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

References in corpus (8)

• Quantum computing with trapped ions
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Structural phase transitions in low-dimensional ion crystals
• Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
• Double wells, scalar fields and quantum phase transitions in ions traps
• Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
• Dipolar bosons in a planar array of one-dimensional tubes
• Ground state of low dimensional dipolar gases: linear and zigzag chains

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• Structural transitions of ion strings in quantum potentials
• Quantum quenches of ion Coulomb crystals across structural instabilities
• Revealing quantum statistics with a pair of distant atoms
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• From classical to quantum criticality
• Degeneracy and Inversion of Band Structure for Wigner Crystals on a Toroidal Helix
• Two-dimensional spectroscopy for the study of ion Coulomb crystals
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
• Stability and dynamics of ion rings in linear multipole traps
• Structural transitions of nearly second order in classical dipolar gases
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature