Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

European Quantum Electronics Conference (EQEC)

Strong correlation in systems of trapped ions

Diego Porras, J. I. Cirac

Published Jan 18, 2006• 0 citations
Publisher

Abstract

In this paper, it is shown that trapped ions can also be used to study a variety of strongly correlated systems, from quantum spin models to systems of interacting bosons, something that would lead to the observation of quantum phase transitions and other phenomena of interest both in the fields of condensed matter and quantum Information.

DOI
10.1109/eqec.2005.1567395

Related papers

Strongly-correlated phases in trapped-ion quantum simulators

Pedro Nevado Serrano

We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.

•Jun 1, 2017•0 citations

Effective spin quantum phases in systems of trapped ions

Xiaolong Deng, Diego Porras, J. I. Cirac

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.

arXiv:quant-ph/0509197•Physical Review A•Dec 19, 2005•183 citations

Bose-Einstein Condensation and Strong-Correlation Behavior of Phonons in Ion Traps

Diego Porras, J. I. Cirac

We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition.

arXiv:quant-ph/0409015•Physical Review Letters•Dec 20, 2004•136 citations

Simulation of Quantum Spin Models and Phase Transitions with Trapped Ions

Diego Porras, J. I. Cirac

We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.

•Jan 1, 2005•2 citations

Experimental Realization of the Rabi-Hubbard Model with Trapped Ions

Q.-X. Mei, B.-W. Li, Y.-K. Wu +5 more

Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.

arXiv:2110.03227•Physical Review Letters•Apr 22, 2022•50 citations

Entanglement States in Ion Traps

Xiaolong Deng

This thesis is devoted to the theoretical study of strongly correlated quantum many-body states with trapped ions interacting with lasers. A system of trapped ions under the action of off--resonant standing--waves can be used to simulate a variety of quantum interacting models. Based on this idea we study in detail effective quantum spin models and Bose-Hubbard model in ion traps. Our numerical calculations with the DMRG show that experiments with ion traps should allow one to access general properties of quantum critical systems. Ion trap quantum spin models and Bose-Hubbard model show novel features due to the peculiarities of induced effective spin-spin and phonon-phonon interactions.

•Jan 1, 2007•0 citations
In this paper, it is shown that trapped ions can also be used to study a variety of strongly correlated systems, from quantum spin models to systems of interacting bosons, something that would lead to the observation of quantum phase transitions and other phenomena of interest both in the fields of condensed matter and quantum Information.
We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.
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 XYXYXY 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.
We show that trapped ions are ideally suited for the simulation of quantum spin systems and for the observation of a rich variety of quantum phase transitions. By changing the laser intensities and polarizations, the dynamics of the internal states of the ions can be controlled in such a way that an Ising or Heisenberg-like interaction is induced between effective spins. Our scheme allows us to build an analog quantum simulator of spin systems with trapped ions and to observe and analyze quantum phase transitions with unprecedented opportunities for the measurement and manipulation of spins. The requirements for our proposal are met by current technology: it does not rely on the use of quantum gates, and striking many-body effects can be observed even when the fidelity of the simulation is smaller than the one required for quantum computation. Our proposal with trapped ions would solve many of the problems that are faced in the implementation of quantum simulations with neutral atoms in optical lattices.
Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.
This thesis is devoted to the theoretical study of strongly correlated quantum many-body states with trapped ions interacting with lasers. A system of trapped ions under the action of off--resonant standing--waves can be used to simulate a variety of quantum interacting models. Based on this idea we study in detail effective quantum spin models and Bose-Hubbard model in ion traps. Our numerical calculations with the DMRG show that experiments with ion traps should allow one to access general properties of quantum critical systems. Ion trap quantum spin models and Bose-Hubbard model show novel features due to the peculiarities of induced effective spin-spin and phonon-phonon interactions.