= Vortex-unbinding crossover in a trapped atomic gas
In 2006, <Zoran Hadzibabic>, <Peter Krüger>, <Marc Cheneau>, <Baptiste Battelier> and <Jean Dalibard> split a cooled <rubidium>-87 cloud into two independent planar gases using an <optical lattice>. After release, the expanding sheets overlapped; <absorption imaging> recorded their <matter-wave interference>. Smooth fringe waviness revealed <thermal phase fluctuations>, while sharp dislocations indicated isolated <vortices>. The initial evaporative-cooling endpoint controlled the preparation; central fringe contrast served as a degeneracy proxy because direct thermometry in the lattice was difficult.<Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas by Zoran Hadzibabic and others>[Pages 1–2, preparation and readout; Fig. 1; temperature control and Fig. 2]{ref}
Loss of extended coherence coincided with increased vortex signatures. The <optical trap> and finite cloud produced a crossover; tightly bound pairs were unresolved, and short-wavelength modes could contaminate high-temperature counts. These were observations of the <vortex>-unbinding mechanism, not a direct measurement of <phase stiffness> or a sharp homogeneous <universal stiffness jump>. The authors left the sample's <superfluidity> open.<Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas by Zoran Hadzibabic and others>[Pages 3–4, Figs. 3–4; geometry, invisible pairs, detection limits and final paragraph on unmeasured superfluidity]{ref}
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