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Physical Review A

Spontaneous Raman scattering from metastable states of Ba +

Timothy Burke, Xiaoyang Shi, Jasmine Sinanan-Singh, Isaac L. Chuang, John Chiaverini

Published Aug 14, 2025• 1 citation
Publisher

Abstract

Quantum logic gates performed via two-photon stimulated Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these processes has predicted no lower bound on the scattering-induced error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near- and far-detuned lasers for initial states in the metastable ${D}_{5/2}$ level of $^{137}\mathrm{Ba}^{+}$. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate approximately equal to ${10}^{\ensuremath{-}4}$ are possible with laser excitation detuned by tens of terahertz or more.

DOI
10.1103/59jw-vycq

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Quantum logic gates performed via two-photon stimulated Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these processes has predicted no lower bound on the scattering-induced error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near- and far-detuned lasers for initial states in the metastable D5/2{D}_{5/2}D5/2​ level of 137Ba+^{137}\mathrm{Ba}^{+}137Ba+. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate approximately equal to 10\ensuremath−4{10}^{\ensuremath{-}4}10\ensuremath−4 are possible with laser excitation detuned by tens of terahertz or more.
Spontaneous Raman scattering from metastable states of Ba+^++
Quantum logic gates performed via two-photon stimulated-Raman transitions in ions and atoms are fundamentally limited by spontaneous scattering errors. Recent theoretical treatment of these scattering processes has predicted no lower bound on the error rate of such gates when implemented with far-detuned lasers, while also providing an extension to metastable qubits. To validate this theoretical model, we provide experimental measurements of Raman scattering rates due to near-, and far-detuned lasers for initial states in the metastable D5/2_{5/2}5/2​ level of 137^{137}137Ba+^++. The measured spontaneous Raman scattering rate is consistent with the theoretical prediction and suggests that metastable-level two-qubit gates with an error rate ≈10−4\approx10^{-4}≈10−4 are possible with laser excitation detuned by tens of terahertz or more.
^{133}Ba^{+} is illuminated by a laser that is far detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental atomic physics limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering.
We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counterrotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground-state qubits in commonly used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in the metastable D5/2{D}_{5/2}D5/2​ manifold, showing that gate errors below ${10}^{\ensuremath{-}4}$ are achievable for all commonly used trapped ions.
Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the preexisting toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable D5/2{D}_{5/2}D5/2​ qubit manifold of a single trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion illuminated by 976 nm light that is $\ensuremath{-}44$ THz detuned from the dipole-allowed transition to the P3/2{P}_{3/2}P3/2​ manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities less than ${10}^{\ensuremath{-}4}$ are possible.
Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of ∼94%\sim 94\%∼94% of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44\,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73\% and a SPAM-corrected Bell state fidelity of 98.61\%. When subtracting erasure errors, this fidelity becomes 99.16\%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.