Research progress of heat transport in trapped-ion crystals

Abstract

Heat transport is one of the most important research topics in physics. Especially in recent years, with deep study on single-molecule devices, people have been paying more and more attention to the problem of heat transport in low-dimensional (i.e., one- and two-dimensional) microsystems. In the research of Fermi-Pasta-Ulam crystals and harmonic crystals, it was widely accepted that heat conduction in low-dimensional systems does not follow Fourier's law. Due to absence of the equipment capable of directly measuring heat current, conducting relevant experiments is proven to be a challenging task. Ion crystals in ion traps are located in vacuum without energy exchange with the external environment. Their crystal structure and temperature can be accurately controlled by electric and optical fields, providing an ideal experimental platform for studying thermal conduction in low-dimensional crystals in classical or quantum states. This article summarizes the recent theoretical research on thermal conduction in ion crystals, including calculating methods of temperature distribution and steady-state heat current in one-dimensional, two-dimensional, and three-dimensional models, as well as the characteristics of heat current and temperature distribution under different ion crystal configurations. Because the nonlinear effect caused by the imbalance among three dimensions hinders the heat transport, the heat current in ion crystals is largest in the linear configuration while smallest in the zig-zag configuration. In addition, this article also introduces the influence of disorder on the thermal conductivity of ion crystals, encompassing the influence on the heat current across various ion crystal configurations such as the linear, the zig-zag and the helical.Notably, the susceptibility of ion crystals to disorder increases with their sizes. Specifically, the zig-zag ion crystal configurations exhibit the largest susceptibility to disorder, whereas linear configurations are least affected. Finally, this article provides a concise overview of experimental investigations for the heat conduction in low-dimensional systems. Examination of the heat conduction in ion crystals offers insights into various cooling techniques employed in ion trap systems, including sympathetic cooling, electromagnetic induced transparency cooling, and polarization gradient cooling. Similar to the macroscopic thermal diode crafted using thermal metamaterials, it is also possible to manufacture microscopic thermal diodes in low-dimensional systems.