Coherence Properties of Shallow Donor Qubits in $\mathrm{Zn}\mathrm{O}$

Defects in crystals are leading candidates for photon-based quantum technologies, but progress in developing practical devices critically depends on improving defect optical and spin properties. Motivated by this need, we study a new defect qubit candidate, the shallow donor in $\mathrm{Zn}\mathrm{O}$. We demonstrate all-optical control of the electron spin state of the donor qubits and measure the spin coherence properties. We find a longitudinal relaxation time $T_1$ exceeding 100 ms, an inhomogeneous dephasing time $T_2^{\ast }$ of $17\pm 2$ ns, and a Hahn-spin-echo time $T_2$ of $50\pm 13\mu \mathrm{s}$. The magnitude of $T_2^{\ast }$ is consistent with the inhomogeneity of the nuclear hyperfine field in natural $\mathrm{Zn}\mathrm{O}$. Possible mechanisms limiting $T_2$ include instantaneous diffusion and nuclear spin diffusion (spectral diffusion). These dephasing mechanisms suggest that with isotope and chemical purification qubit coherence times can be extended. This work should motivate further research on high-purity material growth, quantum-device fabrication, and high-fidelity control of the donor-$\mathrm{Zn}\mathrm{O}$ system for quantum technologies.

Figure 1

(a) Experimental geometry. $\hat{c}$ is the optical propagation axis, $\overrightarrow{B}$ is the magnetic field, and V and H represent vertical polarization ($\hat{\epsilon }\perp \overrightarrow{B}$) and horizontal polarization ($\hat{\epsilon }\parallel \overrightarrow{B}$), respectively. (b) Energy diagram of the donor system in a magnetic field in the Voigt geometry. $|\Uparrow ⟩(|\uparrow ⟩)$ denotes the hole (electron) spin. The shaded area shows the $\mathrm{\Lambda }$ system used for the spin initialization and read-out. (c) Spectra at 0 and 4 T with vertically and horizontally polarized collection. The laser excitation is at 3.446 eV with vertical polarization. The temperature is 5.5 K. The $\mathrm{Ga}$- and $\mathrm{Al}$-donor peaks both split into four different peaks with applied magnetic field. (d) Electron and hole Zeeman splitting of the $\mathrm{Ga}$ donor as function of the magnetic field. The red and blue lines are linear fits of the Zeeman splitting. For these data, both the excitation and the collection spot sizes are approximately $1\mu \mathrm{m}$.

Figure 2

(a) Optical pumping curve at 5 T and 1.5 K. The inset shows the laser sequence. The photoluminescence is detected by an avalanche photodiode with 50-ns timing resolution. (b) The population recovery curve at 5 T and 1.5 K. The inset shows the corresponding laser sequence. The exponential fit of the recovery curve gives $T_1$ = $11.4\pm 0.5$ ms. (c) The longitudinal spin relaxation time $T_1$ as a function of the electron Zeeman energy for donors in $\mathrm{Ga}\mathrm{As}$, $\mathrm{In}\mathrm{P}$, $\mathrm{Cd}\mathrm{Te}$, and $\mathrm{Zn}\mathrm{O}$. The data for $\mathrm{Ga}\mathrm{As}$, $\mathrm{In}\mathrm{P}$, and $\mathrm{Cd}\mathrm{Te}$ are reproduced from Ref. [47]. For the $\mathrm{Zn}\mathrm{O}$ data, the excitation and collection spot sizes are both approximately $1\mu \mathrm{m}$.

Figure 3

(a) $P_{\uparrow }$ (population of $|\uparrow ⟩$) as a function of the single-pulse energy with spin initialized to $|\downarrow ⟩$ and then excited by the ultrafast pulse. Error bars show the $1\sigma$ uncertainty from the Poisson noise in photoluminescence collection. Data points represented by red squares at low powers are taken at the same power as the data points in (c). The red curve is a simultaneous least-squares fit for the data in (a),(c). The inset shows how the state changes in the Bloch sphere with use of the simulated results. (b) A typical Ramsey interference pattern with 18-pJ pulse energy. The inset shows the laser sequence, where $\tau$ is the delay between the two pulses ($\tau =0.8$ ns in this case). The first cw pulse initializes the spin and the second cw pulse is used for read-out. (c) The Ramsey-fringe amplitude $V=(P_{\max }-P_{\min }$)/2 as a function of the single-pulse energy. Error bars show the $2\sigma$ uncertainty from the sinusoid fit of the Ramsey oscillation. The red line is the simulation result from the simultaneous fit. The dotted blue line shows the fit parameter $\gamma$ (excited-state dephasing rate) as a function of pulse energy. For these data, the excitation spot size is approximately $2\mu \mathrm{m}$ and the collection spot size is approximately $0.6\mu \mathrm{m}$. The temperature is 1.5 K and the magnetic field is 5 T. The ultrafast pulses are detuned by $\mathrm{\Delta }/2\pi =3.57$ THz from the $|\downarrow ⟩\iff |\Downarrow \uparrow \downarrow ⟩$ transition.

Figure 4

(a) The Ramsey-fringe amplitude as a function of delay time $\tau$. The red curve shows a fit to $\exp [-(\tau /T_2^{\ast }{)}^2]$, giving $T_{2,\mathrm{expt}}^{\ast }=17\pm 2$ ns. (b) Spin-echo measurement of the dephasing time $T_2$. The delay ${\tau }_1\simeq {\tau }_2$. Oscillations are observed by our changing $\mathrm{\Delta }{\tau }_2$. The oscillation amplitude is measured as a function of ${\tau }_1+{\tau }_2$. The red curve shows a fit to $\exp [-({\tau }_1+{\tau }_2)/T_2]$, giving $T_{2,\mathrm{expt}}=50\pm 13\mu \mathrm{s}$. For comparison, the dashed blue line shows a fit to $\exp -[({\tau }_1+{\tau }_2)/T_2{]}^3$, the expected form for spectral diffusion. For these data, the excitation and collection spot sizes are both approximately $0.6\mu \mathrm{m}$. The temperature is 5.5 K and the magnetic field is 5 T. The ultrafast pulses are detuned by $\mathrm{\Delta }/2\pi =0.9$ THz from the $|\downarrow ⟩\iff |\Downarrow \uparrow \downarrow ⟩$ transition.