Measurements of Forces at the Nanoscale some ideas for measurements at LEPES in 2005 J. Chevrier 18 November 2004

we consider three different forces: - Casimir: hc [J.m] - Electrostatic: e 2 /4  0 [J.m] -Gravity:Gm 2 [J.m]

-electrostatic: Charles A. Coulomb strong force - long range today “Easily” measured -gravity: Henry Cavendish Nice Londres weaker force: (e 2 /4  0 ) / Gm 2  long range a bit more difficult…but still a student training

- Casimir/van der Waals versus electrostatic: hc / (e 2 /4  0 )  137 fine structure constant However unless at very short distances (< 1nm) (if static charges present …not neutral) electrostatic >> Casimir Casimir… short range characteristic distance at the nanoscale Nanosciences Sphere diameter 50  m sphere/surface: 10nm -1  m

origin of van der waals/casimir interaction between two neutral systems in their fundamental state: electron-photon coupling by dipolar interaction -d.E -d.E Fundamental state temps -d.E Electronic excitations  (q,  )

Characteristic length for two metallic surfaces (jellium model) defined by electronic excitations coupled to photons: surface plasmons characteristic length:  p = 2  c/  p Aluminium h  p = 14eV  p  100nm

Surface plasmons  metal (  1 <0) Hy E x E z

Surface plasmons x Hy EE z metal (  1 <0) metal (  2 <0) d<<  p Coupling of

F<0 répulsif F>0 attractif d=10nm Al SiC Plasmon polariton Phonon polariton Plasmon polariton d<<  p

Surface plasmons  metal (  1 <0) Hy E x E z Changing coupling of plasmons with extended photon modes ???

k ph  a k sp  1  2 k x  x ck  1 2 Zn, 2  a nk x  sp k 2,...1,0,n, 2 sin        c k a nk spph k x x ck    /a 1 The way the plasmon-photon coupling is changed

Experiment: Force measurement at distances close to 10nm below the plasma length to be sensitive to surface electronic excitations Using a resonating oscillator perturbed by the van der Waals/Casimir interaction. sample Interaction F k, 

sample

Electrostatic calibration Dispersion force in the non retarded régime

Home made force machine built within the X tip european project at the ESRF in 2004 Pour le LEPES en 2005: extension to measurement at short distances d<<  p under vacuum and at low T (4K) …...

hope we shall avoid such a hard collision next time good point however: parallel surfaces well prepared…. Very very large roughness...

Experimental objective: Combination of sphere on cantilever or on tuning fork + measurement of frequency shift with resolution close to 1mHz

Mario Rodriguez stage de Master 2 ESRF Gauthier Torricelli Thèse LEPES/ESRF Guillaume Jourdan Thèse LEPES/Lab. Kastler Brossel Direction: J. Chevrier/ A. Lambrecht