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Zhongguo kexue. Wulixue Lixue Tianwenxue

离子存储、冷却及在量子频标中的应用

Lijun Wang, ShiGuang WANG, Zhengbo Wang, JianWei ZHANG

Published Apr 1, 2011• 2 citations
Publisher

Abstract

This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.

DOI
10.1360/132011-58

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This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.
The stability properties of radio-frequency traps make them a technology of choice for the design of embedded microwave ion clocks for deep space navigation applications. The main effect limiting the frequency stability of such clocks is the frequency shift induced by the second order Doppler effect which fluctuates with the number of trapped ions. The use of radio-frequency multipole traps in the design of microwave clocks is motivated by a built-in reduction of the radio-frequency driven motion of the ions with the increase of the order of the multipole field. Experimental realizations by NASA-JPL of ion clocks involving higher order multipole traps have demonstrated a stability gain, but no direct measurement has yet been undertaken to clarify wherever this gain is a direct consequence of the number of electrodes in the trap or from a global optimization of the whole setup. One of the objectives of the TADOTI experiment is to conduct a comparative measurement of the velocity distribution over a laser cooled Ca+ ion cloud trapped in a quadrupole and an octupole trap. Observations of cold samples have shown an inhomogeneous spatial distribution of the trapped particles with clustering of the ions in local potential wells. Simulations attribute this organization to a symmetry breaking in the trap, induced by realistic mis-positioning of the electrodes. A prerequisite for the velocity distribution characterization is to restore to symmetry of the potential of the octupole trap by tuning the RF voltage applied to each electrode. This thesis focuses on the analytical description of the potential perturbations induced by the structural deformation of the trap, and proposes a characterization and compensation protocol of the perturbations, based on the localization of the laser-cooled ion in the trap. These tools can be used to create any configuration of three parallel ion clouds in the octupole trap.
The accurate evaluation of the second-order Doppler frequency shift (SODFS) of trapped ions in a linear Paul trap has been studied with experiments and molecular dynamics (MD) simulations. The motion of trapped ions in the trap has three contributions, and we focus on the ion excess micromotion, which is rarely discussed when evaluating the SODFS of ions. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a model to accurately evaluate the total SODFS for an ion ensemble with temperature less than 100 mK, which consists of three contributions of ion motion. The effectiveness of the model has been verified by MD simulation, and the experimental results of the excess micromotion of trapped ions are consistent with the theory. We believe that our model offers advantages in accurately evaluating the SODFS for the ion trap, especially those of laser-cooled ion microwave clocks based on large ion clouds.
A high-performance frequency standard based on (199)Hg(+) ions confined in a hybrid radio frequency (RF)/dc linear ion trap is demonstrated. This trap permits storage of large numbers of ions with reduced susceptibility to the second-order Doppler effect caused by the RF confining fields. A 160-mHz-wide atomic resonance line for the 40.5-GHz clock transition is used to steer the output of a 5-mHz crystal oscillator to obtain a stability of 2 x 10(exp -15) for 24,000-second averaging times. Measurements with a 37-mHz line width for the Hg(+) clock transition demonstrate that the inherent stability for this frequency standard is better than 1 x 10(exp -15) at 10,000-second averaging times.
We discuss frequency standards based on laser-cooled 199Hg+ ions confined in cryogenic rf traps. In one experiment, the frequency of a microwave source is served to the ions' ground-state hyperfine transition at 40.5 GHz. For seven ions and a Ramsey free precession time of 100 s, the fractional frequency stability is 3.3 (2) X 10-13 (tau) -1/2 for measurement times (tau) < 2 h. The ground-state hyperfine interval is measured to be 40 507 347 996.841 59 (14) (41) Hz, where the first number in parentheses is the uncertainty due to statistics and systematic errors, and the second is the uncertainty in the frequency of the time scale to which the standard is compared. In a second experiment under development, a strong-binding cryogenic trap will confine a single ion used for an optical frequency standard based on a narrow electric quadrupole transition at 282 nm. The bandwidth of the laser used to drive this transition is less than 10 Hz at 563 nm.
Several groups have recently used laser cooling to produce ordered arrays of ions, ion crystals, in rf quadrupole ion traps (Paul traps). Laser cooling has been understood using previous theories which ignore ion micromotion and replace the oscillating rf trap potential with a static pseudopotential. We show that in recent experiments, ion micromotion can exceed one wavelength of the cooling radiation and that the resulting Doppler shifts can transform laser cooling into laser heating. Changes in trap voltage, ion position, and laser intensity can all reverse the sign of laser cooling. This, together with ideas of deterministic chaos, can lead to a reinterpretation of experiments on ion crystals. The recognition that effects previously attributed to an experimental artifact, rf heating, may actually be due to a failure of laser cooling opens the door, on the one hand, to precise theories of phase transitions and, on the other, to improved cooling techniques that can permit the creation of larger ion crystals.