Radiation damping of a polarizable particle

A polarizable body moving in an external electromagnetic field will slow down. This effect is referred to as radiation damping and is analogous to Doppler cooling in atomic physics. Using the principles of special relativity we derive an expression for the radiation damping force and find that it solely depends on the scattered power. The cooling of the particle's center-of-mass motion is balanced by heating due to radiation pressure shot noise, giving rise to an equilibrium that depends on the ratio of the field's frequency and the particle's mass. While damping is of relativistic nature, heating has its roots in quantum mechanics.

Figure 1

A particle moving at velocity $\mathbf{v}$ is irradiated by the field ${\mathbf{E}}_i$. The induced dipole $\mathbf{p}$ radiates a field ${\mathbf{E}}_s$ that is observed at location $\mathbf{r}$ and time $t$. In the particle frame, the location and the time are ${\mathbf{r}}^{\prime }$ and $t^{\prime }$, respectively.