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

Physical Review A

Phonon localization in an ion chain under irradiation with a Bessel laser beam

Jun Wen, Jian‐Qi Zhang, L.-L. Yan, Liang Chen, Xiaoming Cai, Mang Feng

Published Jul 16, 2018• 1 citation
Publisher

Abstract

Trapped ions offer an excellent platform to investigate fascinating phenomena in quantum physics. Here we propose an experimental scheme to achieve Anderson localization of phonons using an ion chain under irradiation of a laser Bessel beam. The quasiperiodicity comes from the characteristic of the Bessel beam, which is only relevant to the positions of the individual ions with respect to the standing wave of the Bessel beam, rather than the internal degrees of freedom of the ions. We demonstrate, by the inverse participation ratio, the delocalization-localization transition, which is sensitive to the strength and the phase of the Bessel beam laser. Our model involving long-range phonon hopping could present richer phenomena than the Aubry-Andr\'e model including only nearest-neighbor coupling.

DOI
10.1103/physreva.98.013829

Related papers

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

Jun Wen, Jian‐Qi Zhang, L.-L. Yan +1 more

Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization–delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.

Chinese Physics B•Jan 1, 2019•1 citation

The localization of phonons in ion traps with controlled quantum disorder

A. Bermúdez, Miguel Angel Martin-Delgado, Diego Porras

We show that the vibrations of a chain of trapped ions offer an interesting route to explore the physics of disordered quantum systems. By preparing the internal state of the ions in a quantum superposition, we show how the local vibrational energy becomes a stochastic variable, its statistical properties inherited from the underlying quantum parallelism of the internal state. We describe a minimally perturbing measurement of the resonance fluorescence, which allows us to study effects such as Anderson localization without the need for ground-state cooling or individual addressing and thus paves the way for high-temperature ion experiments.

arXiv:1002.3748•New Journal of Physics•Dec 9, 2010•34 citations

Properties of phonon modes of an ion-trap quantum computer in the Aubry phase

Justin Loye, José Lages, Dima L. Shepelyansky

We study analytically and numerically the properties of phonon modes in an ion quantum computer. The ion chain is placed in a harmonic trap with an additional periodic potential of which dimensionless amplitude $K$ determines three main phases available for quantum computations: at zero $K$ we have the case of Cirac-Zoller quantum computer, below a certain critical amplitude $K<{K}_{c}$ the ions are in the Kolmogorov-Arnold-Moser (KAM) phase, with delocalized phonon modes and free chain sliding, and above the critical amplitude $K>{K}_{c}$ ions are in the pinned Aubry phase with a finite frequency gap protecting quantum gates from temperature and other external fluctuations. For the Aubry phase, in contrast to the Cirac-Zoller and KAM phases, the phonon gap remains independent of the number of ions placed in the trap keeping a fixed ion density around the trap center. We show that in the Aubry phase the phonon modes are much better localized compared to the Cirac-Zoller and KAM cases. Thus in the Aubry phase the recoil pulses lead to local oscillations of ions, while in the other two phases they spread rapidly over the whole ion chains, making them rather sensible to external fluctuations. We argue that the properties of localized phonon modes and phonon gap in the Aubry phase provide advantages for the ion quantum computations in this phase with a large number of ions.

arXiv:2002.03730•Physical Review A•Mar 30, 2020•5 citations

Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain

Shantanu Debnath, Norbert M. Linke, Sheng-Tao Wang +4 more

The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.

arXiv:1711.00216•Physical Review Letters•Feb 12, 2018•52 citations

Simulation of a quantum phase transition of polaritons with trapped ions

Peter A. Ivanov, Svetoslav S. Ivanov, Nikolay V. Vitanov +3 more

We present a system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tuning of the hopping frequency by adjusting the axial trapping frequency and the phonon-phonon repulsion via laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.

