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Sympathetic cooling in a large ion crystal

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Abstract

We analyze the dynamics and steady state of a linear ion array when some of the ions are continuously laser cooled. We calculate the ions’ local temperature measured by its position fluctuation under various trapping and cooling configurations, taking into account background heating due to the noisy environment. For a large system, we demonstrate that by arranging the cooling ions evenly in the array, one can suppress the overall heating considerably. We also investigate the effect of different cooling rates and find that the optimal cooling efficiency is achieved by an intermediate cooling rate. We discuss the relaxation time for the ions to approach the steady state, and show that with periodic arrangement of the cooling ions, the cooling efficiency does not scale down with the system size.

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Notes

  1. Here, the choice of \(d_{0}\) is somewhat arbitrary as long as it characterizes the length scale of the inter-ion spacing. In this article, we define \(d_{0}\) differently in various situations. For instance, in a small harmonic trap (\(N=20\)), we choose \(d_{0}\) to be the smallest spacing in the middle of the chain. In a large non-uniform ion crystal (\(N=121\)), we choose \(d_{0}=\frac{1}{100}\sum _{i=11}^{110}(z_{i+1}^{0}-z_{i}^{0})/100\), a mean value of all ion spacings except that 10 large ones on the edges are excluded.

  2. Throughout this article, we choose ytterbium 171 ions spaced by \(d_{0}=10\,\upmu \)m as examples, so \(\omega _{0}=9.0\) MHz and \(\alpha =2.0\times 10^{-3}\).

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Acknowledgments

This work was supported by the NBRPC 2011CBA00302, the IARPA MUSIQC program, the AFOSR and the ARO MURI program, and the support from National Taiwan University under Grants No. NTU-ERP-103R891401, NTU-ERP-103R891402, and NTU-ERP-103R104021.

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Authors and Affiliations

  1. Center for Quantum Science and Engineering, and Department of Physics, National Taiwan University, Taipei, 10617, Taiwan

    Guin-Dar Lin

  2. Department of Physics, University of Michigan, Ann Arbor, MI, 48109, USA

    L.-M. Duan

  3. Center for Quantum Information, IIIS, Tsinghua University, Beijing, 100084, China

    L.-M. Duan

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Correspondence to Guin-Dar Lin.

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Lin, GD., Duan, LM. Sympathetic cooling in a large ion crystal. Quantum Inf Process 15, 5299–5313 (2016). https://doi.org/10.1007/s11128-015-1161-3

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