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 $^{40}\mathrm{Ca}^{+}$ 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.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 $^{40}\mathrm{Ca}^{+}$ 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.

Physical Review ASep 30, 202013 citations

Crystallization of trapped ions—A quantum approach

Monique Combescure

Annals of PhysicsNov 1, 199018 citations

Ion Coulomb crystals: An exotic form of condensed matter

Giovanna Morigi, J. J. Bollinger, Michael Drewsen +2 more

Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $μ$ eV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $μ$eV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.

arXiv:2508.07374Reviews of Modern PhysicsMar 9, 20262 citations

Crystallization of trapped ions—A quantum approach

Annals of PhysicsSep 1, 19900 citations

^{40}\mathrm{Ca}^{+}

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.

Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of

μ

eV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.