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arXiv:2606.21357 · Physical Review Applied

Quantum Beam-Splitter Cooling and Thermometry in Large Trapped-Ion Crystals

Kirthik Rajakumar, Ansh Das, Abhinay Pandey, Athreya Shankar

quant-phphysics.atom-phSubmitted Jun 19, 2026• Announced Jun 22, 2026• 0 citations
v1 · Jun 19, 2026v2 · Jun 30, 2026
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Abstract

We propose and characterize a protocol for rapid near-ground state cooling of the center-of-mass (c.m.) mode of a large trapped ion crystal. When the initial mean thermal occupation of the mode $\bar{n}_i$ is small compared to the number of ions $N$, a red sideband drive implements a beam-splitter type SWAP operation between the mode and the collective spin of the $N$ ions, with the latter effectively serving as a quantum harmonic oscillator. Subsequently, a reset of the spins removes the entropy, leading to near-ground state cooling of the c.m. mode. We term this protocol as quantum beam-splitter cooling (QBSC). We analyze the impact of several practical imperfections on the final temperature achievable under QBSC, including finite ion number, off-resonant carrier and blue-sideband contributions, and the impact of the sideband drives arising from spectator modes. In addition, we outline practical strategies to eliminate the carrier drive. Furthermore, we show that measuring the population statistics of the ions at the end of the SWAP operation can enable near-optimal quantum beam-splitter thermometry (QBST), with the classical Fisher information approaching the quantum Fisher information of a thermal state. We discuss the connection of QBSC with continuous sideband cooling and compare QBST with a recently proposed rapid adiabatic passage-based thermometry scheme. Our work constitutes an example of harnessing many-body effects to open new routes to laser cooling and thermometry in large trapped ion crystals.

Comments
12 pages, 12 figures;

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We propose and characterize a protocol for rapid near-ground state cooling of the center-of-mass (c.m.) mode of a large trapped ion crystal. When the initial mean thermal occupation of the mode nˉi\bar{n}_inˉi​ is small compared to the number of ions NNN, a red sideband drive implements a beam-splitter type SWAP operation between the mode and the collective spin of the NNN ions, with the latter effectively serving as a quantum harmonic oscillator. Subsequently, a reset of the spins removes the entropy, leading to near-ground state cooling of the c.m. mode. We term this protocol as quantum beam-splitter cooling (QBSC). We analyze the impact of several practical imperfections on the final temperature achievable under QBSC, including finite ion number, off-resonant carrier and blue-sideband contributions, and the impact of the sideband drives arising from spectator modes. In addition, we outline practical strategies to eliminate the carrier drive. Furthermore, we show that measuring the population statistics of the ions at the end of the SWAP operation can enable near-optimal quantum beam-splitter thermometry (QBST), with the classical Fisher information approaching the quantum Fisher information of a thermal state. We discuss the connection of QBSC with continuous sideband cooling and compare QBST with a recently proposed rapid adiabatic passage-based thermometry scheme. Our work constitutes an example of harnessing many-body effects to open new routes to laser cooling and thermometry in large trapped ion crystals.
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Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, NNN, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to 10510^5105 ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated E×B\boldsymbol{E}\times\boldsymbol{B}E×B modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.