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Annual Meeting Optical Society of America

Inhibition of laser cooling in Paul traps

Ralph G. DeVoe, John A. Hoffnagle, Richard G. Brewer

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1988.fa4

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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.
It is currently thought that the laser cooling of an ordered ion array, an ion crystal, is qualitatively the same as that of a single ion. We show that this assumption is strongly violated in recent experiments in Paul traps, due to ion micromotion. Our analysis demonstrates an unexpected laser damping instability that induces an ion-crystal order-chaos transition and also explains why ion crystals in Paul traps have been limited to less than 100 ions. We directly observe the effects of ion micromotion on the laser cooling of a single trapped Ba+{\mathrm{Ba}}^{+}Ba+ ion by a new technique.
Several groups have recently used laser cooling to produce ordered arrays of ions (ion crystals) in rf quadrupole traps. We discuss two physical mechanisms which underlie and explain the behavior of ion crystals. First, we show that deterministic chaos can be responsible for phase transitions between the ordered (crystal) state and the disordered (cloud) state.1 The crystal—cloud transition is explained as an order—chaos transition. Chaos arises from the nonlinear interaction of Coulomb repulsion with the oscillating trap potential.
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
We present recent experimental and theoretical results on the behavior of two-, three-, and four-ion crystals close to the Mathieu instability. In particular, we show that the crystals are stable until the Mathieu instability is reached, i.e., for the parameter space investigated, there is no ``melting'' of the crystals. Laser and rf heating are studied in detail. A simple model of chaotic rf heating as well as a classification of the ion dynamics into four characteristic regimes are presented.
We report the laser cooling and trapping of barium ions in a novel planar Paul trap. Unlike other rf quadrupole traps, the electrodes of a planar Paul trap are confined to one or more parallel planes. They may therefore be constructed on a micrometer scale by the same photolithographic techniques used for semiconductor devices. Such devices are under construction in our laboratory. Micro-traps permit entirely new studies, for example, superradiance of a few ions, which occurs as ion-ion distances approach one wavelength of light. Photolithography can also generate an array of traps on a single substrate for an atomic clock. Our traps consist of one or more parallel planes, one above the other, each plane having either a conducting ring or a hole in a conducting sheet. Thus, a ring or a hole results in a potential well for trapping. A three-ring design produces a quadrupole potential that is harmonic up to eighth-order for a particular choice of ring diameters and spacings. Three-hole traps have been constructed with inner hole radii ranging from 50 to 400 μm, and both single barium ions and clouds have been observed.
An experimental and theoretical study of laser sideband cooling of a trapped ion in a radiofrequency trap is presented. The influence of the micromotion in the time-dependent potential of a Paul trap can lead to a counterintuitive situation, where sideband cooling is possible for positive values of the laser detuning, i.e., for a laser frequency that is higher than the resonance frequency of the ion at rest. The cooling rate and the capture range are calculated in a semiclassical model. Experimental results of laser sideband cooling at positive detuning are demonstrated with a single trapped In+{\mathrm{In}}^{+}In+ ion stored in a miniature Paul trap.