Vacuum Friction on a Rotating Pair of Atoms

Zero-point quantum fluctuations of the electromagnetic vacuum create the widely known London–van der Waals attractive force between two atoms. Recently, there has been a revived interest in the interaction of rotating matter with the quantum vacuum. Here, we consider a rotating pair of atoms maintained by London–van der Waals forces and calculate the frictional torque they experience due to zero-point radiation. Using a semiclassical framework derived from the fluctuation dissipation theorem, we take into account the full electrostatic coupling between induced dipoles. Considering the case of zero temperature only, we find a braking torque proportional to the angular velocity and to the third power of the fine structure constant. Although very small compared to London–van der Waals attraction, the torque is strong enough to induce the formation of dimers in binary collisions. This new friction phenomenon at the atomic level should induce a paradigm change in the explanation of irreversibility.

Figure 1

A rotating pair of atoms. The atomic pair represented in its rotation plane. In the inertial frame $\overrightarrow{I},\overrightarrow{J},\overrightarrow{K}$ (upper case letters), the segment linking the two oscillators turns with angular velocity $\mathrm{\Omega }$; its unit vector, fixed in the rotating frame $\overrightarrow{i},\overrightarrow{j},\overrightarrow{k}$ (italic lowercase letters), is $\overrightarrow{i}=\text{cos}\theta \overrightarrow{I}+\text{sin}\theta \overrightarrow{J}$ with $\theta =\mathrm{\Omega }t$.

Figure 2

Effect of the dissipative torque on a binary collision. (a) The effective potential (van der $\text{Waals}+\text{centrifugal}$) seen by the two-atom system depends on the angular momentum $L$. Effective energy for $L^2=10{\hslash }^2$ (solid line); the apex is at $(r/a_0)\sim 4.5$ for an effective energy $V_{\mathrm{eff}}$ (dashed line). (b) Numerical integration of the classical dynamics of the two atoms with $L^2=10{\hslash }^2$ and effective energy slightly under $V_{\mathrm{eff}}$. The plain line takes into account the dissipative torque (9), while the dashed line does not. In both cases, the system is “orbiting” at $(r/a_0)\sim 4.5$. If no energy is lost to the field, the dynamics is reversible and the atoms finally separate. Vacuum friction prevents the separation and finally induces the two atoms to fall one towards the other.