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.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.

arXiv:2402.19022Physical Review AJun 25, 20245 citations

A New Approach to Measurement of Heating Rate of Trapped Ions

徐酉阳, 周飞, 谢艺

理论物理通讯：英文版Jan 1, 20100 citations

Towards Trapped-Ion Thermometry Using Cavity-Based EIT

Abhijit Kundu, Vijay Bhatt, Arijit Sharma

We present a technique for measuring ion temperature using cavity-based electromagnetically induced transparency (EIT) applicable for cavity QED systems. This method enables efficient extraction of the ion's phonon occupation number following sub-Doppler cooling close to the motional ground state. The proposed method requires operation in the resolved-sideband regime, where individual motional states can be selectively addressed for all relevant transitions either by selecting appropriate energy levels for the three-level system or by employing strong confinement with high secular frequencies ( $\sim 10 MHz$ ). It relies on monitoring the cavity probe transmission while scanning the probe laser frequency to establish cavity-induced EIT using a control beam, thereby significantly simplifying the measurement procedure. We establish a theoretical model that demonstrates the influence of the thermal state of the trapped ion vis-à-vis the EIT linewidth measured. We show through numerical simulations how the cavity-induced EIT transmission may be used as a thermometry tool to deduce the ion temperature as well as its motional state in the sub-Doppler cooling regime, even for systems that are in the weak coupling regime.We present a technique for measuring ion temperature using cavity-based electromagnetically induced transparency (EIT) applicable for cavity QED systems. This method enables efficient extraction of the ion's phonon occupation number following sub-Doppler cooling close to the motional ground state. The proposed method requires operation in the resolved-sideband regime, where individual motional states can be selectively addressed for all relevant transitions either by selecting appropriate energy levels for the three-level system or by employing strong confinement with high secular frequencies ($\sim 10 MHz$). It relies on monitoring the cavity probe transmission while scanning the probe laser frequency to establish cavity-induced EIT using a control beam, thereby significantly simplifying the measurement procedure. We establish a theoretical model that demonstrates the influence of the thermal state of the trapped ion vis-à-vis the EIT linewidth measured. We show through numerical simulations how the cavity-induced EIT transmission may be used as a thermometry tool to deduce the ion temperature as well as its motional state in the sub-Doppler cooling regime, even for systems that are in the weak coupling regime.

quant-pharXiv:2602.12823Feb 16, 20260 citations

Millikelvin spatial thermometry of trapped ions

B. G. Norton, Erik W. Streed, M J Petrasiunas +2 more

We demonstrate millikelvin thermometry of laser-cooled trapped ions with high-resolution imaging. This equilibrium approach is independent of the cooling dynamics and has lower systematic error than Doppler thermometry, with ±5 mK accuracy and ±1 mK precision. We used it to observe the highly anisotropic dynamics of a single ion, finding temperatures of <60 mK and >15 K simultaneously along different directions. This thermometry technique can offer new insights into quantum systems sympathetically cooled by ions, including atoms, molecules, nanomechanical oscillators and electric circuits.We demonstrate millikelvin thermometry of laser-cooled trapped ions with high-resolution imaging. This equilibrium approach is independent of the cooling dynamics and has lower systematic error than Doppler thermometry, with ±5 mK accuracy and ±1 mK precision. We used it to observe the highly anisotropic dynamics of a single ion, finding temperatures of <60 mK and >15 K simultaneously along different directions. This thermometry technique can offer new insights into quantum systems sympathetically cooled by ions, including atoms, molecules, nanomechanical oscillators and electric circuits.

arXiv:1106.1708New Journal of PhysicsNov 17, 201119 citations

Trapped Ion Temperature

Springer eBooksNov 9, 20050 citations

\sim 10 MHz

). It relies on monitoring the cavity probe transmission while scanning the probe laser frequency to establish cavity-induced EIT using a control beam, thereby significantly simplifying the measurement procedure. We establish a theoretical model that demonstrates the influence of the thermal state of the trapped ion vis-à-vis the EIT linewidth measured. We show through numerical simulations how the cavity-induced EIT transmission may be used as a thermometry tool to deduce the ion temperature as well as its motional state in the sub-Doppler cooling regime, even for systems that are in the weak coupling regime.