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arXiv:2407.15182 · Physical Review Applied

Thermometry of trapped ions based on bichromatic driving

Xie-Qian Li, Yi Tao, Ting Chen, Wei Wu, Yi Xie, Chun-Wang Wu, Ping-Xing Chen

Published Dec 5, 2024• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevapplied.22.064022

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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.
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.
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.
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.
Coulomb crystals of cold trapped ions are a leading platform for the realisation 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 1D linear chain of 4 ions and a 2D 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.
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.
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.