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arXiv:1406.5740 · Physical Review B

Coherent manipulation of dipolar coupled spins in an anisotropic environment

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

Published Nov 4, 2014• 10 citations
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Abstract

We study coherent dynamics in a system of dipolar coupled spin qubits diluted in a solid and subjected to a driving microwave field. In the case of rare earth ions, an anisotropic crystal background results in anisotropic $g$ tensor and thus modifies the dipolar coupling. We develop a microscopic theory of spin relaxation in a transient regime for the frequently encountered case of axially symmetric crystal field. The calculated decoherence rate is nonlinear in the Rabi frequency. We show that the direction of a static magnetic field that corresponds to the highest spin $g$ factor is preferable in order to obtain a higher number of coherent qubit operations. The results of calculations are in excellent agreement with our experimental data on Rabi oscillations recorded for a series of $\mathrm{CaW}{\mathrm{O}}_{4}$ crystals with different concentrations of $\mathrm{N}{\mathrm{d}}^{3+}$ ions.

DOI
10.1103/physrevb.90.174402

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We study coherent dynamics in a system of dipolar coupled spin qubits diluted in a solid and subjected to a driving microwave field. In the case of rare earth ions, an anisotropic crystal background results in anisotropic ggg tensor and thus modifies the dipolar coupling. We develop a microscopic theory of spin relaxation in a transient regime for the frequently encountered case of axially symmetric crystal field. The calculated decoherence rate is nonlinear in the Rabi frequency. We show that the direction of a static magnetic field that corresponds to the highest spin ggg factor is preferable in order to obtain a higher number of coherent qubit operations. The results of calculations are in excellent agreement with our experimental data on Rabi oscillations recorded for a series of CaWO4\mathrm{CaW}{\mathrm{O}}_{4}CaWO4​ crystals with different concentrations of Nd3+\mathrm{N}{\mathrm{d}}^{3+}Nd3+ ions.
Contrary to the well-known spin qubits, rare-earth-metal qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground state which nutates (for several $\ensuremath{\mu}\mathrm{s}$) and the Rabi frequency ${\ensuremath{\Omega}}_{R}$ is anisotropic. Here, we present a study of the variations of ${\ensuremath{\Omega}}_{R}({\stackrel{\ensuremath{\rightarrow}}{H}}_{0})$ with the magnitude and direction of the static magnetic field ${\stackrel{\ensuremath{\rightarrow}}{H}}_{0}$ for the odd 167Er^{167}\mathrm{Er}167Er isotope in a single crystal CaWO4:Er3+{\mathrm{CaWO}}_{4}\mathrm{\text{:}}{\mathrm{Er}}^{3+}CaWO4​:Er3+. The hyperfine interactions split the ${\ensuremath{\Omega}}_{R}({\stackrel{\ensuremath{\rightarrow}}{H}}_{0})$ curve into eight different curves which are fitted numerically and described analytically. These ``spin-orbit qubits'' should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields.
We investigate the erbium flip-flop dynamics as a limiting factor of the electron-spin lifetime and more generally as an indirect source of decoherence in rare-earth-doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the ggg factor. In Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​, we observe in a 10-ppm doped sample a 3 orders-of-magnitude variation of the erbium flip-flop rate, as expected from the dipolar coupling term between identical spins with an anisotropic ggg tensor. We can estimate the correct order of magnitude for a 50-ppm concentration, but we can only reproduce qualitatively the orientational variation of the flip-flop rate.
Rare earth ion doped crystals are state-of-the-art platforms for processing quantum information, particularly thanks to their excellent optical and spin coherence properties at cryogenic temperatures. Experimental observations have shown that the application of a static magnetic bias field significantly improves the coherence times in the rare earth ions ensemble, but only a few studies have focused on its dependency as a function of both magnetic field direction and amplitude. This is especially true for magnetic field amplitudes under the mT, and for low magnetic dipole moment ions. In this paper, we investigate the relationship between the magnetic field parameters and the decoherence caused by magnetic dipole-dipole coupling with the nearest-neighbor nuclear spins in the crystal. The primary non-Kramers rare earth ions investigated here are europium and praseodymium, but we also extend our study to the ytterbium Kramers ion due to its low magnetic dipole in the mT range. We perform theoretical investigations and simulations of the energy structure and coherence time evolution and identify good correspondences between experimental and simulated spin echo data. This work allows us to pinpoint the most relevant decoherence mechanisms in the considered magnetic field regime, and to predict favorable magnetic configurations.
Electrical control of single spin qubits is a major frontier for nanoscale, high-speed, and scalable quantum devices. Yet, extending it to highly shielded rare-earth 4f electrons remains an experimental challenge across solid-state platforms. Here we demonstrate all-electrical coherent control of a single Er electron spin, which is exchange-coupled to a nearby Ti atom. Scanning tunneling microscopy-based electron spin resonance with three-dimensional magnetic-field control enables comprehensive mapping of the resonance and Rabi frequencies, revealing pronounced anisotropies in both the Er g-tensor and the Er-Ti exchange interaction. The electrical modulation of the anisotropic Er-Ti coupling results in an efficient drive of the Er spin, allowing us to achieve near-gigahertz Rabi frequencies - a ten-fold improvement over the present record for rare-earth spin qubits. By establishing anisotropic exchange as a general resource for electrically accessing shielded rare-earth spins, our results open a new route to ultrafast and local control of rare-earth spins in solid-state quantum devices.
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.
Rare-earth doped crystals have long coherence times and the potential to provide quantum interfaces between microwave and optical photons. Such applications benefit from a high cooperativity between the spin ensemble and a microwave cavity---this motivates an increase in the rare-earth ion concentration which in turn impacts the spin coherence lifetime. We measure spin dynamics of two rare-earth spin species, 145Nd^{145}\mathrm{Nd}145Nd and Yb, doped into Y2SiO5{\mathrm{Y}}_{\text{2}}{\mathrm{SiO}}_{\text{5}}Y2​SiO5​, coupled to a planar microwave resonator in the high-cooperativity regime, in the temperature range 1.2K1.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}1.2K to 14mK14\phantom{\rule{0.16em}{0ex}}\mathrm{mK}14mK. We identify relevant decoherence mechanisms, including instantaneous diffusion arising from resonant spins and temperature-dependent spectral diffusion from impurity electron and nuclear spins in the environment. We explore two methods to mitigate the effects of spectral diffusion in the Yb system in the low-temperature limit, first, using magnetic fields of up to 1 T to suppress impurity spin dynamics and, second, using transitions with low effective ggg factors to reduce sensitivity to such dynamics. Finally, we demonstrate how the ``clock transition'' present in the 171Yb^{171}\mathrm{Yb}171Yb system at zero field can be used to increase coherence times up to T2=6(1)ms{T}_{2}=6(1)\phantom{\rule{0.16em}{0ex}}\mathrm{ms}T2​=6(1)ms.