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Physica Scripta

From a single ion to a mesoscopic system - crystallization of ions in Paul traps

HERBERT WALTHER

Published Jan 1, 1995• 20 citations
Publisher

Abstract

In the paper experiments dealing with the formation of ordered ion structures in Paul traps are reviewed. The transition from an ion cloud to a crystal-like structure corresponds to a chaos-order transition. Furthermore recent experiments in polarization gradient cooling of ions in a quadrupole ring trap are described. The results show that it should be possible to cool the trapped ions into their vibrational ground state.

DOI
10.1088/0031-8949/1995/t59/049

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Physica Scripta•Jan 1, 1995•6 citations
In the paper experiments dealing with the formation of ordered ion structures in Paul traps are reviewed. The transition from an ion cloud to a crystal-like structure corresponds to a chaos-order transition. Furthermore recent experiments in polarization gradient cooling of ions in a quadrupole ring trap are described. The results show that it should be possible to cool the trapped ions into their vibrational ground state.
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.
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.
The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.
We report on the results on various aspects of the formation of ion Coulomb crystals in linear Paul traps, for plasmas containing from a few hundred to several thousand laser-cooled 24Mg+{}^{24}{\mathrm{Mg}}^{+}24Mg+ ions. The presented studies include observations of changes in emitted fluorescence, changes in plasma aspect ratio, and the formation of shell structure, during the transition from the cloudlike to the crystalline state. The competition between rf heating and laser cooling is observed to result in a very dramatic transition from the cloudlike disordered state to a liquidlike state. After the liquid state is reached ordering into shell structure takes place as a continuous process at even higher plasma coupling parameters. This is in contrast to earlier observations of few-ion plasmas in hyperbolic rf traps.