It is currently thought that the laser cooling of an ordered ion array, an ion crystal, is qualitatively the same as that of a single ion. We show that this assumption is strongly violated in recent experiments in Paul traps, due to ion micromotion. Our analysis demonstrates an unexpected laser damping instability that induces an ion-crystal order-chaos transition and also explains why ion crystals in Paul traps have been limited to less than 100 ions. We directly observe the effects of ion micromotion on the laser cooling of a single trapped ${\mathrm{Ba}}^{+}$ ion by a new technique.It is currently thought that the laser cooling of an ordered ion array, an ion crystal, is qualitatively the same as that of a single ion. We show that this assumption is strongly violated in recent experiments in Paul traps, due to ion micromotion. Our analysis demonstrates an unexpected laser damping instability that induces an ion-crystal order-chaos transition and also explains why ion crystals in Paul traps have been limited to less than 100 ions. We directly observe the effects of ion micromotion on the laser cooling of a single trapped ${\mathrm{Ba}}^{+}$ ion by a new technique.

Physical Review AMay 1, 198968 citations

Structural phase transition of the ion crystals embedded in an optical lattice

Zhi-Chao Liu, Liang Chen, Ji Li +6 more

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

Laser Cooling of Trapped Ions

Ferdinand Schmidt‐Kaler, Jürgen Eschner, R. Blatt +3 more

Springer eBooksJan 1, 200210 citations

Optimizing Doppler laser cooling protocols for quantum sensing with 3D ion crystals in a Penning trap

John Zaris, Wes Johnson, Athreya Shankar +4 more

Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$ , in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.

quant-pharXiv:2602.22541Feb 27, 20260 citations

{\mathrm{Ba}}^{+}

ion by a new technique.

^{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.

N

, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to

10^5

ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated

\boldsymbol{E}\times\boldsymbol{B}

modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.