Micromechanical oscillators in the Casimir regime: A tool to investigate the existence of hypothetical forces

1. Micromechanical oscillators in the Casimir regime: A tool to investigate the existence of hypothetical forces Ricardo S. Decca Department of Physics, IUPUI

2. Collaborators Daniel López Argonne National Labs Ephraim Fischbasch Purdue University Dennis E. Krausse Wabash College and Purdue University Valdimir M. Mostepanenko Noncommercial Partnership “Scientific Instruments”, Russia Galina L. Klimchitskaya North-West Technical University, Russia Ho Bun Chan University of Florida Jing Ding IUPUI Hua Xing IUPUI NSF, DOE, LANL Funding

3. The strength of gravity for various numbers of large extra dimensions n, compared to the strength of electromagnetism (dotted) Without extra dimensions, gravity is weak relative to the electromagnetic force for all separation distances. With extra dimensions, the gravitational force rises steeply for small separations and may become comparable to electromagnetism at short distances. Jonathan L. Feng, Science 301, 795 (’03) What is the background?

4. Attractive force! • Dominant electronic force at small (~ 1 nm) separations • Non-retarded: van der Waals • Retarded: Casimir 2a No mode restriction on the outside

5. Importance of the Casimir effect • Consequences in nanotechnology (MEMS and NEMS) “Long-range” interaction between moving parts Possibility of controlling the interaction by engineering materials • Consequences in quantum field theory • Thermal dependence • Consequences in gravitation and cosmology • Background to measure deviations from Newtonian potential at small • separations • Source of “missing mass”

6. Yukawa-like potential • Arises from very different pictures: • Compact extra-dimensions • Exchange of single light (but massive, • m =1/l) boson • Moduli; Graviphotons; Dilatons; • Hyperphotons; Axions  f1 f2 1 2 PRL 98, 021101 (2007)

7. Arises from very different pictures: • Compact extra-dimensions • Exchange of light (but massive, m =1/l) boson • -Moduli • -Graviphotons • -Dilatons • -Hyperphotons • -Axions Yukawa-like potential How do we establish limits? Measure background and subtract it Get rid of the background altogether

8. Experimental setup

9. Dynamic measurements

10. zg Separation measurement zg = (2389.6 ± 0.1) nm, interferometer zi= ~(10000.0 ± 0.2) absolute interferometer zo = (6960.1 ± 0.5) nm, electrostatic calibration b = (210 ± 3) mm, optical microscope Q = ~(1.000 ± 0.001) mrad zmeas is determined using a known interaction zi, Q are measured for each position

11. Separation measurement Electrostatic force calibration • Determine: • R • VAu • do • k Originally using the whole expression, lately using the 8 term fit found on Mohideen’s papers

12. Pressure determination

13. Comparison with theory AFM image of the Au plane vi: Fraction of the sample at separation zi

14. Comparison with theory

15. Al2O3 Al2O3 Al2O3 “Casimir-less” experiments Au Au Ge Si MTO

16. “Casimir-less” experiments Signal optimization: Work at wo!!! Heterodyne Oscillate plate at f1, sphere at f2 such that f1 + f2 = fo

17. z = 500 nm 1 sec 10 sec 100 sec 1000 sec

18. “Casimir-less” experiments Signal optimization: Work at wo!!! Oscillate plate at f1, sphere at f2 such that f1 + f2 = fo 95% confidence level Net force! F

19. Sanity check: more samples! “Casimir-less” experiments

20. F

21. Background Motion not parallel to the axis (too small) Step (0.1 nm needed) Difference in electrostatic force (0.1 mV needed) Difference in Au coating (unlikely) Au coating not thick enough (unlikely) Al2O3 Au Au Au Ge Si MTO

22. -Improve signal -Reduce background What next?

24. About five orders of magnitude improvement Two orders of magnitude improvement

25. Conclusions • Most sensitive measurements of the Casimir Force • and Casimir Pressure • Unprecedented agreement with theory • First realization of a “Casimir-less” experiment • Improvement of about three orders of magnitude in Yukawa-like • hypothetical forces

26. Separation measurement Electrostatic force calibration … and time Vomust be constant as a function of separation…

27. Comparison with theory PRD 75, 077101 • Dark grey, Drude model approach • -Light grey, Leontovich impedance approach

28. Distance measurement Interferometer (Yang et al., Opt. Lett. 27, 77 (2005) lLC =(1240 +/- D) nm (low coherence), lCW1550 nm (high coherence) in Readout Mirror (v ~ 10 mm/s) x Dx = zi -Problems in lack of parallelism (curvature of wavefronts) are compensated when subtracting the two phases -Gouy phase effect is ~ , and gives an error much smaller than the random one

29. Distance measurement Interferometer (Yang et al., Opt. Lett. 27, 77 (2005) lLC =(1240 +/- D) nm (low coherence), lCW1550 nm (high coherence) in Readout Mirror (v ~ 10 mm/s) x Dx = zi -Phases obtained doing a Hilbert transform of the amplitude -Changes in D (about 2 nm) give different curves. Intersections provide Dx -Quite insensitive to jitter. Only 2DDx’/(lCW)2 Instead of 2Dx’/lCW

30. w t Experimental setup w, t = 2mm

31. Experimental setup