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

arXiv:1210.8349 · Physical Review A

Topological phenomena in trapped-ion systems

Tao Shi, J. I. Cirac

Published Jan 8, 2013• 17 citations
arXivHTMLPDF

Abstract

We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with nontrivial topological properties, which are caused by the breaking of time-reversal symmetry induced by the lasers. We investigate the appearance of edge modes, as well as their robustness against perturbations. Long-range hopping of phonons caused by the Coulomb interaction gives rise to flat bands which, together with induced phonon-phonon interactions, can be used to produce and explore strongly correlated states. Furthermore, some of these ideas can also be implemented with cold atoms in optical lattices.

DOI
10.1103/physreva.87.013606

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

Observation of a Topological Berry Phase with a Single Phonon in an Ion Microtrap Array

Justin F. Niedermeyer, Nathan K. Lysne, Katherine C. McCormick +11 more

Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 $μ$m on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.

quant-pharXiv:2512.08037•Dec 10, 2025•0 citations

Artificial magnetic fields in spin chains with long-range interactions - fractal energy spectra and topological phases

Tobias Graß, Christine A. Muschik, Alessio Celi +2 more

Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here, we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with non-vanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in waveguides are given.

•Dec 18, 2014•0 citations

Excitation band topology and edge matter waves in Bose–Einstein condensates in optical lattices

Shunsuke Furukawa, Masahito Ueda

We show that Bose–Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose–Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.

arXiv:1506.04556•New Journal of Physics•Nov 27, 2015•49 citations

Synthetic magnetic fluxes and topological order in one-dimensional spin systems

Tobias Graß, Christine A. Muschik, Alessio Celi +2 more

Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely, trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with nonvanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in wave guides are given.

arXiv:1412.6059•Physical Review A•Jun 11, 2015•44 citations

Effects of smooth boundaries on topological edge modes in optical lattices

Michael Buchhold, Daniel Cocks, Walter Hofstetter

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.

arXiv:1204.0016•Physical Review A•Jun 18, 2012•68 citations
We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with nontrivial topological properties, which are caused by the breaking of time-reversal symmetry induced by the lasers. We investigate the appearance of edge modes, as well as their robustness against perturbations. Long-range hopping of phonons caused by the Coulomb interaction gives rise to flat bands which, together with induced phonon-phonon interactions, can be used to produce and explore strongly correlated states. Furthermore, some of these ideas can also be implemented with cold atoms in optical lattices.
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.
Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 μμμm on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.
Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here, we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with non-vanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in waveguides are given.
We show that Bose–Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose–Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.
Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely, trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with nonvanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in wave guides are given.
Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.