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arXiv:1603.09322 · Physical Review A

Raman sideband cooling of a Ba+138 ion using a Zeeman interval

Christopher M. Seck, Mark Kokish, Matthew Dietrich, Brian Odom

Published May 17, 2016• 10 citations
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Abstract

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 $^{138}\mathrm{Ba}^{+}$ of sufficient fidelity for QLS without an extremely narrow-band laser or the use of a species with hyperfine structure. We use the two ${S}_{1/2}$ Zeeman sublevels of $^{138}\mathrm{Ba}^{+}$ 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 $^{138}\mathrm{Ba}^{+}$ 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 $\overline{n}=0.15(6)$.

DOI
10.1103/physreva.93.053415

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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 n‾\ensuremath≪1\overline{n}\ensuremath{\ll}1n\ensuremath≪1. We additionally employ a second, far-off-resonant laser driving Raman \ensuremathπ\ensuremath{\pi}\ensuremathπ 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).
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).
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.
Raman sideband cooling of 25^{25}25Mg+^++ -27^{27}27Al+^++ ions pair and observation of quantum logic spectra
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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.
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.
Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultracold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional-ground-state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground-state cooling schemes for single 25Mg+{}^{25}{\mathrm{Mg}}^{+}25Mg+ ions and sympathetic ground-state cooling of 24MgH+{}^{24}{\mathrm{MgH}}^{+}24MgH+. In particular, we show that robust cooling is achieved by combining pulsed Raman sideband cooling with continuous quench cooling. Furthermore, we experimentally demonstrate an efficient strategy for ground-state cooling outside the Lamb-Dicke regime.