I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January 2010 The Casimir effect for existing and new materials I. G. Pirozhenko (BLTP, JINR)

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January The Casimir effect as a mechanical manifestation of quantum vacuum fluctuations  The quantum field as the infinite set of harmonic oscillators with energy L x y z But the part of the vacuum energy which depends on the distance between plates is finite!  The vacuum energy density is infinite: The Casimir force: In its simplest form the Casimir effect is the attraction between two electrically neutral, infinitely large, parallel perfectly conducting plates in vacuum. [H. B. G. Casimir, 1948]  For the EM field in the presence of perfectly conducting plates : The vacuum energy:

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Generalisation: the dispersion forces [all kinds of fluctuation induced forces between arbitrary bodies with finite conductivity and at finite temperature] The Lifshits theory (1956) for dielectrics with flat boundaries at finite temperature The Lifshits theory as limiting cases reproduces all results by Casimir [1948], London [1930], Casimir-Polder [1948]. Reflection coefficients of the plates at imaginary Matsubara frequencies The electromagnetic Casimir effect in the presence of real material boundaries is a subset of general dispersion forces and closely connected to condensed matter physics

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Directions of modern research  Modern precision measurements [S.K.Lamoreaux (torsion pendulum,1998), U. Mihideen and Roy(AFM, since 1998), R. Decca (micromacined oscillator, since 2003) etc.] Precise and reproducible measurement of the Casimir force is a complicated scientific and technological problem [to measure a tiny force between tiny bodies at micro(nano)scales]  Precise theoretical evaluation of the force for comparison with modern experiments requires account for geometry of the bodies, finite conductivity, anisotropy, finite temperature, and roughness of the surfaces. zgzg Microelectronical machine by R.S.Decca et al., Phys.Rev.D68:116003, 2003

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January The preliminary measurement [ellipsometry] of the optical properties is required for samples used in the Casimir experiments. For a given separation L the optical data should cover the interval of about 4 orders of magnitude around the characteristic frequency For L=100 nm [10meV, 100 eV]. The account for the dispersion of the dielectric permittivity The material properties enter the Lifshitz formula (and generalizations) through the reflection coefficients at imaginary frequencies defined by dielectric permittivity at imaginary frequencies The dielectric permittivity at imaginary frequencies is obtained from the optical data by Cramers-Cronig integration [optical data] If measurement at ‘all’ frequencies is not possible, the data should be extrapolated to inaccessible frequencies by making use of a reliable model, with parameters obtained from the data fit [ex. Drude model for metals] I.Pirozhenko, A.Lambrecht, V.Svetovoy, New J. Phys. 8, 238 (2006)

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January The Casmir force for existing materials The force between metals tends to the prefect Casimir force at “large” separations [the reduction factor goes to 1] The force between semiconductors is much lower.

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Changing the force by modulation of the conductivity: Doped Silicon F. Chen, G.L. Klimchitskaya, V.M. Mostepanenko, and U. Mohideen, Optics Express 15, 4823 (2007) I. Pirozhenko, A. Lambrecht, Phys. Rev. A 77, (2008)  Intrinsic Si  P-doped Si  Laser illuminated Si

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January R. Castillo-Garza et al, Phys.Rev. A75, (2007)[experiment proposal] I. Pirozhenko, A. Lambrecht, Phys. Rev. A 77, (2008) Insulator-metal phase transition -> Casimir “switch” The optical properties and thus the Casimir force undergo a step change at the transition temperature T=340 K.

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January B. T. Draine, Astrophys. J. 598, 1026 (2003); B.T. Draine, H. M. Lee, H.M. Astrophys. J. 285, 89 (1984) Casimir force for anisotropic uniaxial material

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Gold-Gold [Leicester data] Graphite-Gold The frequency shift measurement by G. Torricelli (University of Leicester) Each curve is the average of 40 measurements

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Metamaterials and the Casimir effect Properties Reversed refraction law Reversed Doppler effect Reversed Cherenkov radiation No contradiction with Pointing theorem V.G. Veselago, Sov. Phys. Usp. 10, 509 (1968)

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January 2010 Design of the metamaterials The idea: micro (nano) inclusions change the properties of host media.  The carriers confined in the metallic inclusions change the dielectric permittivity  The time varying magnetic field excites currents in micro (nano) wires. The oscillating current leads to a magnetic moment perpendicular to plane of the current “Optomagnetic composite medium with conducting nanoelements” L. V. Panina, et al, PHYS. REV. B 66, (2002) Example: split ring resonators working like magnetic antennas LC circuit resonance frequency scales inversely with the lateral size of the SRR, provided that resonance frequency does not come close to the metal plasma frequency is the filling fraction Geometrical scaling law for the resonance frequency brakes down at about 300 THz [M.W.Klein et al., Optics Letters 21, 1259 (2006)] [R.A. Shelby, D.R. Smith, S. Schultz, "Science", 292,77-79 (2001)]

