Dynamics of an ion chain in a harmonic potential

Details Dynamics of an ion chain in a harmonic potential Dynamics of an ion chain in a harmonic potential

2004-07-26

arxiv.org/abs/cond-mat/0407675v1

Phys. Rev. E 70, 066141 (2004).

Physics

Condensed Matter

Statistical Mechanics

14 pages, 7 figures

Scientific paper

10.1103/PhysRevE.70.066141

Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, thus the eigenmodes are not phononic-like waves. We study chains of N>>1 ions and evaluate analytically the long wavelength modes and the density of states in the short wavelength limit. These results reproduce with good approximation the dynamics of chains consisting of dozens of ions. Moreover, they allow to determine the critical transverse frequency required for the stability of the linear structure, which is found in agreement with results obtained by different theoretical methods [D.H.E. Dubin, Phys. Rev. Lett. 71, 2753 (1993)] and by numerical simulations [J.P. Schiffer, Phys. Rev. Lett. 70, 818 (1993)]. We introduce and explore the thermodynamic limit for the ion chain. The thermodynamic functions are found to exhibit deviations from extensivity.

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