Structural phase transitions in low-dimensional ion crystals

Abstract

A chain of singly-charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the particle number. This structural change is a phase transition of second order, whose order parameter is the crystal displacement from the chain axis. We study analytically the transition using Landau theory and find full agreement with numerical predictions by [J. Schiffer Phys. Rev. Lett. 70, 818 (1993)] and [Piacente et al Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine analytically the system's behaviour at the transition point.

12 pages, 8 figures. Revised version, to appear in Phys. Rev. B

References in corpus (10)

• Effective quantum spin systems with ion traps
• Quantum dynamics of cold trapped ions, with application to quantum computation
• The Ion Trap Quantum Information Processor
• Generic properties of a quasi-one dimensional classical Wigner crystal
• Observation of Three-dimensional Long-range Order in Smaller Ion Coulomb Crystals in an rf Trap
• Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction
• Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential
• Dynamics of an ion chain in a harmonic potential
• Trapped ion chain as a neural network
• Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation

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• Nanofriction in Cold Ion Traps
• Double wells, scalar fields and quantum phase transitions in ions traps
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• Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals
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