Delocalization and heat transport in multidimensional trapped ion systems

Heat rectification, heat fluxes, and spectral matching

Heat rectifiers would facilitate energy management operations such as cooling or energy harvesting, but devices of practical interest are still missing. Understanding heat rectification at a fundamental level is key to helping us find or design such devices. The match or mismatch of the phonon band spectrum of device segments for forward or reverse temperature bias of the thermal baths at device boundaries was proposed as the mechanism behind rectification. However, no explicit theoretical relation derived from first principles had been found so far between heat fluxes and spectral matching. We study heat rectification in a minimalistic chain of two coupled ions. The fluxes and rectification can be calculated analytically. We propose a definition of the matching that sets an upper bound for the heat flux. In a regime where the device rectifies optimally, matching and flux ratios for forward and reverse configurations are found to be proportional. The results can be extended to a system of N particles in arbitrary traps with nearest-neighbor linear interactions.

Spatial configurations and temperature profiles in nonequilibrium steady state of two-species trapped ion systems

We study Coulomb crystals containing two ion species simultaneously confined in radio frequency traps and coupled to different thermal reservoirs located in two separate regions. We use a three-dimensional model to simulate the trapped bicrystal and show in a numerically rigorous manner the effects of the mass dependence of the trapping frequencies on the underlying nonequilibrium dynamics and the temperature profiles. By solving the classical Langevin equations of motion, we obtain the spatial probability densities of the two ion species and the kinetic temperature profiles across the axial direction of the trap in the nonequilibrium steady state. We analyze trapping conditions leading to bicrystals that exhibit ion conformations ranging from a linear chain of alternating ion species to two- and three-dimensional configurations. The results evidence the spatial segregation of the two ion species due to the mass dependence of the trapping frequencies and the increase of ion delocalization for heavier ion species and/or weaker trapping confinements. We also show the correlation between the increase of the temperature gradient in the bulk and this enhancement of ion delocalization through the trap.

Asymmetric heat transport in ion crystals

We numerically demonstrate heat rectification for linear chains of ions in trap lattices with graded trapping frequencies, in contact with thermal baths implemented by optical molasses. To calculate the local temperatures and heat currents we find the stationary state by solving a system of algebraic equations. This approach is much faster than the usual method that integrates the dynamical equations of the system and averages over noise realizations.