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January The system giving repulsion. Predictions of the Lifshitz theory (T=0) Magnetoelectric materials: Metamaterials with 1A1ABA L d O.Kennet, I.Klich, A.Mann, M.Revzen, Phys.Rev.Lett (2002) C.Henkel, K.Joulain. Europhys. Lett. 9(6), (2005); U.Leonhardt and T.G.Philbin, New J. Phys (2007); I.G.Pirozhenko, A.Lambrecht, J.Phys.A:Math.Theor (2008); D.A.R.Dalvit, F.S.S.Rosa, P.W.Milonni, Phys.Rev.Lett (2008), Phys.Rev.A (2008); R.Zhao, J.Zhou, Th.Koschny, E.N.Economou, C.M.Soukoulis, Phys.Rev.Lett. 103, (2009) 233

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January The Casimir between two equal mirrors one of which is coated by a metamaterial The force is much weaker than It is repulsive at separations From the experimental viewpoint: Repulsion should occur at distances smaller than several microns where the force is still measurable. Materials with in a wide range at optical wavelengths are needed. A B

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January 2010 Effective medium approach  Anisotropic compound material is seen as a homogeneous media having effective and.  The effective medium approach is valid for wavelengths longer than the “lattice constant” of the meta-material. In other words, the theoretical estimations for the force are trustable for plate separations large in comparison with the “lattice constant” of the meta-material.  The effective dielectric permittivity and magnetic permeability are obtained numericaly through solving the Maxwell-equations in compound media (scattering of EM waves on the nano-inclusions) Metallic inclusions create mainly dielectric materials which give no repulsion I.G.Pirozhenko, A.Lambrecht, J.Phys.A:Math.Theor (2008); The dielectric inclusions seem more promising V. Yanopapas, 2009

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Casimir repulsion trough liquids with L<20nm [gold-bromobenzene-teflon, gold - p-xylene - teflon] repulsion A.Milling, P.Mulvaney, I.Larson, J.Coll.Int.Sc.,180, (1996); L<10 nm [teflon - cyclohexane - alpha-alumina or silica] repulsion S.Lee and W.M.Sigmund, J.Coll.Int.Sc., 243, 365 (2001); Coll.Surf.A: Phys.Eng.Asp.,204,43(2002). L>30 nm [gold-bromobenzene-silica] repulsion J. Munday, F. Capasso et al.:2007,2008,2009 L<50 nm Silica-Methanol-Au attraction ! P.J. van Zwol et al.,arXiv: , (2009) Experimental status cyclohexane, ethanol, or bromobenzene 1-2-3Hamaker const. Teflon-Ethanol- Au Teflon-Ethanol- Alumina Alumina- cyclohexane- Teflon −2.363 Silica- cyclohexane- Teflon −0.866 Teflon- Bromobenzene-Au L. Bergstrom, Adv.in. Colloid Interf. Sc. 70,125(1997) Short distances

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Repulsive Casimir force using the dielectric response of the materials Gold Silica Bromobenzene The condition is satisfied for For the discussion of the model’s applicability see J. Munday et al, Nature 457, 170 (2009) (supplementary info), and P.J. Zwal et al., arXiv: (2009)

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Comparison of the force with the short distance plasmon asymptotics Temperature corrections should be taken into account

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Conclusions  The Casimir effect is an interdisciplinary subject [quantum field theory, quantum optics and condensed matter physics etc.]  The modern experiments prove that the Casimir effect is central in nanotechnology Negative: the Casimir sticking of movable parts in micromachines Positive: nonlinear micromechanical Casimir oscillator, changing the force with optical modulation Technological challenge: motion transfer without contact in a rack and pinion set-up using lateral force Promising: Casimir force between metamaterials [materials with designed magnetodielectric response, Casimir repulsion (?)]

I.G. Pirozhenko, The Casimir effect for existing and new materials Program Advisory Committee for Condensed Matter Physics, 31 st meeting, January Collaboration  V.V. Nesterenko (BLTP JINR)  M. Bordag(Uni. Leipzig, Germany) [Heisenberg-Landau programme]  A. Lambrecht (Laboratoire Kastler Brossel, UPMC & ENS, CNRS, France)  C. Binns, G. Torricelli (Uni. Leicester, UK) [experiment]  European project NANOCASE “Nanoscale machines exploiting Casimir force”  ESF Research Network CASIMIR