Quantum zigzag transition in ion chains

Abstract

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one dimensional optical lattice.

4 pages, 1 figure. Revised version, to appear in Phys. Rev. Lett

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Cited by in corpus (68)

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• Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals
• Assembling a ring-shaped crystal in a microfabricated surface ion trap
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• Structural transitions of ion strings in quantum potentials
• Spin-Peierls Quantum Phase Transitions in Coulomb Crystals
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• Quantum superpositions of crystalline structures
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• Manipulating phonons of a trapped-ion system using optical tweezers
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• From classical to quantum criticality
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• Ab-initio characterization of the quantum linear-zigzag transition using DMRG
• Two-dimensional spectroscopy for the study of ion Coulomb crystals
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
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• Quantum simulation of extended polaron models using compound atom-ion systems
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• Non-equilibrium quantum thermodynamics in Coulomb crystals
• Micromotion-Enhanced Fast Entangling Gates For Trapped Ion Quantum Computing
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• Thermoelectricity of cold ions in optical lattices
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• Structural transitions of nearly second order in classical dipolar gases
• Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model
• Wigner crystal diode
• Multi-mode Bose-Hubbard model for quantum dipolar gases in confined geometries
• Critical behavior of the quasi-periodic quantum Ising chain
• Dynamics of quantum discommensurations in the Frenkel-Kontorova chain
• Quantum Phase Transitions and Heat Capacity in a two-atoms Bose-Hubbard Model
• Spatiotemporal Oscillation Patterns in the Collective Relaxation Dynamics of Interacting Particles in Periodic Potentials
• Fractal ground state of ion chains in periodic potentials
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions
• Soft quantum vibrations of PT-symmetric nonlinear ion chain
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature
• Observing the dynamics of octupolar structural transitions in trapped-ion clusters
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model