Research progress of heat transport in trapped-ion crystals

Heat transport is one of the most important research topics in physics. Especially in recent years, with thein depth study on single-molecule devices, heat transport in low-dimensional (i.e. one- and two-dimensional)microsystems has received more and more attention. In the research of Fermi-Pasta-Ulam crystals and harmoniccrystals, it is widely accepted that heat conduction in low-dimensional system does not follow Fourier's law.Due to the lack of the equipment that can directly measure heat current, it has been proven to be a challengingtask to carry out relevant experiments. Ion crystal in ion trap is located in vacuum and does not exchangeenergy with the external environment. The crystal structure and temperature can be accurately controlled byelectric field and optical field, providing an ideal experimental platform for studying thermal conduction in low-dimensional crystals in classical state or quantum state. Herein we summarize the recent theoretical research onthermal conduction in ion crystals, including the methods of calculating temperature distribution and steady-state heat current in one-dimensional, two-dimensional, and three-dimensional models, as well as thecharacteristics of heat current and temperature distribution under different ion crystal configurations. Becausethe nonlinear effect caused by the imbalance among three dimensions hinders the heat transport, the heatcurrent in ion crystal is largest in the linear configuration while smallest in the zig-zag configuration. Inaddition, we also introduce the influence of disorder on the thermal conductivity of ion crystal, including theinfluence on the heat current across various ion crystal configurations such as the linear, the zig-zag and thehelical configuration. Notably, the susceptibility of ion crystal to disorder increases with crystal size increasing.Specifically, the zig-zag ion crystal configuration exhibits the largest susceptibility to disorder, whereas thelinear configuration is least affected. Finally, we provide a concise overview of experimental studies of the heatconduction in low-dimensional systems. Examination of the heat conduction in ion crystal offers a valuableinsight into various cooling techniques employed in ion trap systems, including sympathetic cooling,electromagnetically induced transparency cooling, and polarization gradient cooling. Just like macroscopicthermal diodes made by thermal metamaterials, it is possible that the microscopic thermal diodes can also bemade in low-dimensional systems.