Fluctuation-induced forces between atoms and surfaces: the Casimir-Polder interaction

Electromagnetic fluctuation-induced forces between atoms and surfaces are generally known as Casimir-Polder interactions. The exact knowledge of these forces is rapidly becoming important in modern experimental set-ups and for technological applications. Recent theoretical and experimental investigations have shown that such an interaction is tunable in strength and sign, opening new perspectives to investigate aspects of quantum field theory and condensed-matter physics. In this Chapter we review the theory of fluctuation-induced interactions between atoms and a surface, paying particular attention to the physical characterization of the system. We also survey some recent developments concerning the role of temperature, situations out of thermal equilibrium, and measurements involving ultra-cold atoms.Comment: 44 pages, 14 figure. Invited review paper to appear in Lecture Notes in Physics for a volume on "Casimir physics" edited by D. Dalvit, P. Milonni, D. Roberts, and F. da Rosa. Publisher Springer-Verlag (2010

Surface-atom force out of thermal equilibrium and its effect on ultra-cold atoms

The surface-atom Casimir-Polder-Lifshitz force out of thermal equilibrium is investigated in the framework of macroscopic electrodynamics. Particular attention is devoted to its large distance limit that shows a new, stronger behaviour with respect to the equilibrium case. The frequency shift produced by the surface-atom force on the the center-of-mass oscillations of a harmonically trapped Bose-Einstein condensate and on the Bloch oscillations of an ultra-cold fermionic gas in an optical lattice are discussed for configurations out of thermal equilibrium.Comment: Submitted to JPA Special Issue QFEXT'0

New asymptotic behaviour of the surface-atom force out of thermal equilibrium

The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like $1/z^3$ at large distances (i.e. slower than at equilibrium), exhibits a sizable temperature dependence and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are considered.Comment: 4 pages, 3 figures. In press on Phys. Rev. Let

Measurement of the Temperature Dependence of the Casimir-Polder Force

We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87-Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be nearly 3 times larger for a 605 K substrate than for a room-temperature substrate, showing a clear temperature dependence in agreement with theory.Comment: 4 pages, 4 figures, published in Physical Review Letter

Casimir-Lifshitz force out of thermal equilibrium

We study the Casimir-Lifshitz interaction out of thermal equilibrium, with particular attention devoted to the surface-surface and surface-atom configurations. A systematic investigation of the contributions to the force coming from the propagating and evanescent components of the electromagnetic radiation is performed. The large distance behaviors of such interactions is discussed, and both analytical and numerical results are compared with the equilibrium ones. A detailed analysis of the crossing between the surface-surface and the surface-rarefied body, and finally the surface-atom force is shown, and a complete derivation and discussion of the recently predicted non-additivity effects and new asymptotic behaviors is presented.Comment: 26 pages, 11 figures. Published version, revised and more detaile

Radiation induced force between two planar waveguides

We study the electromagnetic force exerted on a pair of parallel slab waveguides by the light propagating through them. We have calculated the dependence of the force on the slab separation by means of the Maxwell--Stress tensor formalism and we have discussed its main features for the different propagation modes: spatially symmetric (antisymmetric) modes give rise to an attractive (repulsive) interaction. We have derived the asymptotic behaviors of the force at small and large separation and we have quantitatively estimated the mechanical deflection induced on a realistic air-bridge structure.Comment: 10 pages, 6 figure

Reconciliation of quantum local master equations with thermodynamics

The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modelling of transport in mesoscopic systems, consists in using {\it local} master equations containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of local master equations based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.Comment: Published versio

Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate

We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center of mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in details and various regimes (van der Waals-London, Casimir-Polder and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for the case of a sapphire dielectric substrate interacting with a harmonically trapped condensate of $^{87}$Rb atoms. We find that at distances of $4-8 \mu m$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order $10^{-4}$ and hence accessible experimentally. The effects of non linearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.Comment: 28 pages, 10 figures. Submitted to PR

Non-equilibrium Casimir forces: Spheres and sphere-plate

We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.Comment: 6 pages, 6 figure

Conductivity of dielectric and thermal atom-wall interaction

We compare the experimental data of the first measurement of a temperature dependence of the Casimir-Polder force by Obrecht et al. [Phys. Rev. Lett. {\bf 98}, 063201 (2007)] with the theory taking into account small, but physically real, static conductivity of the dielectric substrate. The theory is found to be inconsistent with the data. The conclusion is drawn that the conductivity of dielectric materials should not be included in the model of the dielectric response in the Lifshitz theory. This conclusion obtained from the long separation measurement is consistent with related but different results obtained for semiconductors and metals at short separations.Comment: 4 pages, 2 figures; page size is correcte