Quantum Rolling Friction

An atom moving in a vacuum at constant velocity and parallel to a surface experiences a frictional force induced by the dissipative interaction with the quantum fluctuations of the electromagnetic field. We show that the combination of nonequilibrium dynamics, the anomalous Doppler effect, and spin-momentum locking of light mediates an intriguing interplay between the atom’s translational and rotational motion. In turn, this deeply affects the drag force in a way that is reminiscent of classical rolling friction. Our fully non-Markovian and nonequilibrium description reveals counterintuitive features characterizing the atom’s velocity-dependent rotational dynamics. These results prompt interesting directions for tuning the interaction and for investigating nonequilibrium dynamics as well as the properties of confined light.

Figure 1

Schematic description of the two mechanisms behind Eqs. (1). (a) In the near field two counterpropagating virtual surface excitations give rise to spin-zero photons (corresponding to a linearly polarized electromagnetic field $\mathbf{E}$) that are absorbed by the atom, which gets excited (anomalous Doppler effect). The atom then emits linearly polarized photons, predominantly in the direction of the motion. The corresponding recoil momentum gives rise to ${\mathbf{F}}^t$. (b) When the atomic rotational degrees of freedom are involved in the dynamics, the atom can also absorb photons with nonzero spin (corresponding to circularly polarized electromagnetic field $\mathbf{E}$). For a motion along the positive $x$ axis, surface excitations with negative spin are predominantly absorbed, producing a clockwise rotation of the atom around the $y$ axis. In this case, the atom prevalently emits photons with nonzero spin in the negative $x$ direction, corresponding to the recoil force ${\mathbf{F}}^r$ oriented in the direction of the motion.

Figure 2

Frictional acceleration, $a=a^t+a^r$, on a ${}^{87}\mathrm{Rb}$ atom (${\alpha }_0=4\pi {\epsilon }_0\times 47.28{\AA }^3$, ${\omega }_a=1.3\mathrm{eV}$, $m_{\mathrm{Rb}}=86.9$ u [28]) as a function of its velocity. The particle moves at $z_a=5\mathrm{nm}$ from a gold surface, described by a Drude permittivity $\epsilon (\omega )=1-{\omega }_p^2/[\omega (\omega +\mathrm{i}\mathrm{\Gamma }){]}^{-1}$ (${\omega }_p=9\mathrm{eV}$, $\mathrm{\Gamma }=35\mathrm{meV}$ [29], giving $\rho =\mathrm{\Gamma }/[{\epsilon }_0{\omega }_p^2]=3.21\times {10}^{-8}\mathrm{\Omega }\mathrm{m}$). The two competing contributions $a^t$ (dash-dotted line) and $a^r$ (dashed line) in Eqs. (1) are represented. At small velocity the total acceleration (full line) scales as the sum of the expressions in Eq. (6) divided by the atomic mass (dotted line), while at high velocity friction is enhanced by a resonant interaction [21]. The inset shows that at low velocities $F^r$ compensates more than 70% of $F^t$. The percentage decreases at higher velocity.