Dynamics of an ion chain in a harmonic potential

TL;DR

This paper analytically studies the vibrational modes and stability of long ion chains in harmonic traps, revealing non-uniform density effects and deviations from thermodynamic extensivity.

Contribution

It provides analytical expressions for eigenmodes and density of states in large ion chains, and introduces the thermodynamic limit for such systems.

Findings

Analytical long wavelength mode spectrum

Critical transverse frequency for stability

Deviations from extensivity in thermodynamic functions

Abstract

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.