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Inventiones mathematicae

Long-range many-body scattering

Israel Michael Sigal, Avy Soffer

Published Dec 1, 1990• 91 citations
Publisher
DOI
10.1007/bf01234413

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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.

Physical Review Letters•Dec 4, 1995•90 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 9Be+^{9}\mathrm{Be}^{+}9Be+ ions in a Penning trap. Long-range order emerges in approximately spherical clouds with as few as 5 \ifmmode\times\else\texttimes\fi{} 104{10}^{4}104 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{} 105{10}^{5}105 trapped ions (${r}_{0}\ensuremath{\approx}65a$), with Bragg scattering patterns characteristic of a body-centered cubic lattice.