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arXiv:1601.02765 · Physical Review A

Spectroscopic signatures of quantum friction

Juliane Klatt, Robert G. Bennett, Stefan Yoshi Buhmann

Published Dec 1, 2016• 26 citations
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Abstract

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.

DOI
10.1103/physreva.94.063803

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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.
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.
Casimir-Polder interactions cause energy and momentum exchange between microscopic and macroscopic bodies, a process mediated by quantum fluctuations in the coupled matter-electromagnetic field system. The dynamics of such effects are yet to be experimentally investigated due to the dominance of static effects at currently attainable atomic velocities. However, Y. Guo and Z. Jacob [Opt. Express 22, 26193 (2014)] have proposed a nonstatic two-plate setup where quantum-fluctuation-mediated effects have a strong velocity-dependent resonance, leading to a giant friction force on the plates. Here a more easily realizable setup, a moving atom between two stationary plates, is analyzed within a QED framework to establish the spectroscopic Casimir-Polder effects on the atom and their velocity dependence. While no large velocity-dependent enhancement is found, expressions for the plate-induced spectroscopic effects on the atom were found and further shown to be equivalent to the Doppler-shifted static result within certain velocity constraints. A numerical analysis investigates the behavior of this system for the well-studied case of the $6{D}_{3/2}\ensuremath{\rightarrow}7{P}_{1/2}$ transition in 133Cs^{133}\mathrm{Cs}133Cs interacting with sapphire plates.
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.
The description of an open quantum system's decay almost always requires several approximations so as to remain tractable. In this Letter, we first revisit the meaning, domain, and seeming contradictions of a few of the most widely used of such approximations: (semigroup) Markovianity, linear response theory, Wigner-Weisskopf approximation, and rotating-wave approximation. Second, we derive an effective time-dependent decay theory and corresponding generalized quantum regression relations for an open quantum system linearly coupled to an environment. This theory covers all timescales and subsumes the Markovian and linear-response results as limiting cases. Finally, we apply our theory to the phenomenon of quantum friction.
We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean field and single-atom density matrix approximations. This makes it possible to correctly take into account the effects caused by the free motion of atoms in a gas, which lead to a nonlinear dependence of the spectroscopic signal on the atomic density even in the absent of a direct interatomic interaction (e.g., dipole-dipole interaction). Within the framework of this approach, analytical expressions for the light field were obtained for an arbitrary number of resonant waves and arbitrary optical thickness of a gas medium. Sub-Doppler spectroscopy in the transmission signal for two counterpropagating and co-propagating waves has been studied in detail. A previously unknown red shift of a narrow sub-Doppler resonance is predicted in a counterpropagating waves scheme, when the frequency of one wave is fixed and the frequency of the other wave is varied. The magnitude of this shift depends on the atomic density and can be more than an order of magnitude greater than the known shift from the interatomic dipole-dipole interaction (Lorentz-Lorenz shift). The found effects, caused by the free motion of atoms, require a significant revision of the existing picture of spectroscopic effects depending on the density of atoms in a gas. Apart of fundamental aspect, obtained results are important for precision laser spectroscopy and optical atomic clocks.
In this paper we study the dissipative effects and decoherence induced on a particle moving at constant speed in front of a dielectric plate in quantum vacuum, developing a closed-time-path (CTP) integral formulation in order to account for the corrections to these phenomena generated by finite temperatures. We compute the frictional force of the moving particle and find that it contains two different contributions: a pure quantum term due to quantum fluctuations (even present at vanishing temperatures) and a temperature-dependent component generated by thermal fluctuations (the bigger the contribution, the higher the temperature). We further estimate the decoherence timescale for the internal degree of freedom of the quantum particle. As expected, decoherence time is reduced by temperature; however, this feature is stronger for large velocities and for resonant situations. When the particle approaches relativistic speed, decoherence time becomes independent of temperature. The finite temperature corrections to the force or even in the decoherence timescale could be used to track traces of quantum friction through the study of the velocity dependence since the sole evidence of this dependence provides an indirect testimony of the existence of a quantum frictional force.