Observation of power-law scaling for phase transitions in linear trapped ion crystals

We report an experimental confirmation of the power-law relationship betwee n the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled cal cium ions confined in a linear radio-frequency trap. Measurements for up to ten ions are in good agreement with theoretical and numeric predictions. I mplications on an upper limit to the size of data registers in ion trap qua ntum computers are discussed.