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Physica A Statistical Mechanics and its Applications

Quantum friction in a periodic potential

A. D. Jannussis, A. Leodaris, V. Papatheou, N. Patargias, Kostas Vlachos

Published Apr 1, 1981• 2 citations
Publisher
DOI
10.1016/0378-4371(81)90130-8

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Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations
The quantum motion of nuclei, generally ignored in the physics of sliding friction, can affect in an important manner the frictional dissipation of a light particle forced to slide in an optical lattice. The density matrix-calculated evolution of the quantum version of the basic Prandtl-Tomlinson model, describing the dragging by an external force of a point particle in a periodic potential, shows that purely classical friction predictions can be very wrong. The strongest quantum effect occurs not for weak but for strong periodic potentials, where barriers are high but energy levels in each well are discrete, and resonant Rabi or Landau-Zener tunneling to states in the nearest well can preempt classical stick-slip with nonnegligible efficiency, depending on the forcing speed. The resulting permeation of otherwise unsurmountable barriers is predicted to cause quantum lubricity, a phenomenon which we expect should be observable in the recently implemented sliding cold ion experiments.
Friction in atomistic systems is usually described by the classical Prandtl-Tomlinson model suitable for capturing the dragging force of a nanoparticle in a periodic potential. Here we consider the quantum mechanical version of this model in which the dissipation is facilitated by releasing heat to an external bath reservoir. The time evolution of the system is captured with the Liouville-von Neumann equation through the density matrix of the system in the Markov approximation. We examine several kinetic and dissipative properties of the nanoparticle by delineating classical vs quantum mechanical effects. We find that the Landau-Zener tunneling is a key factor in the overall reduction of the frictional dissipation when compared to the classical motion in which such tunneling is absent. Other regimes of motion, controlled by the corrugation parameter and other properties, are also found. This in-depth study analyzes the interplay between velocity, strength of interaction, and temperature to control the frictional force and provide useful guidelines for experimental data interpretation.
We have investigated the localization of atoms in two configurations of laser fields: monochromatic and bichromatic standing waves. A quasi resonant monochromatic laser field creates a spatially periodic potential field with period equal to half of the wavelength. If the atomic kinetic energy is less than the height of the potential wells then atoms could be trapped in the wells. The motion of atoms in a standing wave is governed by the gradient force, friction force, and momentum diffusion. We studied one dimensional localization of sodium atoms in such a standing wave, as well as the influence of friction and diffusion on the motion of these atoms. The effect of accumulation of atoms at the bottom of potential wells (nodes of a standing wave) was observed. This leads to a new scheme of laser cooling of atoms with a minimum temperature below the Doppler limit.