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arXiv:1610.04737 · Physical review. B./Physical review. B

Coherent spin dynamics in a gadolinium-doped CaWO4 crystal

E. I. Baibekov, Marat Revgerovich Gafurov, Д. Г. Зверев, I. N. Kurkin, Alexander A. Rodionov, Malkin Boris Zalmanovich, B. Barbara

Published Feb 24, 2017• 29 citations
arXivHTMLPDF

Abstract

We report the first observation of Rabi oscillations in the spin-7/2 ensemble of trivalent gadolinium ions hosted in $\mathrm{CaW}{\mathrm{O}}_{4}$ single crystal. A number of transitions within the lowest electronic multiplet ${}^{8}{S}_{7/\phantom{72}\phantom{\rule{0.0pt}{0ex}}2}$ of $\mathrm{G}{\mathrm{d}}^{3+}$ ion are studied using a combination of continuous-wave and pulsed electron paramagnetic resonance spectroscopy. The corresponding Rabi damping curves and the spin coherence times are detected at varying strengths of the microwave field. These data are well reproduced by a theoretical model which accounts for the intrinsic inhomogeneity of the microwave field within the microwave resonator and the magnetic dipole interactions in the diluted spin ensemble. The results indicate that the studied 8-level ground manifold of $\mathrm{G}{\mathrm{d}}^{3+}$ ion can represent an effective three-qubit quantum system.

DOI
10.1103/physrevb.95.064427

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We report the first observation of Rabi oscillations in the spin-7/2 ensemble of trivalent gadolinium ions hosted in CaWO4\mathrm{CaW}{\mathrm{O}}_{4}CaWO4​ single crystal. A number of transitions within the lowest electronic multiplet 8S7/722{}^{8}{S}_{7/\phantom{72}\phantom{\rule{0.0pt}{0ex}}2}8S7/722​ of Gd3+\mathrm{G}{\mathrm{d}}^{3+}Gd3+ ion are studied using a combination of continuous-wave and pulsed electron paramagnetic resonance spectroscopy. The corresponding Rabi damping curves and the spin coherence times are detected at varying strengths of the microwave field. These data are well reproduced by a theoretical model which accounts for the intrinsic inhomogeneity of the microwave field within the microwave resonator and the magnetic dipole interactions in the diluted spin ensemble. The results indicate that the studied 8-level ground manifold of Gd3+\mathrm{G}{\mathrm{d}}^{3+}Gd3+ ion can represent an effective three-qubit quantum system.
Optically addressable solid-state spins have been extensively studied for quantum technologies, offering unique advantages for quantum computing, communication, and sensing. Advancing these applications is generally limited by finding materials that simultaneously provide lifetime-limited optical and long spin coherences. Here, we introduce 171Yb3+ ions doped into a CaWO4 crystal. We perform high-resolution spectroscopy of the excited state, and demonstrate all-optical coherent control of the electron-nuclear spin ensemble. We find narrow inhomogeneous broadening of the optical transitions of 185 MHz and radiative-lifetime-limited coherence time up to 0.75 ms. Next to this, we measure a spin-transition ensemble line width of 5 kHz and electron-nuclear spin coherence time reaching 0.15 seconds at zero magnetic field between 50 mK and 1 K temperatures. These results demonstrate the potential of 171Yb3+:CaWO4 as a low-noise platform for building quantum technologies with ensemble-based memories, microwave-to-optical transducers, and optically addressable single-ion spin qubits. The authors identify 171Yb3+:CaWO4 as a promising material for quantum technological applications, revealing lifetime-limited optical coherence of 0.75 ms and spin coherence of 0.15 s, highlighting its potential for quantum memories and transducers.
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Abstract Recent electron spin resonance experiments on CaWO 4_44​ 4 :Gd 3+^{3+}3+ 3 + and other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance, together with another microwave field (image drive) with a frequency smaller than the Larmor frequency. These observations are confirmed by the new experimental results reported in this paper. We use numerical and analytical techniques to study the interplay between the microwave drives and three different mechanisms of relaxation. The first model describes a magnetic moment subject to microwave fields, interacting with a bath of two-level systems which acts as a source of decoherence and dissipation. The second model describes identical, interacting magnetic moments, subject to the same microwave fields. The decay of the Rabi oscillations is now due to the interactions. Third, we study Rabi oscillation decay due to the inhomogeneity of the microwave radiation. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that are not readily accessible experimentally. Graphic abstract
Coherent spin dynamics of impurity Yb3+{\text{Yb}}^{3+}Yb3+ ions in the CaWO4{\text{CaWO}}_{4}CaWO4​ single crystal has been studied using XXX- and WWW-band EPR. Rabi oscillations of the sample magnetization with damping times comparable to their period, driven by pulses of the microwave field with duration up to $5\text{ }\ensuremath{\mu}\text{s}$, were observed. The largest value of the single-qubit figure of merit $(\ensuremath{\sim}6400)$ is obtained for the high-field component in the 171Yb^{171}\text{Y}\text{b}171Yb XXX-band EPR spectrum. The spin-lattice relaxation time of the Yb3+{\text{Yb}}^{3+}Yb3+ ions shortens with the increasing resonance frequency while the phase memory time, in contrast, grows noticeably. Variations of the phase memory times are interpreted in terms of spectral and instantaneous diffusions. The increase of the coherence time at the WWW band can be used for the application of rare-earth ions as qubits in quantum computing as it has been proposed recently.
Optically addressable shallow donors in ZnO combine efficient spin-selective optical transitions with the potential for long spin coherence in an isotopically purifiable host lattice, making them an attractive platform for spin-photon quantum technologies. A key missing capability, however, has been coherent control beyond the small-angle rotations accessible with ultrafast optical pulses. Here we demonstrate coherent microwave control of implanted 115In^{115}\mathrm{In}115In donors in ZnO. Resonant optical pumping initializes and reads out the donor electron spin. Pulsed optically-detected magnetic resonance resolves the ten hyperfine transitions associated with the coupled 115In^{115}\mathrm{In}115In nuclear spin (I = 9/2) and reveals optical-pumping-induced nuclear spin polarization. We observe coherent Rabi oscillations with a maximum Rabi frequency of Ω/2π=36.2±0.7Ω/2π= 36.2 \pm 0.7Ω/2π=36.2±0.7\;MHz, corresponding to a πππ-pulse time of 13.8$\pm$0.3\;ns, and characterize the spin coherence using Ramsey, Hahn echo and dynamical-decoupling measurements. Unexpectedly, the measured coherence is substantially shorter than reported in previous optical studies of donor spins in ZnO at high magnetic field. Control experiments rule out several simple explanations including microwave heating and instantaneous diffusion from the driven donor ensemble, leaving an open question regarding the origin of decoherence at low magnetic field in microwave-controlled ZnO donors. These results establish microwave control of ZnO donor qubits with resonant optical access to specific donor species. More broadly, they demonstrate that coherent microwave control can be achieved in optically addressable spin systems with nanosecond-scale inhomogeneous dephasing, enabling field-, temperature-, and materials-dependent studies of coherence-limiting mechanisms and the development of optically interfaced electron-nuclear spin registers.
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