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Chinese Physics B

Simulation and experiment of the cooling effect of trapped ion by pulsed laser*

Chang-Da-Ren Fang, Yao Huang, Hua Guan, Qian Yuan, Kelin Gao

Published Apr 19, 2021• 0 citations
Publisher

Abstract

We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation (MD-Simulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single 40Ca+ ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single 27Al+ ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.

DOI
10.1088/1674-1056/abf91f

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arXiv:1902.00302•Feb 1, 2019•0 citations
We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation (MD-Simulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single 40Ca+ ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single 27Al+ ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.
We describe a simple approach to the problem of incorporating the response time of an atom or ion being Doppler-cooled into the theory of the cooling process. The system being cooled does not in general respond instantly to the changing laser frequencies it experiences in its rest frame, and this ‘dynamic effect’ can affect significantly the temperatures attainable. It is particularly important for trapped ions when there is a slow decay out of the cooling cycle requiring the use of a repumping beam. We treat the cases of trapped ions with two and three internal states, then apply the theory to 40Ca+. For this ion experimental data exist showing the ion to be cold under conditions for which heating is predicted if the dynamic effect is neglected. The present theory accounts for the observed behaviour.
We present experimental results on adiabatic cooling of a single 40Ca+ ion in a linear radiofrequency trap. After a period of laser cooling, the secular frequency along the rf-field-free axis is adiabatically lowered by nearly a factor of eight from 583 kHz to 75 kHz. For an ion originally Doppler laser cooled to a temperature of 0.65 +/- 0.03 mK, a temperature of 87 +/- 7 μK is measured after the adiabatic expansion. Applying the same adiabatic cooling procedure to a single sideband cooled ion in the ground state (P0 = 0.978 +/- 0.002) resulted in a final ground state occupation of 0.947 +/- 0.005. Both results are in excellent agreement with an essentially fully adiabatic behavior. The results have a wide range of perspectives within such diverse fields as ion based quantum information science, high resolution molecular ion spectroscopy and ion chemistry at ultra-low temperatures.
Doppler cooling with lasers is essential to ion trapping and is also a preliminary step toward achieving ultracold ions. It requires substantial technological effort to experimentally monitor the ion temperature in the cooling process. Based on the simplified three-level $\mathrm{\ensuremath{\Lambda}}$ configuration, we analytically explore an one-dimensional Doppler cooling process of trapped ions, exemplified by 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+, by solving the friction coefficient in Doppler cooling with respect to a thermal bath; in particular, for a bath with large heating rate. We propose a practical method for measuring the Rabi frequency by the Doppler cooling window, which helps for monitoring the final temperature of the Doppler-cooled ions. With our approach, the obtained results are analytical in the case of a weak thermal bath, whereas for the strong thermal bath numerical treatment is partially needed due to the involvement of the Doppler shift and a large Lamb-Dicke parameter. Our analytic treatments are applied to understand many experimental observations, such as configuration phase transition, phonon lasers, and thermodynamics regarding hot trapped ions, and could help for further our understanding three-dimensional Doppler cooling in realistic ion-trap experiments.
A detailed investigation of ion crystals produced by laser and sympathetic cooling in a linear RF trap has been conducted.\n\nThe laser cooling methods were examined and applied to the trapped ^24Mg^(positive) ions. The crystals produced by the laser cooling were studied, including the dependence on RF voltage, end cap DC voltage, laser power and laser frequency. By manipulating the different RF voltages and endcap DC voltages, the structure phase transition of the ion crystals was observed.\n\nIn addition, the sympathetic cooling of different ion species with the laser cooled 24Mg^(positive) was carried out. In this process, the mixed Mg^(positive) and He^(positive) crystals were created andidentified, and mixed Mg^(positive) and H2^(positive) crystals were produced. The effect of an unwanted chemical reaction of Mg^(positive) and H2 was observed and minimized. After sympathetic cooling of light ion species, the sympathetic cooling of heavy molecular ions such as fullerene ions was also carried out. The efficiencies and final temperature in both cases are very different. Theoretically to interpret the results, molecular dynamics simulations of the laser cooling and sympathetic cooling were implemented. And the simulations were compared with the experimental results.\n\nIn the process of carrying out this research, the optics were rebuilt to provide reliable UV sources for the photoionization and laser cooling of Mg ions. The imaging\nsystem was reconfigured to take the images of ion crystals. New elements were added tin the ion trap to improve the ability to manipulate ions.
We present the results of some simulations of the laser cooling process for a single ion in a Penning ion trap. The situation is rather more complicated than in an r.f. trap, due to the presence of the magnetron drift. We show that under some circumstances the ion can get into an orbit which is different from the usual one in the trap, and that in order to apply laser cooling in this case one has to use a different procedure from the conventional one. We also present heating and cooling curves for the ion as a function of laser frequency and as a function of time.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by 40^{40}40Ca+^{+}+, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetically induced transparency and propose a practical method for measuring the Rabi frequency by the Doppler cooling window. In addition, the final temperature of the laser-cooled ions can be obtained analytically in the case of a weak thermal bath, whereas for the strong thermal bath this requires numerical treatment due to involvement of the Doppler shift and large Lamb-Dicke parameter. Our analytic results would help for understanding many experimental observations, such as configuration phase transition, phonon laser and thermodynamics regarding hot trapped ions.