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Scientific Reports

Exploring structural phase transitions of ion crystals

L.-L. Yan, Wei Wan, Liang Chen, Fei Zhou, Shijing Gong, X. Tong, Mang Feng

Published Feb 11, 2016• 44 citations
Publisher

Abstract

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.

DOI
10.1038/srep21547

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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.
Thermal fluctuation usually damages observations in physical systems. But here we demonstrate a unique contribution made by thermal fluctuation, that is, our observation of linear-zigzag phase transitions induced solely by temperature of the 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion crystals in a surface-electrode trap. In contrast to the previously observed counterparts based on change in the mechanical equilibrium conditions of the ions, our presented structural phase transition occurs due to controllable influence of thermal fluctuation. The ions' temperature is well controlled by tuning the cooling laser and the experimental observation could be fully understood by classical Langevin equation in addition to the effects from thermal fluctuation. Our experimental investigation indicates the possibility of the positive role thermal fluctuation played in the thermodynamic process at the atomic level, which might bridge the thermodynamics from the macroscopic domain to the quantum regime.
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.
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.
The structural phase transition (SPT) occurring in trapped-ion systems is a typical many-body physics, and the SPT induced by the thermal effect represents a special thermodynamic phenomenon between traditional thermodynamics and quantum thermodynamics. We explore this thermal-effect-induced SPT by embedding trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion crystals in an optical lattice, in which the ion crystals are confined by a surface-electrode trap and laser-cooled down to a temperature of several millikelvins. The considered thermal effect, leading to a temperature variation of tens of microkelvins in the SPT, comes completely from the optical lattice, which is independent of the laser irradiation regarding cooling of the ion crystals. In comparison with previous work [J. Li et al., Phys. Rev. A 99, 063402 (2019)], the present investigation helps to further clarify the effect of thermal fluctuation and further explore the positive role of the fluctuation in thermodynamics at the atomic level, even for potentially practical applications.
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.