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arXiv:2402.19022 · Physical Review A

Mode-resolved thermometry of a trapped ion with deep learning

Yi Tao, Ting Chen, Hongyang Wang, Jie Zhang, Ting Zhang, Yi Xie, Ping-Xing Chen, Wei Wu

Published Jun 25, 2024• 5 citations
arXivHTMLPDF

Abstract

In a trapped-ion system, accurate thermometry of ions is crucial for precisely evaluating the system state and performing quantum operations. However, when the motional state of a single ion is far away from the ground state, the spatial dimensionality of the phonon state sharply increases. Then it is difficult to realize accurate and mode-resolved thermometry with existing methods. In this work, we apply deep learning to the thermometry of a trapped ion and propose an efficient and mode-resolved method for accurately estimating large mean phonon numbers. We have also conducted experimental verification based on a self-developed surface trap. The result has shown the significant accuracy and efficiency of the method for thermometry of a single ion with large mean phonon numbers. The mode-resolved feature of our method makes it better applied to the characterization of system parameters, such as evaluating cooling effectiveness and analyzing surface trap noise. Our trained neural network model can be easily extended to other experimental setups and parameter ranges without modification of the experimental setups.

DOI
10.1103/physreva.109.062434

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In a trapped-ion system, accurate thermometry of ions is crucial for precisely evaluating the system state and performing quantum operations. However, when the motional state of a single ion is far away from the ground state, the spatial dimensionality of the phonon state sharply increases. Then it is difficult to realize accurate and mode-resolved thermometry with existing methods. In this work, we apply deep learning to the thermometry of a trapped ion and propose an efficient and mode-resolved method for accurately estimating large mean phonon numbers. We have also conducted experimental verification based on a self-developed surface trap. The result has shown the significant accuracy and efficiency of the method for thermometry of a single ion with large mean phonon numbers. The mode-resolved feature of our method makes it better applied to the characterization of system parameters, such as evaluating cooling effectiveness and analyzing surface trap noise. Our trained neural network model can be easily extended to other experimental setups and parameter ranges without modification of the experimental setups.
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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.
Accurate thermometry of laser-cooled ions is crucial for the performance of the trapped-ion quantum computing platform. However, most existing methods face a computational exponential bottleneck. Recently, a thermometry method based on bichromatic driving was theoretically proposed by Vybornyi et al. [PRX Quantum 4, 040346 (2023)] to overcome this obstacle, which allows the computational complexity to remain constant with the increase of ion numbers. In this paper, we provide a detailed statistical analysis of this method and prove its robustness regarding several imperfect experimental conditions using Floquet theory. We then experimentally verify its good performance on a linear-segmented-surface-electrode-ion-trap platform. This method is proven to be effective from near the motional ground state to a few mean phonon numbers. Our theoretical analysis and experimental verification demonstrate that the scheme can accurately and efficiently measure the temperature in ion crystals.
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Resolved sideband cooling is a standard technique for cooling trapped ions below the Doppler limit to near their motional ground state. Yet, the most common methods for sideband cooling implicitly rely on low Doppler-cooled temperatures and tightly confined ions, and they cannot be optimized for different experimental conditions. Here, we introduce a framework which calculates the fastest possible sideband cooling sequence for any set of experimental parameters and verify its improvement compared to traditional methods using a trapped 171^{171}171Yb+^++ ion. After extensive cooling, we find that the ion motional distribution is distinctly non-thermal and thus not amenable to standard thermometry techniques. We therefore develop and experimentally validate an improved method to measure ion temperatures after sideband cooling. These techniques will enable more efficient cooling and thermometry within any trapped-ion system, especially those with high initial temperatures or spatially-extended ion wavepackets.
Abstract To achieve high-fidelity operations on a large-scale quantum computer, the parameters of the physical system must be efficiently characterized with high accuracy. For trapped ions, the entanglement between qubits are mediated by the motional modes of the ion chain, and thus characterizing the motional-mode parameters becomes essential. In this paper, we develop and explore physical models that accurately predict both magnitude and sign of the Lamb–Dicke parameters when the modes are probed in parallel. We further devise an advanced characterization protocol that shortens the characterization time by more than an order of magnitude, when compared to that of the conventional method that only uses mode spectroscopy. We discuss potential ramifications of our results to the development of a scalable trapped-ion quantum computer, viewed through the lens of system-level resource trade offs.