxation under illumination in this time scale, whereas excitation of $\mid +\rangle \leftrightarrow \mid A_{+}^{\prime }\rangle$ rapidly depopulates |+〉. Bottom: The pulse envelope created by the acousto-optic modulator used to gate the resonant, narrow-line laser.

Fig. 3. LZS interferometry of kh VV absorption spectrum.

(A) Monochromatic LZS interferometry of kh VV absorption spectrum. Top: Pulse sequence used to observe LZS interferometry. The interference pattern of $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ is measured as a function of $\mathcal{A}$, the induced Stark shift amplitude. Bottom: Interference fringes of $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ absorption arise in PLE spectroscopy as electric field magnitude |F| is increased (|F_∥,max| ≈ 2 MV/m), proportionally increasing $\mathcal{A}$. Total acquisition time was 19.5 hours. (B) Bichromatic LZS interferometry of kh VV absorption spectrum. Top: Pulse sequence used to observe bichromatic LZS interferometry. The interference pattern of $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ is measured as a function of the relative phase ϕ of the two drives. Bottom: PLE of a single kh VV under two electric field drives (ω₁ = 2π × 1 GHz, ω₂ = 2π × 2 GHz, ${\mathcal{A}}_1/{\mathrm{\omega }}_1={\mathcal{A}}_2/{\mathrm{\omega }}_2\approx 2.4048$) as a function of ϕ. Multiphoton resonances arise at 1 × n GHz and 2 × n GHz optical detunings, resulting in fringes from constructive and destructive interference of the two drives. Total acquisition time was 9.1 hours. kcps, kilocounts per second.

Fig. 4. Near-ZEFOZ spin control and dynamics of single kh VVs.

(A) ZEFOZ transitions near zero effective magnetic field. Energy dispersion with respect to B_z shows the vanishing first derivative of the spin transition energies, ν_{|0〉 ↔ |±〉} and ν_{|+〉 ↔ |–〉}, at B_z,eff = 0. (B) Top: Pulse sequence used to observe Rabi oscillations between |0〉 and |+〉. Bottom: Rabi oscillations of the ground-state spin between |0〉 and |+〉. PL measured from $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ excitation. (C) Top: Pulse sequence used to observe Rabi oscillations between |+〉 and |–〉. Bottom: Rabi oscillations of ground-state spin between |+〉 and |–〉. PL measured from $\mid -\rangle \leftrightarrow \mid A_{-}^{\prime }\rangle$ excitation. The nearby $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ transition increases background and reduces the contrast of Rabi oscillations. (D) Ramsey interferometry of a spin superposition prepared in $\mid {\mathrm{\psi }}_0\rangle =\frac{1}{\sqrt{2}}(\mid 0\rangle +\mid +\rangle )$. Dephasing mechanisms evolve the initial state ρ(0) = ∣ψ₀〉〈ψ₀∣ into ρ(t). A MW detuning of +100 kHz is added to increase visibility of the decay envelope. Readout is performed using $\mid 0\rangle \leftrightarrow \mid A_0^{\prime }\rangle$ PL. (E) Hahn-echo coherence of $\mid {\mathrm{\psi }}_0\rangle =\frac{1}{\sqrt{2}}(\mid 0\rangle +\mid +\rangle )$. A Gaussian decay envelope suggests the dominant source of spin decoherence is from the fluctuations of the ²⁹Si and ¹³C nuclear spin bath.