  In this work, we study quantum heat transport in a single trapped ion, driven
by laser excitation and coupled to thermal reservoirs operating at different
temperatures. Our focus lies in understanding how different laser coupling
scenarios impact the system dynamics. As the laser intensity reaches a regime
where the ion's electronic and motional degrees of freedom strongly couple,
traditional approaches using phenomenological models for thermal reservoirs
become inadequate. Therefore, the adoption of the dressed master equation (DME)
formalism becomes crucial, enabling a deeper understanding of how distinct
laser intensities influence heat transport. Analyzing the heat current within
the parameter space defined by detuning and coupling strength, we observe
intriguing circular patterns which are influenced by the ion's vibrational
frequency and laser parameters, and reveal nuanced relationships between heat
transport, residual coherence, and system characteristics. Our study also
reveals phenomena such as negative differential heat conductivity and asymmetry
in heat current flow, offering insights into the thermal properties of this
essential quantum technology setup.
