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Physical Review A

Laser-cooling limits and single-ion spectroscopy

David J. Wineland, Wayne M. Itano, Jonas Bergquist, Randall G. Hulet

Published Sep 1, 1987• 165 citations
Publisher

Abstract

The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in ${10}^{18}$. .AE

DOI
10.1103/physreva.36.2220

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•Nov 23, 1995•0 citations
The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in 1018{10}^{18}1018. .AE
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
Laser cooling of a single trapped ion in a Paul trap is discussed theoretically in the Lamb-Dicke limit, with full consideration of the time dependence of the trapping potential. Resulting mean kinetic energies are defined as time averages over one period of the micromotion and are compared with final temperatures expected from the laser-cooling treatment with harmonic traps. For laser-atom detunings close to the micromotion frequency the results differ significantly from those expected for a harmonic trap potential. A physical interpretation is given and simple formulas are derived for the strong confinement case.
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.
A single Hg+ ion that is confined in an rf (Paul) trap can be laser cooled so that the amplitude of its motion is much less than an optical wavelength (the Dicke limit for optical transitions).1 More recently, we used the technique of sideband cooling to reach the zero point of motion.2 This realizes for the first time, we believe, the fundamental limit of laser cooling and the ideal of an isolated atomic particle at rest in free space to within the quantum mechanical limits imposed by the surrounding apparatus. In both limits, Doppler effects to all orders become negligible, the interrogation time is arbitrarily long, and the fundamental shot noise limit of a single atom is readily attained. We report these results and our progress toward the 2S1/2—2D5/2 282-nm transition with a resolution approaching the 2-Hz natural linewidth.
We demonstrate efficient resolved sideband laser cooling ($99\ifmmode\pm\else\textpm\fi{}1%$ ground-state population) of a single 40Ca+{}^{40}{\mathrm{Ca}}^{+}40Ca+ ion in a large linear Paul trap (electrode spacing of 7 mm) operated at an rf drive frequency of just 3.7 MHz. For ion oscillation frequencies in the range 280--585 kHz, heating rates below or about one motional quantum per second have been measured at room temperature. The results, obtained under these unconventional sideband cooling conditions, pave the way for a range of new types of cold ion experiments, including spectroscopy of molecular ions as well as ultracold chemistry.
Abstract The ions trapped, whether in the Paul trap or in the Penning trap, usually have energies of the order of 1 eV, that is, a temperature of about 10 000 K. High temperature means high kinetic energy, and this is un favourable to most trap-based experiments for the following reasons. First, with high kinetic energy, amplitudes of ion oscillations are high and consequently the chances of ion losses are high; this results in loss of sensitivity. Second, high kinetic energy enhances both the first-order and the second-order Doppler effects; so, unless the ions are cooled, all spectroscopic experiments are adversely affected in a major way. While isolation of the ions in the trapped condition does not permit ion energy to be easily dissipated to the surroundings, for the same reason, the trapped ions can be effectively cooled and, once cooled, they can be retained cold in the trap. In recent years, most of the trap-based experiments have used ion cooling of one kind or the other. In this chapter we present an overview of various cooling methods and their applications.