Quantum friction in arbitrarily directed motion

Quantum friction, the electromagnetic fluctuation-induced frictional force decelerating an atom which moves past a macroscopic dielectric body, has so far eluded experimental evidence despite more than three decades of theoretical studies. Inspired by the recent finding that dynamical corrections to such an atom's internal dynamics are enhanced by one order of magnitude for vertical motion—compared with the paradigmatic setup of parallel motion—we generalize quantum friction calculations to arbitrary angles between the atom's direction of motion and the surface in front of which it moves. Motivated by the disagreement between quantum friction calculations based on Markovian quantum master equations and time-dependent perturbation theory, we carry out our derivations of the quantum frictional force for arbitrary angles by employing both methods and compare them.

Figure 1

Atom moving next to a macroscopic body with velocity $\mathit{v}$ at zero temperature. The atomic charge distribution fluctuates, which leads to a rearrangement of the charged constituents in the body and thereby to the buildup of mirror charge distributions. For the resting atom, this interaction with the mirror image leads to the Casimir–Polder (CP) force ${\mathit{F}}_{\text{CP}}$ attracting the atom towards the surface. In case of relative motion, the spatial distribution of former mirror images leads to a tilt of the total force $\mathit{F}$. Additionally to the normal CP force, the atom experiences then a force ${\mathit{F}}_v$ which counteracts the relative motion.