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arXiv:1104.0451 · New Journal of Physics

Trapped ions in optical lattices for probing oscillator chain models

Thaned Pruttivarasin, Michael T. Ramm, Ishan Talukdar, Axel Kreuter, Hartmut Häffner

Published Jul 29, 2011• 99 citations
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Abstract

We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.

DOI
10.1088/1367-2630/13/7/075012

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We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.
We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range Hamiltonians acting on an internal degree of freedom of the ions. For large anharmonicities, on the other hand, the spatial motion of the ions itself represents a spin-1/2 model with frustrated dipolar XY interactions. We illustrate the latter setup with three systems: the linear chain, the zigzag ladder and the triangular lattice. In the frustrated zigzag ladder with dipolar interactions we find chiral ordering beyond what was predicted previously for a next-nearest-neighbor model. In the frustrated anisotropic triangular lattice with nearest-neighbor interactions we find that the transition from the one-dimensional (1D) gapless spin-liquid phase to the 2D spiraling ordered phase passes through a gapped spin-liquid phase, similar to what has been predicted for the same model with Heisenberg interactions. Further, a second gapped spin-liquid phase marks the transition to the 2D Néel-ordered phase.
The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose-Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. In addition to that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, such as models with attractive or site-dependent phonon-phonon interactions.
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.
We present experimental results of using trapped ions for the study of energy transport and quantum correlations in many-body systems. We investigate energy propagation by locally exciting one end of an ion chain and then observing the subsequent dynamics. The experimental results agree with the presented normal mode model of ion motion, and signify the first steps towards realizing theoretical proposals of studying many-body physics with the motional degree of freedom of trapped ions. Additionally, we present a method for detecting correlations between an open quantum system and its environment by acting only locally on the open system. We implement this method using a single trapped ion and discuss our current work towards extending the results to larger systems. Lastly, we demonstrate how the presented method for local detection of quantum correlations can be used for detection of quantum phase transitions.
We experimentally study energy transport in chains of trapped ions. We use a pulsed excitation scheme to rapidly add energy to the local motional mode of one of the ions in the chain. Subsequent energy readout allows us to determine how the excitation has propagated throughout the chain. We observe energy revivals that persist for many cycles. We study the behavior with an increasing number of ions of up to 37 in the chain, including a zig-zag configuration. The experimental results agree well with the theory of normal mode evolution. The described system provides an experimental toolbox for the study of thermodynamics of closed systems and energy transport in both classical and quantum regimes.