arXiv:0911.4818 · Physical Review Letters

Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

Sylvain Bertaina, Jeong Hyun Shim, Serge Gambarelli, Malkin Boris Zalmanovich, B. Barbara

Published Nov 24, 2009• 37 citations

Abstract

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 $^{167}\mathrm{Er}$ isotope in a single crystal ${\mathrm{CaWO}}_{4}\mathrm{\text{:}}{\mathrm{Er}}^{3+}$. 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.

DOI: 10.1103/physrevlett.103.226402

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Publisher’s Note: Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields [Phys. Rev. Lett.103, 226402 (2009)]

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arXiv:0911.4818 · Physical Review Letters

Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

Sylvain Bertaina, Jeong Hyun Shim, Serge Gambarelli, Malkin Boris Zalmanovich, B. Barbara

Published Nov 24, 2009• 37 citations

arXiv HTML PDF

Abstract

\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

^{167}\mathrm{Er}

isotope in a single crystal

{\mathrm{CaWO}}_{4}\mathrm{\text{:}}{\mathrm{Er}}^{3+}

. 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.

DOI: 10.1103/physrevlett.103.226402

Related papers

Coherent manipulation of dipolar coupled spins in an anisotropic environment

E. I. Baibekov, Marat Revgerovich Gafurov, Д. Г. Зверев +3 more

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.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.

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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.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.

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Publisher’s Note: Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields [Phys. Rev. Lett.103, 226402 (2009)]

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Physical Review LettersSep 4, 20141 citation

Spectroscopic Theories and First-principles Calculations for Using Rare-Earth Ions Doped in Nanofabricated Materials to Build Quantum Computers: Showcases of RE3+ Doped Y2SiO5

Yau Yuen Yeung, Meng Ju

Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded $4 f$ shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for $\mathrm{Er}^{3+}$ to 6 hours for $\mathrm{Eu}^{3+}$ ) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like ${ }^{167} \mathbf{E r}$ and ${ }^{171} \mathbf{Y b}$ doped in yttrium orthosilicate ${Y}_{2} {SiO}_{5}$ (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.Without using any trapping lasers, rare-earth (RE) ions can be doped into some nanofabricated materials in form of nanocrystals in a solid state matrix, thus rendering a natural trap for potential application as a quantum computing device. In particular, passive nuclear spin states of RE ions can be utilized as (i) optical quantum memory (with huge density as yielded from nanocrystals), (ii) qubits by encoding in ground hyperfine states and operated as (iii) two-qubit gate when transferring them to active magnetized electronic states. A feasible implementation of qubits is realised by using those doped RE ions whose open-shell (for inner highly shielded $4 f$ shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for $\mathrm{Er}^{3+}$ to 6 hours for $\mathrm{Eu}^{3+}$) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like ${ }^{167} \mathbf{E r}$ and ${ }^{171} \mathbf{Y b}$ doped in yttrium orthosilicate ${Y}_{2} {SiO}_{5}$ (YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.

IEEE International Conference Nanomaterials: Applications & Properties (NAP)Sep 8, 20240 citations

\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

^{167}\mathrm{Er}

isotope in a single crystal

{\mathrm{CaWO}}_{4}\mathrm{\text{:}}{\mathrm{Er}}^{3+}

. The hyperfine interactions split the

{\ensuremath{\Omega}}_{R}({\stackrel{\ensuremath{\rightarrow}}{H}}_{0})

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.

4 f

shell electrons) energy levels and statevectors are well described by the crystal field (CF) interaction and hyperfine coupling in which the Hamiltonian is composed of various freeion interactions, the CF potential, electronic and nuclear Zeeman effects as well as the hyperfine interaction. For those qubit encoded in the two ground hyperfine states of RE ions, they can have fairly long lifetimes of days and coherence times (from 1.3s for

\mathrm{Er}^{3+}

to 6 hours for

\mathrm{Eu}^{3+}

) due to the unique spectroscopic properties of RE ions. Because of the recent progress in optical single-ion detection for addressing individual qubits with a specific frequency channel, RE ions could be packed in a solid state 3D matrix at nanometer spacing, hence rendering very high qubit densities for quantum memories. Meanwhile, this configure also leads to strong dipole-dipole interactions (or high connectivity) between qubits which are not nearest neighbors. In this study, Kramers ions like

{ }^{167} \mathbf{E r}

and

{ }^{171} \mathbf{Y b}

doped in yttrium orthosilicate

{Y}_{2} {SiO}_{5}

(YSO) nanocrystals will be investigated as a promising system for quantum computing because of their weak spin bath and possibility for being directly milled in single nanocrystals as nano-resonators. By using the famous Wien2k package to carry out the first-principles calculations, we can obtain the CF parameters and hyperfine constants as well as various electronic properties like energy gap and band structure for those Kramers RE ions doped in YSO. We shall present some essential findings from first-principles calculations to obtain various properties of the ground and excited CF and hyperfine states for those RE ions with an aim to optimize RE ions doping in YSO nanocrystals for quantum memories and qubits, contributing to scalable quantum computing architectures.