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:2503.02109 · Entropy

Structural Transitions and Melting of Two-Dimensional Ion Crystals in RF Traps

B. V. Pashinsky, Alexander Kato, B. B. Blinov

Published Mar 21, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate the structural properties and melting behaviors of two-dimensional ion crystals in an RF trap, focusing on the effects of ion temperature and trap potential symmetry. We identify distinct crystal structures that form under varying trapping conditions and temperatures through experimental observations and theoretical analyses. As the temperature increases or the trap potential becomes more symmetric, we observe a transition from a lattice arrangement to elongated ring-like formations aligned along the trap axes. Our experimental and theoretical efforts enhance our understanding of phase transitions in low-dimensional, confined systems, offering insights into the controlled formation of quantum crystals for applications in quantum simulations and many-body physics.

DOI
10.3390/e27040325

Related papers

Exploring structural phase transitions of ion crystals

L.-L. Yan, Wei Wan, Liang Chen +4 more

Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled (40)Ca(+) ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.

Scientific Reports•Feb 11, 2016•44 citations

Structure and dynamics of ion clusters in linear octupole traps: Phase diagrams, chirality, and melting mechanisms

Ersin Yurtsever, E. Doruk Onal, F. Calvo

The stable structures and melting dynamics of clusters of identical ions bound by linear octupole radiofrequency traps are theoretically investigated by global optimization methods and molecular dynamics simulations. By varying the cluster sizes in the range of 10--1000 ions and the extent of trap anisotropy by more than one order of magnitude, we find a broad variety of stable structures based on multiple rings at small sizes evolving into tubular geometries at large sizes. The binding energy of these clusters is well represented by two contributions arising from isotropic linear and octupolar traps. The structures generally exhibit strong size effects, and chiral arrangements spontaneously emerge in many crystals. Sufficiently large clusters form nested, coaxial tubes with different thermal stabilities. As in isotropic octupolar clusters, the inner tubes melt at temperatures that are lower than the overall melting point.

Physical Review A•May 24, 2011•6 citations

Radial Two-Dimensional Ion Crystals in a Linear Paul Trap

Marissa D’Onofrio, Yuanheng Xie, A. J. Rasmusson +3 more

We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.

arXiv:2012.12766•Physical Review Letters•Jul 9, 2021•40 citations

Multiple structural phase transitions in trapped ion Coulomb crystals

Dawei Liu, Ying Jiang, M. T. Song +2 more

Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 2, 2025•0 citations

Two-dimensional ion crystals in radio-frequency traps for quantum simulation

Philip Richerme

The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental ion trap quantum simulation is a promising approach for studying these lattice spin models, but has so far been limited to one-dimensional systems. This work argues that such quantum simulation techniques are extendable to a two-dimensional (2D) ion crystal confined in a radio-frequency (rf) trap. Using appropriately chosen parameters, driven ion motion due to the rf fields can be made small and will not limit the types of quantum spin models that can be experimentally encoded. The rf-driven motion is calculated to modestly reduce the stability region of a 2D crystal and must be considered when designing the 2D trap. The system will be scalable to 100+ quantum particles, far beyond the realm of classical intractability, while maintaining the traditional ion trap strengths of individual-ion control, long quantum coherence times, and site-resolved projective spin measurements.

arXiv:1604.08523•Physical Review A•Sep 20, 2016•44 citations

Crystallization of Ca+ ions in a linear rf octupole ion trap

K. Okada, Kazuhiro Yasuda, Toshinobu Takayanagi +3 more

A laser-cooling experiment with ${\mathrm{Ca}}^{+}$ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled ${\mathrm{Ca}}^{+}$ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.

Physical Review A•Mar 22, 2007•52 citations
We investigate the structural properties and melting behaviors of two-dimensional ion crystals in an RF trap, focusing on the effects of ion temperature and trap potential symmetry. We identify distinct crystal structures that form under varying trapping conditions and temperatures through experimental observations and theoretical analyses. As the temperature increases or the trap potential becomes more symmetric, we observe a transition from a lattice arrangement to elongated ring-like formations aligned along the trap axes. Our experimental and theoretical efforts enhance our understanding of phase transitions in low-dimensional, confined systems, offering insights into the controlled formation of quantum crystals for applications in quantum simulations and many-body physics.
Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled (40)Ca(+) ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.
The stable structures and melting dynamics of clusters of identical ions bound by linear octupole radiofrequency traps are theoretically investigated by global optimization methods and molecular dynamics simulations. By varying the cluster sizes in the range of 10--1000 ions and the extent of trap anisotropy by more than one order of magnitude, we find a broad variety of stable structures based on multiple rings at small sizes evolving into tubular geometries at large sizes. The binding energy of these clusters is well represented by two contributions arising from isotropic linear and octupolar traps. The structures generally exhibit strong size effects, and chiral arrangements spontaneously emerge in many crystals. Sufficiently large clusters form nested, coaxial tubes with different thermal stabilities. As in isotropic octupolar clusters, the inner tubes melt at temperatures that are lower than the overall melting point.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
Abstract We investigate the structural transitions of ion Coulomb crystals (ICCs) using molecular dynamics simulations, focusing on the effects of ion number and the anisotropy of the confining potential. Our simulations reveal transitions from linear to zigzag to shell formation and dissolution to a two-dimensional plane finally. We characterized the phase transition points, the number of phase transitions. This study provides a more detailed analysis than previous works and establishes a power-law relationship between the critical anisotropy parameter and ion number. Our results offer valuable insights for the precise determination of ICC structure, trapped ion counting, and trapping potential parameters in experimental settings.
The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental ion trap quantum simulation is a promising approach for studying these lattice spin models, but has so far been limited to one-dimensional systems. This work argues that such quantum simulation techniques are extendable to a two-dimensional (2D) ion crystal confined in a radio-frequency (rf) trap. Using appropriately chosen parameters, driven ion motion due to the rf fields can be made small and will not limit the types of quantum spin models that can be experimentally encoded. The rf-driven motion is calculated to modestly reduce the stability region of a 2D crystal and must be considered when designing the 2D trap. The system will be scalable to 100+ quantum particles, far beyond the realm of classical intractability, while maintaining the traditional ion trap strengths of individual-ion control, long quantum coherence times, and site-resolved projective spin measurements.
A laser-cooling experiment with Ca+{\mathrm{Ca}}^{+}Ca+ ions trapped in a linear rf octupole ion trap is presented. The phase transition of the laser-cooled Ca+{\mathrm{Ca}}^{+}Ca+ ions from the cloud to the crystal state is observed by an abrupt dip of the laser-induced fluorescence spectrum and indicates that mK temperatures are obtained. We have also performed molecular dynamics simulations under various conditions to confirm this property by deducing axially symmetric structures of Coulomb crystals and by evaluating the translational temperatures of the laser-cooled ions. The simulation results show that for small numbers of ions novel ring-shaped crystals are produced. As the number of ions is increased, cylindrical layers in the ring crystal are sequentially formed. For more than 100 ions, also hexagonal and spiral structures emerge in parts of the large-size ion crystal, which has a length on the order of millimeters for the present geometrical arrangement and voltages. An advantage of the linear rf octupole trap is its large almost-field-free region in the middle of the trap, where the micromotion amplitude is small for trapped ions. These results demonstrate that such a multipole trap has attractive features for quantum computing and ultracold ion-atom collision studies.