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arXiv:2508.02026

Zeeman Degenerate Sideband Cooling in $^{176}$Lu$^+$

Qin Qichen, Qi Rui Zhao, Michael Dao Kang Lee, Zhao Zhang, N. Jayjong, K. J. Arnold, M. D. Barrett

Published Aug 4, 2025• 0 citations
arXivHTMLPDF

Abstract

We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between $|F,m_F\rangle\rightarrow |F,m_F-1\rangle$ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as $\bar{n}$ where $\bar{n}$ is the average phonon number in the initial thermal state. We demonstrate proof-of-concept in $^{176}\mathrm{Lu}^+$ by coupling neighboring Zeeman levels on the motional sideband for the $F=7$ hyperfine level in $^3D_1$. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with $\sim10$ pulses. A theoretical description is given that applies to any $F$ level and demonstrates how effective this approach can be.

DOI
10.48550/arxiv.2508.02026

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Zeeman Degenerate Sideband Cooling in 176^{176}176Lu+^++
We explore degenerate Raman sideband cooling in which neighboring Zeeman states of a fixed hyperfine level are coupled via a two-photon Raman transition. The degenerate coupling between ∣F,mF⟩→∣F,mF−1⟩|F,m_F\rangle\rightarrow |F,m_F-1\rangle∣F,mF​⟩→∣F,mF​−1⟩ facilitates the removal of multiple motional quanta in a single cycle. This method greatly reduces the number of cooling cycles required to reach the ground state compared to traditional sideband cooling. We show that near ground state cooling can be achieved with a pulse number as low as nˉ\bar{n}nˉ where nˉ\bar{n}nˉ is the average phonon number in the initial thermal state. We demonstrate proof-of-concept in 176Lu+^{176}\mathrm{Lu}^+176Lu+ by coupling neighboring Zeeman levels on the motional sideband for the F=7F=7F=7 hyperfine level in 3D1^3D_13D1​. Starting from a thermal distribution with an average phonon number of 6, we demonstrate near ground-state cooling with ∼10\sim10∼10 pulses. A theoretical description is given that applies to any FFF level and demonstrates how effective this approach can be.
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for 138^{138}138Ba+^++ of sufficient fidelity for QLS without an extremely narrowband laser or the use of a species with hyperfine structure. We use the two S1/2_{1/2}1/2​ Zeeman sublevels of 138^{138}138Ba+^++ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, near-resonant Raman sideband cooling of 138^{138}138Ba+^++ requires only the Doppler cooling lasers and two additional AOMs. Observing the near-resonant Raman optical pumping fluorescence, we estimate a final average motional quantum number nˉ≈0.17\bar{n}\approx0.17nˉ≈0.17. We additionally employ a second, far-off-resonant laser driving Raman π\piπ-pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final nˉ=0.15(6)\bar{n} = 0.15(6)nˉ=0.15(6).
Motional ground state cooling and internal state preparation are important elements for quantum logic spectroscopy (QLS), a class of quantum information processing. Since QLS does not require the high gate fidelities usually associated with quantum computation and quantum simulation, it is possible to make simplifying choices in ion species and quantum protocols at the expense of some fidelity. Here, we report sideband cooling and motional state detection protocols for 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ of sufficient fidelity for QLS without an extremely narrow-band laser or the use of a species with hyperfine structure. We use the two S1/2{S}_{1/2}S1/2​ Zeeman sublevels of 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ to Raman sideband cool a single ion to the motional ground state. Because of the small Zeeman splitting, continuous near-resonant Raman sideband cooling of 138Ba+^{138}\mathrm{Ba}^{+}138Ba+ requires only the Doppler cooling lasers and two additional acousto-optic modulators. Observing the near-resonant Raman optical pumping fluorescence, we extract relevant experimental parameters and demonstrate a final average motional quantum number $\overline{n}\ensuremath{\ll}1$. We additionally employ a second, far-off-resonant laser driving Raman $\ensuremath{\pi}$ pulses between the two Zeeman sublevels to provide motional state detection for QLS and to confirm the sideband cooling efficiency, measuring a final n‾=0.15(6)\overline{n}=0.15(6)n=0.15(6).
