Strontium-88 Trapped-Ion Qubit

Figure

Description

The strontium-88 trapped-ion qubit encodes quantum information in the optical transition between the $5S_{1/2}$ ground state and the $4D_{5/2}$ metastable excited state of ${}^{88}{\text{Sr}}^{+}$, driven by a narrow electric quadrupole transition at 674 nm. With zero nuclear spin ($I=0$), ${}^{88}{\text{Sr}}^{+}$ has no hyperfine structure, yielding a clean two-level optical qubit with a natural lifetime of approximately 390 ms for the $4D_{5/2}$ state (corresponding to a natural linewidth of ~0.4 Hz).

The absence of hyperfine structure is both the defining advantage and limitation of ${}^{88}{\text{Sr}}^{+}$. On the advantage side, the simple level structure eliminates complications from multiple ground-state sublevels, simplifying state preparation and readout. Doppler cooling uses the strong $5S_{1/2}\to 5P_{1/2}$ transition at 422 nm with repumping from $4D_{3/2}$ at 1092 nm and $4D_{5/2}$ at 1033 nm. Photoionization loading is efficient via a two-photon process: 461 nm excites neutral Sr atoms from $5s^2{}^1{S}_0$ to $5s5p{}^1{P}_1$, followed by 405 nm to reach the continuum. All primary wavelengths are in the visible or near-IR, avoiding the UV lasers required by ${\text{Ca}}^{+}$ (397 nm) and ${\text{Yb}}^{+}$ (369.5 nm).

On the limitation side, without hyperfine clock states the qubit coherence is limited by the metastable state lifetime ($T_1\approx 390$ ms) and magnetic field sensitivity (the Zeeman sublevels have first-order magnetic field dependence). This makes ${}^{88}{\text{Sr}}^{+}$ less suitable as a memory qubit compared to hyperfine species but well-suited as an interface qubit for photonic networking and integrated-photonics experiments, where its visible and near-UV transitions are accessible with mature laser and detector technology. Long-distance fiber networking would still generally require wavelength conversion.

Hamiltonian

The optical qubit Hamiltonian in the rotating frame is:

$H=\frac{\hslash \delta }{2}{\sigma }_z+\frac{\hslash \Omega }{2}{\sigma }_x$

where $\delta$ is the detuning of the 674 nm laser from the $5S_{1/2}\to 4D_{5/2}$ quadrupole transition and $\Omega$ is the Rabi frequency. The Zeeman splitting in an external magnetic field $B$ is:

$\Delta E=(g_J^{\prime }{m}_J^{\prime }-g_J{m}_J){\mu }_{B}B$

where $g_J(S_{1/2})=2.0023$ and $g_J(D_{5/2})=1.2$. The qubit is typically encoded in $|S_{1/2},m_J=-1/2⟩\leftrightarrow |D_{5/2},m_J=-1/2⟩$ to minimize sensitivity to field fluctuations via dynamical decoupling.

Motivation

${}^{88}{\text{Sr}}^{+}$ occupies a unique niche among trapped-ion qubits. Its visible-wavelength transitions make it the leading candidate for integrated photonic ion traps, where on-chip waveguides can deliver all necessary laser frequencies without UV damage to optical components. The 408 nm photon emitted during the $5P_{1/2}\to 4D_{5/2}$ decay provides a natural interface for ion-photon entanglement and quantum networking. The efficient two-photon photoionization loading and absence of isotope selection requirements (88 is the dominant isotope at 82.6% natural abundance) simplify trap loading compared to rare isotopes like ${}^{43}\text{Ca}$ (0.14%) or ${}^{137}\text{Ba}$ (11%).

Experimental Status

Early qubit demonstrations (~2000–2009):

• Multiple groups (Los Alamos, Imperial College, Innsbruck) demonstrated coherent manipulation of the $5S_{1/2}\to 4D_{5/2}$ optical qubit using stabilized 674 nm diode lasers.
• Resolved-sideband cooling to the motional ground state with 98.6% occupation demonstrated.

Integrated photonics (2024) — Mehta et al.:

• Chip-scale photonic integrated circuit delivering a 674 nm Brillouin laser stabilized to the ${}^{88}{\text{Sr}}^{+}$ quadrupole transition.
• 6 kHz laser linewidth, 60 μs Ramsey coherence time, 99% SPAM fidelity.
• Rabi oscillations demonstrated without bulk free-space optics.

Trapped-ion review — Bruzewicz et al. (2019):

• Comprehensive review covering ${}^{88}{\text{Sr}}^{+}$ among other ion species, documenting the state of trapped-ion quantum computing including gate implementations, coherence properties, and scaling challenges.

Key Metrics

Metric	Value	Notes	Fidelity reference
$T_1$ (metastable)	~390 ms	$4D_{5/2}$ radiative lifetime	Bruzewicz et al. 2019
$T_2$ (Ramsey)	~60 μs	Chip-integrated laser, limited by laser coherence	Mehta et al. 2024
Qubit transition	674 nm	$5S_{1/2}\to 4D_{5/2}$ electric quadrupole	—
Cooling transition	422 nm	$5S_{1/2}\to 5P_{1/2}$; visible, no UV	—
SPAM fidelity	99%	Chip-integrated system	Mehta et al. 2024
Natural abundance	82.6%	Dominant isotope; no enrichment needed	—
Nuclear spin	$I=0$	No hyperfine structure	—
Operating temperature	~4 K (trap)	Ions laser-cooled to ~mK	—

Scaling Considerations

• Integrated photonics: the visible-wavelength transitions of ${}^{88}{\text{Sr}}^{+}$ are uniquely compatible with silicon nitride and other photonic platforms, enabling on-chip laser delivery and photon collection.
• No clock states: without hyperfine structure, there are no magnetically insensitive clock transitions. Coherence is limited by magnetic field fluctuations and the metastable state lifetime, unlike hyperfine qubits (${}^{171}{\text{Yb}}^{+}$, ${}^{43}{\text{Ca}}^{+}$, ${}^{137}{\text{Ba}}^{+}$) which can achieve >1000 s coherence.
• Networking interface: the 408 nm photon from the $5P_{1/2}\to 4D_{5/2}$ decay provides an efficient ion-photon interface for quantum networking, making ${}^{88}{\text{Sr}}^{+}$ a natural choice for hybrid systems using hyperfine ions as data qubits and Sr as network qubits.
• Abundant isotope: 82.6% natural abundance eliminates the need for isotope-enriched sources or isotope-selective loading, simplifying trap loading.
• Photoionization loading: the two-photon scheme (461 nm + 405 nm) provides deterministic, fast, and low-background ion loading compatible with microfabricated traps.

References

Review

• C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, “Trapped-ion quantum computing: Progress and challenges,” Appl. Phys. Rev. 6, 021314 (2019) | arXiv:1904.04178

Integrated photonics

• K. K. Mehta et al., “Integrated optical control of a trapped-ion qubit,” arXiv:2402.16742 (2024)

Linked Papers

• bruzewicz-2019-trapped-ion-review
• mehta-2024-integrated-optical-sr

Related Entries

• trapped-ion-qubit — parent platform
• ytterbium-hyperfine-qubit — alternative species; hyperfine qubit with UV transitions
• barium-137-ion-qubit — alternative species; visible-wavelength hyperfine qubit
• calcium-43-ion-qubit — alternative species; microwave-driven hyperfine qubit