skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effective spin quantum phases in systems of trapped ions

Abstract

A system of trapped ions under the action of off-resonant standing waves can be used to simulate a variety of quantum spin models. In this work, we describe theoretically quantum phases that can be observed in the simplest realization of this idea: quantum Ising and XY models. Our numerical calculations with the density matrix renormalization group method show that experiments with ion traps should allow one to access general properties of quantum critical systems. On the other hand, ion trap quantum spin models show a few unusual features due to the peculiarities of induced effective spin-spin interactions which lead to interesting effects like long-range quantum correlations and the coexistence of different spin phases.

Authors:
; ;  [1]
  1. Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, Garching, D-85748 (Germany)
Publication Date:
OSTI Identifier:
20786332
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063407; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CORRELATIONS; DENSITY MATRIX; IONS; ISING MODEL; J-J COUPLING; RENORMALIZATION; SPIN; STANDING WAVES; TRAPPING; TRAPS

Citation Formats

Deng, X.-L., Porras, D., and Cirac, J. I.. Effective spin quantum phases in systems of trapped ions. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Deng, X.-L., Porras, D., & Cirac, J. I.. Effective spin quantum phases in systems of trapped ions. United States. doi:10.1103/PHYSREVA.72.0.
Deng, X.-L., Porras, D., and Cirac, J. I.. Thu . "Effective spin quantum phases in systems of trapped ions". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786332,
title = {Effective spin quantum phases in systems of trapped ions},
author = {Deng, X.-L. and Porras, D. and Cirac, J. I.},
abstractNote = {A system of trapped ions under the action of off-resonant standing waves can be used to simulate a variety of quantum spin models. In this work, we describe theoretically quantum phases that can be observed in the simplest realization of this idea: quantum Ising and XY models. Our numerical calculations with the density matrix renormalization group method show that experiments with ion traps should allow one to access general properties of quantum critical systems. On the other hand, ion trap quantum spin models show a few unusual features due to the peculiarities of induced effective spin-spin interactions which lead to interesting effects like long-range quantum correlations and the coexistence of different spin phases.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • The authors present a novel path integral formulation for the effective field theory describing d-dimensional quantum spin models. The new approach avoids the coherent states representation, but at very low temperatures reproduces all known results obtained with the latter technique for describing excitations of the Neel state. The possibility of exploring higher-temperature, unbroken-symmetry state excitations (such as those appropriate for the quantum spin-liquid state) within this method is illustrated.
  • We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to themore » harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.« less
  • We derive an effective Hamiltonian that describes a cross-Kerr-type interaction in a system involving a two-level trapped ion coupled to the quantized field inside a cavity. We assume a large detuning between the ion and field (dispersive limit) and this results in an interaction Hamiltonian involving the product of the (bosonic) ionic vibrational motion and field number operators. We also demonstrate the feasibility of operation of a phase gate based on our Hamiltonian. The gate is insensitive to spontaneous emission, an important feature for the practical implementation of quantum computing.
  • We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
  • A Comment on the Letter by T. Mizushima, K. Machida, and M. Ichioka, Phys. Rev. Lett. 94, 060404 (2005)