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Physical Review Letters

Long-Range Order in Laser-Cooled, Atomic-Ion Wigner Crystals Observed by Bragg Scattering

Joseph N. Tan, J. J. Bollinger, B. M. Jelenkovic, David J. Wineland

Published Dec 4, 1995• 90 citations

Abstract

We report the first observation of Bragg scattering from atomic ions confined in an electromagnetic trap. The results reveal long-range order and give evidence for bulk behavior in a strongly coupled collection of laser-cooled $^{9}\mathrm{Be}^{+}$ ions in a Penning trap. Long-range order emerges in approximately spherical clouds with as few as 5 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ ions (cloud radius ${r}_{0}\ensuremath{\approx}37a$ where $a\ensuremath{\equiv}\mathrm{W}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{r}\ensuremath{-}\mathrm{S}\mathrm{e}\mathrm{i}\mathrm{t}\mathrm{z}\phantom{\rule{0ex}{0ex}}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}$). Bulk behavior is evident with 2.7 \ifmmode\times\else\texttimes\fi{} ${10}^{5}$ trapped ions (${r}_{0}\ensuremath{\approx}65a$), with Bragg scattering patterns characteristic of a body-centered cubic lattice.

DOI: 10.1103/physrevlett.75.4198

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Nature Communications•Oct 7, 2013•58 citations

We report the first observation of Bragg scattering from atomic ions confined in an electromagnetic trap. The results reveal long-range order and give evidence for bulk behavior in a strongly coupled collection of laser-cooled

^{9}\mathrm{Be}^{+}

ions in a Penning trap. Long-range order emerges in approximately spherical clouds with as few as 5 \ifmmode\times\else\texttimes\fi{}

{10}^{4}

ions (cloud radius

{r}_{0}\ensuremath{\approx}37a

where

a\ensuremath{\equiv}\mathrm{W}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{r}\ensuremath{-}\mathrm{S}\mathrm{e}\mathrm{i}\mathrm{t}\mathrm{z}\phantom{\rule{0ex}{0ex}}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}

). Bulk behavior is evident with 2.7 \ifmmode\times\else\texttimes\fi{}

{10}^{5}

trapped ions (

{r}_{0}\ensuremath{\approx}65a

), with Bragg scattering patterns characteristic of a body-centered cubic lattice.

We describe some recent experiments that use a new Penning trap to trap and laser‐cool more than 105 Be+ ions. In this wrok the Coulomb coupling parameter was estimated to by typically greter than 100 and in some cases greater than 300. Shell structure was difficult to observe in the ion fluorescence from these large clouds. An initial Bragg scattering experiment to obtain information on the ion correlations is described. We also briefly review our work on the electrostatic modes of a Penning trap plasma including the use fo the modes to diagnose the shape and density of a cryogenic electron plasma. Some applications of laser‐cooled plasmas in Penning traps, such as atomic clocks, are discussed.

We describe some recent experiments that use a new Penning trap to trap and laser‐cool more than 105 Be+ ions. In this wrok the Coulomb coupling parameter was estimated to by typically greter than 100 and in some cases greater than 300. Shell structure was difficult to observe in the ion fluorescence from these large clouds. An initial Bragg scattering experiment to obtain information on the ion correlations is described. We also briefly review our work on the electrostatic modes of a Penning trap plasma including the use fo the modes to diagnose the shape and density of a cryogenic electron plasma. Some applications of laser‐cooled plasmas in Penning traps, such as atomic clocks, are discussed.

In this work, laser-cooled ion crystals containing 1000 to 100000 singly charged magnesium ions (Mg+) were prepared in a Penning trap. The properties of the ion crystals and their structure displaying long-range ordering were analyzed by various non-destructive techniques. After creation of the Mg + ions in the form of ion bunches in an external source, the ions were injected into the Penning trap where their temperature was reduced by eight orders of magnitude within seconds using a combination of buffer gas cooling and Doppler laser cooling. The achieved temperatures in the millikelvin-regime were close to the theoretical Doppler-cooling limit and sufficiently low to induce the transition to a crystal phase exhibiting long-range ordering. The structure of these mesoscopic ion crystals is in agreement with a model describing the crystal as a set of planar shells. This allows for a derivation of properties such as the charge density or the temperature of the observed crystals. For the process of combined buffer-gas and Doppler laser cooling an analytical model has been developed, which explains the time development of the temperature and the fluorescence signal in agreement with the experimental results.

Laser-cooled atomic ions form ordered structures in radiofrequency ion traps and in Penning traps. Here we demonstrate in a Penning trap the creation and manipulation of a wide variety of ion Coulomb crystals formed from small numbers of ions. The configuration can be changed from a linear string, through intermediate geometries, to a planar structure. The transition from a linear string to a zigzag geometry is observed for the first time in a Penning trap. The conformations of the crystals are set by the applied trap potential and the laser parameters, and agree with simulations. These simulations indicate that the rotation frequency of a small crystal is mainly determined by the laser parameters, independent of the number of ions and the axial confinement strength. This system has potential applications for quantum simulation, quantum information processing and tests of fundamental physics models from quantum field theory to cosmology.