arXiv:0905.2593•Physical Review A•Dec 3, 2009•66 citations

Controlled melting of a Wigner ion crystal with atomic resolution

Yong Xu, W.-D. Zhao, YunLei Hou +7 more

The solid-liquid phase transition (melting) is a long-standing problem for which a complete understanding is challenging because of the strong many-body interactions. A trapped-ion Wigner crystal is a suitable platform for a controlled study of this phase transition with its unprecedented resolution of individual atomic ions. Here we study the melting dynamics of a linear chain of $^{174}\mathrm{Yb}^{+}$ ions, which is initially cooled to the Doppler temperature and is then periodically heated and detected by a focused laser beam. We achieve controlled melting of the ion chain and observe unusual partial melting of long chains (coexistence of solid and liquid phases). We also observe a counterintuitive nonuniform energy distribution over the chain under localized heating. These results are further confirmed by molecular dynamics simulations to rule out other heating mechanisms.

Physical Review A•Dec 28, 2020•5 citations
Trapped ions offer an excellent platform to investigate fascinating phenomena in quantum physics. Here we propose an experimental scheme to achieve Anderson localization of phonons using an ion chain under irradiation of a laser Bessel beam. The quasiperiodicity comes from the characteristic of the Bessel beam, which is only relevant to the positions of the individual ions with respect to the standing wave of the Bessel beam, rather than the internal degrees of freedom of the ions. We demonstrate, by the inverse participation ratio, the delocalization-localization transition, which is sensitive to the strength and the phase of the Bessel beam laser. Our model involving long-range phonon hopping could present richer phenomena than the Aubry-Andr'e model including only nearest-neighbor coupling.
Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization–delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.
We show that the vibrations of a chain of trapped ions offer an interesting route to explore the physics of disordered quantum systems. By preparing the internal state of the ions in a quantum superposition, we show how the local vibrational energy becomes a stochastic variable, its statistical properties inherited from the underlying quantum parallelism of the internal state. We describe a minimally perturbing measurement of the resonance fluorescence, which allows us to study effects such as Anderson localization without the need for ground-state cooling or individual addressing and thus paves the way for high-temperature ion experiments.
We study analytically and numerically the properties of phonon modes in an ion quantum computer. The ion chain is placed in a harmonic trap with an additional periodic potential of which dimensionless amplitude KKK determines three main phases available for quantum computations: at zero KKK we have the case of Cirac-Zoller quantum computer, below a certain critical amplitude K<KcK<{K}_{c}K<Kc​ the ions are in the Kolmogorov-Arnold-Moser (KAM) phase, with delocalized phonon modes and free chain sliding, and above the critical amplitude K>KcK>{K}_{c}K>Kc​ ions are in the pinned Aubry phase with a finite frequency gap protecting quantum gates from temperature and other external fluctuations. For the Aubry phase, in contrast to the Cirac-Zoller and KAM phases, the phonon gap remains independent of the number of ions placed in the trap keeping a fixed ion density around the trap center. We show that in the Aubry phase the phonon modes are much better localized compared to the Cirac-Zoller and KAM cases. Thus in the Aubry phase the recoil pulses lead to local oscillations of ions, while in the other two phases they spread rapidly over the whole ion chains, making them rather sensible to external fluctuations. We argue that the properties of localized phonon modes and phonon gap in the Aubry phase provide advantages for the ion quantum computations in this phase with a large number of ions.
The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.
We present a system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tuning of the hopping frequency by adjusting the axial trapping frequency and the phonon-phonon repulsion via laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.
The solid-liquid phase transition (melting) is a long-standing problem for which a complete understanding is challenging because of the strong many-body interactions. A trapped-ion Wigner crystal is a suitable platform for a controlled study of this phase transition with its unprecedented resolution of individual atomic ions. Here we study the melting dynamics of a linear chain of 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ ions, which is initially cooled to the Doppler temperature and is then periodically heated and detected by a focused laser beam. We achieve controlled melting of the ion chain and observe unusual partial melting of long chains (coexistence of solid and liquid phases). We also observe a counterintuitive nonuniform energy distribution over the chain under localized heating. These results are further confirmed by molecular dynamics simulations to rule out other heating mechanisms.