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arXiv:1610.02264 · Physical Review Letters

Will a Decaying Atom Feel a Friction Force?

Matthias Sonnleitner, Nils Trautmann, Stephen Mark Barnett

Published Feb 3, 2017• 36 citations
arXivHTMLPDF

Abstract

We show how a simple calculation leads to the surprising result that an excited two-level atom moving through a vacuum sees a tiny friction force of first order in v/c. At first sight this seems to be in obvious contradiction to other calculations showing that the interaction with the vacuum does not change the velocity of an atom. It is even more surprising that this change in the atom's momentum turns out to be a necessary result of energy and momentum conservation in special relativity.

DOI
10.1103/physrevlett.118.053601

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We show how a simple calculation leads to the surprising result that an excited two-level atom moving through a vacuum sees a tiny friction force of first order in v/c. At first sight this seems to be in obvious contradiction to other calculations showing that the interaction with the vacuum does not change the velocity of an atom. It is even more surprising that this change in the atom's momentum turns out to be a necessary result of energy and momentum conservation in special relativity.
It is known that, when an excited atom spontaneously emits one photon, two effects are produced. First, the atom's internal and external states are entangled with the states of the emitted photon. Second, the atom receives a momentum transfered from the photon. In this work, the dynamics of such an atom in vacuum is studied. Through a specific calculation, it is demonstrated that these effects cause the atom to experience, on average, a friction force opposite to its initial velocity. Properties of the force are also discussed.
The usual multipolar Hamiltonian for atom-light interaction features a nonrelativistic moving atom interacting with electromagnetic fields which inherently follow Lorentzian symmetry. This combination can lead to situations where atoms appear to experience a friction force, when in fact they only change their internal mass-energy due to the emission or absorption of a photon. Unfortunately, the simple Galilean description of the atom's motion is not sufficient to distinguish between a change in momentum due to acceleration and a change in momentum due to a change in internal mass-energy. In this work we show how a low-order relativistic correction can be included in the multipolar atom-light Hamiltonian. We also give examples how this affects the most basic mechanical interactions between atoms and photons.
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.
Our present investigation into a rather rudimentary problem is motivated by two classes of problems studied since the 70's, cosmological particle creation and its more accessible analog, the dynamical Casimir effect on the one hand, and quantum friction a neutral atom moving along a dielectric surface would experience, on the other. The backreaction effects of produced particles being able to isotropize the expansion of the universe, or to slow down the moving mirror can be understood via the concept of vacuum viscosity arising from fluctuations of the quantum field. We want to track down the origin of this effect by asking the question whether a moving massive MMM object with a charged internal degrees of freedom χχχ interacting with a free unbounded classical field φφφ at zero temperature would experience a viscous force, similar to the said precedents. Adopting a microphysics model for optomechanics which can treat the unequal tripartite χχχ-φφφ-MMM interactions, we first perform a nonrelativistic calculation, which seems perfectly legitimate considering the needs of atomic physics, and found the answer to be yes, but a relativistic covariant calculation says no. We identify where the nonrelativistic framework is defective. The resolution of this latent yet real conflict is technically nontrivial but physically quite inspirational. It results in added enriched contents to Newton's first and second laws when the principles of special relativity are enforced, and rules to follow to get the correct nonrelativistic answer
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 know that in empty space there is no preferred state of rest. This is true both in special relativity but also in Newtonian mechanics with its associated Galilean relativity. It comes as something of a surprise, therefore, to discover the existence a friction force associated with spontaneous emission. The resolution of this paradox relies on a central idea from special relativity even though our derivation of it is non-relativistic. We examine the possibility that the physics underlying this effect might be explored in an ion trap, via the observation of a superposition of different mass states.