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arXiv:1902.07738 · Physical Review A

Zeno friction and antifriction from quantum collision models

Daniel Grimmer, Achim Kempf, Robert B. Mann, Eduardo Martín-Martínez

Published Oct 2, 2019• 5 citations
arXivHTMLPDF

Abstract

We analyze the quantum mechanics of the friction experienced by a small system as it moves nondestructively with velocity $v$ over a surface. Specifically, we model the interactions between the system and the surface with a collision model. We show that under weak assumptions, the magnitude of the friction induced by this interaction decreases as $1/v$ for large velocities. Specifically, we predict that this phenomenon occurs in the Zeno regime, where each of the system's successive couplings to subsystems of the surface is very brief. In order to investigate the friction at low velocities and with velocity-dependent coupling strengths, we motivate and develop one-dimensional convex collision models. Within these models, we obtain an analytic expression for the general friction-velocity dependence. We are thus able to exactly determine the conditions under which the usual friction-velocity dependency arises. Finally, we give examples that demonstrate the possibility, in principle, of antifriction, in which case the system is accelerated by its interaction with the surface, a phenomenon associated with active materials and inverted level populations.

DOI
10.1103/physreva.100.042702

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We analyze the quantum mechanics of the friction experienced by a small system as it moves nondestructively with velocity vvv over a surface. Specifically, we model the interactions between the system and the surface with a collision model. We show that under weak assumptions, the magnitude of the friction induced by this interaction decreases as 1/v1/v1/v for large velocities. Specifically, we predict that this phenomenon occurs in the Zeno regime, where each of the system's successive couplings to subsystems of the surface is very brief. In order to investigate the friction at low velocities and with velocity-dependent coupling strengths, we motivate and develop one-dimensional convex collision models. Within these models, we obtain an analytic expression for the general friction-velocity dependence. We are thus able to exactly determine the conditions under which the usual friction-velocity dependency arises. Finally, we give examples that demonstrate the possibility, in principle, of antifriction, in which case the system is accelerated by its interaction with the surface, a phenomenon associated with active materials and inverted level populations.
Quantum mechanics predicts the occurrence of random electromagnetic field fluctuations, or virtual photons, in vacuum. The exchange of virtual photons between two bodies in relative motion could lead to non-contact quantum vacuum friction or Casimir friction. Despite its theoretical significance, the non-contact Casimir frictional force has not been observed and its theoretical predictions have varied widely. In this work, we report the first measurement of the non-contact Casimir frictional force between two moving bodies. By employing two mechanical oscillators with resonant frequencies far lower than those in Lorentz models of electrons in dielectric materials, we have amplified the Casimir frictional force at low relative velocities by several orders of magnitude. We directly measure the non-contact Casimir frictional force between the two oscillators and show its linear dependence on velocity, proving the dissipative nature of Casimir friction. This advancement marks a pivotal contribution to the field of dissipative quantum electrodynamics and enhances our understanding of friction at the nanoscale.
We report on a microscopic theory of quantum friction. Our approach investigates the interplay between the dispersive response and the relative center-of-mass motion of two ground-state atoms. This coupling yields a quantum force, which can be expressed as a power series in the velocity. The significance of each contribution depends on its order parity: while even-order terms are reversible, odd-order terms are irreversible and only survive in the presence of an internal dissipation mechanism. In addition, we obtain general, model-independent properties for the work performed by these contributions for arbitrary scattering trajectories. These results enable an unambiguous identification of odd-parity terms with microscopic quantum friction. At room temperature, the dominant microscopic quantum friction is of first order in the velocity and presents a strong quantum character. Our microscopic theory reveals that several properties of quantum friction obtained in specific settings -- such as the cubic dependence on velocity at zero temperature -- are indeed universal features already present at the atomic scale.
Bodies in relative motion, spatially separated in vacuum, experience a tiny friction force known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. Herein, we give quantitative details so as to track traces of the quantum friction by measuring coherences in the atom. We notice that the environmentally induced decoherence can be decomposed into contributions of different signature: corrections induced by the electromagnetic vacuum in the presence of the dielectric sheet and those induced by the motion of the particle. In this direction, we show that noncontact friction enhances the decoherence of the moving atom. Further, its effect can be enlarged by a thorough selection of the two-level particle and the Drude-Lorentz parameters of the material. In this context, we suggest that measuring decoherence times through velocity dependence of coherences could indirectly demonstrate the existence of quantum friction.
We present a formula for the spectroscopically accessible level shifts and decay rates of an atom moving at an arbitrary angle relative to a surface. Our Markov formulation leads to an intuitive analytic description whereby the shifts and rates are obtained from the coefficients of the Heisenberg equation of motion for the atomic flip operators but with complex Doppler-shifted (velocity-dependent) transition frequencies. Our results conclusively demonstrate that for the limiting case of parallel motion the shifts and rates are quadratic or higher in the atomic velocity. We show that a stronger, linear velocity dependence is exhibited by the rates and shifts for perpendicular motion, thus opening the prospect of experimentally probing the Markovian approach to the phenomenon of quantum friction.
Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is already different from the previously studied population-decay problem, even without taking into account any back action from the environment. For many two-level systems interacting with a common environment, multiple transitions between Zeno and anti-Zeno regimes are predicted. Finally, if the system-environment coupling strength is not weak, we show that the nontrivial evolution of the environment between measurements can considerably alter the quantum Zeno and anti-Zeno effects. This is qualitatively different from population-decay models where the environment state is reset to equilibrium after each measurement.
Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature). The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the anti-Zeno effect has already been observed, though not recognized as such.