We developed a resolved Raman sideband cooling scheme that can efficiently prepare a single optically trapped cesium (Cs) atom in its motional ground states. A two-photon Raman process between two outermost Zeeman sublevels in a single hyperfine state is applied to reduce the phonon number. Our scheme is less sensitive to the variation in the magnetic field than the commonly used scheme where the two outermost Zeeman sublevels belonging to the two separate ground hyperfine states are taken. Fast optical pumping with less spontaneous emission guarantees the efficiency of the cooling process. After cooling for 50 ms, 82% of the Cs atoms populate their three-dimensional ground states. Our scheme improves the long-term stability of Raman sideband cooling in the presence of magnetic field drift and is thus suitable for cooling other trapped atoms or ions with abundant magnetic sublevels.
A method of sideband Raman cooling to the vibrational ground state of the m=0m=0m=0 Zeeman sublevel in a far-detuned two-dimensional optical lattice is proposed. In our scheme, the Raman coupling between vibrational manifolds of the adjacent Zeeman sublevels is shifted to the red sideband due to the ac Stark effect induced by a weak pump field. Thus cooling and optical pumping to m=0m=0m=0 are achieved by purely optical means with coplanar cw laser beams. The optical lattice and cooling parameters are estimated in the framework of simple theoretical models. An application of the transverse sideband cooling method to frequency standards is discussed. Coherent population trapping for the sideband Raman transitions between the degenerate vibrational levels is predicted.
Summary form only given. Laser cooled atoms play a critical role in modern designs of frequency standards such as atomic fountains. Recently, an elegant and efficient method of two-dimensional cooling to the vibrational ground state of a far-off resonance optical lattice has been demonstrated. This method is a variant of Raman sideband cooling based on the Raman transitions between the vibrational manifolds of adjacent Zeeman substates. A static magnetic field is used to tune the Zeeman levels so that Raman resonance occurs on the red sideband and results in cooling. Two circularly polarized fields are used to recycle the atoms for repetitive Raman cooling. Unfortunately, a direct application of this scheme to frequency standards meets with several difficulties. Stimulated by these concepts and results, we propose a new variant of transverse sideband cooling, where these problems are avoided, while still maintaining most of the attractive features. The field configuration used for the optical lattice consists of three linearly polarized beams having equal amplitudes and propagating in the xy plane with angles of 2/spl pi//3 between each other. The polarization vectors of these beams are tilted through a small angle with respect to the z-axis. All the beams have the same frequency far-detuned to the red of the D/sub 2/ resonance line. Raman transitions between vibrational levels of adjacent magnetic substates are induced by the small in-plane component of the field. Two other important requirements for Raman sideband cooling are a uniform energy shift of the magnetic sublevels and optical pumping.
Efficient cooling of trapped ions is a prerequisite for various applications of the ions in precision spectroscopy, quantum information, and coherence control. Raman sideband cooling is an effective method to cool the ions to their motional ground state. We investigate both numerically and experimentally the optimization of Raman sideband cooling strategies and propose an efficient one, which can simplify the experimental setup as well as reduce the number of cooling pulses. Several cooling schemes are tested and compared through numerical simulations. The simulation result shows that the fixed-width pulses and varied-width pulses have almost the same efficiency for both the first-order and the second-order Raman sideband cooling. The optimized strategy is verified experimentally. A single 25Mg+{^{25}\mathrm{Mg}}^{+}25Mg+ ion is trapped in a linear Paul trap and Raman sideband cooled, and the achieved average vibrational quantum numbers under different cooling strategies are evaluated. A good agreement between the experimental result and the simulation result is obtained.