Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential

Abstract

The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phonons. We calculate the long wavelength modes in the continuum limit, and evaluate the density of states in the short wavelength limit for chains of $N\gg 1$ ions. Remarkably, the results that are found analytically in the thermodynamic limit provide a good estimate of the spectrum of excitations of small chains down to few tens of ions. The spectra are used to compute the thermodynamic functions of the chain. Deviations from extensivity of the thermodynamic quantities are found. An analytic expression for the critical transverse frequency determining the stability of a linear chain is derived.

4 pages, 4 figures

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• Roton-maxon spectrum and stability of trapped dipolar condensates
• Exciting Collective Oscillations in a Trapped 1D Gas
• Testing the stability of fundamental constants with the 199Hg+ single-ion optical clock
• Coulomb crystallization in expanding laser-cooled neutral plasmas

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• Ramsey interferometry with a spin embedded in a Coulomb chain
• Temperature driven structural phase transition for trapped ions and its experimental detection
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• Ion dynamics in a linear radio-frequency trap with a single cooling laser
• Ab-initio characterization of the quantum linear-zigzag transition using DMRG
• Entangling two defects via a surrounding crystal
• Simultaneous cooling of axial vibrational modes in a linear ion-trap
• Observing different phases for the dynamics of entanglement in an ion trap
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• Quantum reservoirs with ion chains
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• Dynamical ion transfer between coupled Coulomb crystals in a double well potential
• Correlations and pair emission in the escape dynamics of ions from one-dimensional traps
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