Casimir Momentum in Complex Media Bart van Tiggelen

Casimir Momentum in Complex Media? Bart van Tiggelen Grenoble Collaborators: • Geert Rikken (LNCMI Grenoble/Toulouse) • Sébastien Kawka (Ph. D Grenoble ENS Pisa) • James Babington (postdoc ANR Grenoble) Costas Soukoulis 60 years, June 2011

Momentum from Nothing B 0 E 0 ε, μ, g

Bi-anisotropic Media Fresnel dispersion law Rotatory power Fizeau effect v kx -2 10 10 -8 Magneto-electric birefringence ky E 0 x B 0 10 -15

phenomenological continuum theory cut-off in X-ray ? Inertial mass of quantum vacuum? Photonic momentum in dielectric media? classical « Abraham » contribution already controversial UV catastrophe of vacuum energy ? Lorentz invariance of quantum vacuum? Inertia of quantum vacuum?

UV catastrophe in sonoluminescence (> 1934) Schwinger (1993) cut-off in the UV ?

The UV catastrophe is real Free electron g. ME(ω)/n magnetic dipole + Electric quadruole g. ME = 10 -17 -- 10 -11 Rizzo etal, 2003 -2009, Babington & BAv. T, 2011

Casimir momentum, if infinite, is Lorentz invariant Bi-anisotropic Lorentz-invariant vacuum Fluctuation. Dissipation Zero energy flow infinite momentum density Lorentz scalar

Classical Abraham momentum in crossed EM fields B 0 E 0(t) v ε E 0(t) (Walker Nature, 1976) + - v

E=450 V/mm; B=1 T Ex: Helium Classical abraham force Feigel QED with cut-off 0. 1 nm Regularization of vacuum energy in a=10 cm (Milton, 2000) QED harmonic oscillator (Kawka, 2010)

dp/dt=Abraham force Acoustic pressure V= 8 nm/sec+- 0. 8 Feigel : 2 nm/sec E=450 V/mm; B=1 T; f= 7. 6 k. Hz p/(EB) Experiment: Geert Rikken α(0)

Casimir momentum: 1/4 QED of harmonic oscillator in crossed fields E 0 +e -e B 0

Casimir momentum: 2/4 QED of harmonic oscillator in crossed fields E 0 +e -e Conjugate momenta ≠ kinetic momentum Pseudomomentum is conserved B 0

Casimir momentum: 3/4 QED of harmonic oscillator in crossed fields +e -e E 0 B 0

Casimir momentum: 4/4 QED of harmonic oscillator in crossed fields E 0 +e -e B 0 K 1 : 2 % QED correction to Abraham force K 2: 0. 01 % QED correction Kawka & Van Tiggelen, EPL 2010

A quantum vacuum force F= g d. B/dt ? ε ε B 0 Chiral geometry with electric polarizabilities Faraday Rotation

A quantum vacuum force F= g d. B/dt ? µ µ B 0 Chiral geometry with magnetic polarizabilities Faraday Rotation Na Tetraeder L=10 nm g/m = 1 nm/sec/T

momentum of quantum vacuum to shed new light on the controversial nature of zero-point energy Corsica, 2006 Congratulations Costas!