1. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Casimir force measurements using mechanical transducers: sensitivity, noise and background Ricardo S. Decca Department of Physics, IUPUI

2. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Dominant electronic force at small (~ 1 nm) separations Non-retarded: van der Waals Retarded: Casimir Attractive interaction z No mode restriction on the outside

3. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 In principle, a simple task System to measure the interaction -Mechanical oscillators with soft springs. -It actually is a transducer, and either a deflection (linear or angular) or a frequency shift is measured. -A calibration against a known interaction is needed. An electrostatic interaction between the bodies is used. -It needs to be free of systematic effects. But nobody succeeds. System to measure the separation between bodies -Two-color interferometer yields absolute positioning. -One point needs to be obtained in a different way. Characterization of the system and samples -Measurement of all parameters involved. -Minimization of backgrounds. -Characterization of the materials used Comparison with theory

4. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Collaborators Funding Daniel LópezArgonne National Lab Ephraim FischbaschPurdue University Dennis E. Krause Wabash College and Purdue University Valdimir M. MostepanenkoNoncommercial Partnership “Scientific Instruments”, Russia Galina L. KlimchitskayaNorth-West Technical University, Russia Jing Ding, Brad ChenIUPUI Edwin Tham, Hua Xing Vladimir Aksyuk CNST/Univ. of Maryland Diego Dalvit Los Alamos National Lab Peter Milonni Los Alamos National Lab Francesco IntravaiaLos Alamos National Lab Paul DavidsSandia National Lab Il Woong JungArgonne National Lab NSF, DOE, LANL, DARPA

5. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Outline 1.- Review of experimental results 2.- Characteristics of a system 3.- Measurement of the interaction 4.-Measurement of the separation 5.- Sample preparation, and characterization 6.- Comparison with theory 7.- Effects of environment 8.- Low temperature measurements 9.- Potential approaches to get better results? 10.- Summary

6. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Review of experimental results Observation of the thermal Casimir force A. O. Sushkov, W. J. Kim, D. A. R. Dalvit & S. K. Lamoreaux Nature Physics 7, 230–233 (2011)

7. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Roberto Onofrio's group at Dartmouth College G. Bressi, G. Carugno, R. Onofrio, G. Ruoso, "Measurement of the Casimir force between Parallel Metallic Surfaces", Phys. Rev. Lett. 88 041804 (2002) Review of experimental results

8. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 A. Roy, C.Y. Lin and U. Mohideen, "Improved precision measurement of the Casimir force," Physical Review D, Rapid Communication, Vol. 60, pp.111101-05 (1999). Review of experimental results

9. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Review of experimental setups Measurement of dispersive forces between evaporated metal surfaces in the range below 100 nm P.J. van Zwol, G. Palasantzas, M. van de Schootbrugge, J. Th. M. De Hosson

10. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 D. Chavan, G. Gruca, S. de Man, M. Slaman, J. H. Rector, K. Heeck, and D. Iannuzzi, Ferrule-top atomic force microscope, Rev. Sci. Instrum. 81, 123702 Review of experimental results

11. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Review of experimental results

12. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force; Chan, Aksyuk, Kleiman, Bishop, Capasso Science 291, 1941 Nonlinear Micromechanical Casimir Oscillator; Phys. Rev. Lett. 87, 211801 Review of experimental results

13. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Effect of hydrogen-switchable mirrors on the Casimir force Iannuzzi, Lisanti, and Capasso Proc. Nat. Acad. of Sci. 101, 4019 Review of experimental results

14. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 More yet! Lateral Casimir effect Measurements on corrugated samples Phase-change materials Indium-Tin Oxide (ITO) Review of experimental results

15. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 - Base pressure: ~ 1x10 -7 Torr - Mounted in an active damping control air table - Passive magnetic damping on floating system - 5 axis (xyz, rock and tilt) stepper motor drive - 3 axis (xyz, not seen) closed loop 70 micron range piezo stage - Two color interferometer integrated into the system for continuous absolute position measurement - Total position stability control better than 0.2 nm Characteristics of a system

16. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Characteristics of a system

17. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Characteristics of a system Not considering intrinsic losses Newell(1986) Optimal strategy: Decrease , increase Q, work at fo, and low T

18. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Characteristics of a system What is  ? Noise (thermal, vibrational, 1/f), actual forces (known and unknown: Electrostatic, patch effects, Casimir, gravitational, …) f(Hz)

19. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Lately, we have changed the setup: the sphere is on the oscillator, the plate is on top. -Different sample (nanostructured), cannot be made on the oscillator’s plate. -Larger sample, requires different deposition. Characteristics of a system

20. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Characteristics of a system

21. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Measurement of the interaction

22. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Determined by: -Looking into the response of the oscillator in the thermal bath. Or -Inducing a time dependent separation between the plate and the sphere (preferred). Measurement of the interaction

23. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Measurement of the interaction ErrorsMinimum values Frequency: 6 mHz~28 mHz (at 750 nm) b 2 /I:0.0005  g -1 1.2432  g -1 R:0.2  m150  m

24. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Measurement of the separation z g = (2172.8 ± 0.1) nm, interferometer z i = ~(10000.0s ± 0.2) absolute interferometer z o = (8162.3 ± 0.5) nm, electrostatic calibration b = (207 ± 2)  m, optical microscope  = ~(1.000 ± 0.001)  rad zgzg z o is determined using a known interaction z i,  are measured for each position

25. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Electrostatic force calibration Measurement of the separation

26. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Electrostatic force calibration z = 3.5  m Measurement of the separation

27. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Electrostatic force calibration V o is constant as a function of separation… … and time Otherwise, V o needs to be determined at each point 10 x 10 grid, 5  m pitch Measurement of the separation

28. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Electrostatic force calibration -After measuring the deflection (expressed as force here), we adjust for the unknown separation. -The figure shows the  F e for the optimal and one off by 1.5 nm Measurement of the separation

29. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 -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 (Yang et al., Opt. Lett. 27, 77 (2005) Interferometer LC =(1240 +/-  ) nm (low coherence), CW 1550 nm (high coherence) in x Mirror (v ~ 10  m/s)  x = z i Readout Measurement of the separation

30. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 LC =(1240 +/-  ) nm (low coherence), CW 1550 nm (high coherence) input x Mirror (v ~ 10  m/s)  x = z i Readout (independent at each wavelength) -Phases obtained doing a Hilbert transform of the amplitude -Changes in  about 2 nm) give different curves. Intersections provide  x -Quite insensitive to jitter. Only 2  x’/( CW ) 2 Instead of 2  x’/ CW (Yang et al., Opt. Lett. 27, 77 (2005) Interferometer zizi Measurement of the separation

31. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Sample preparation and characterization -Au on the sapphire sphere is deposited by thermal evaporation. -Au on the oscillator is also deposited by thermal evaporation but on large samples it is deposited by electroplating (on Si[111]) -Samples are characterized by measuring resistance as a function of temperature, AFM measurements and also ellipsometry in the electrodeposited sample. -The sample to be used is mounted as quickly as possible into the system, baked to ~ 60 o C for ½ hour (not the oscillator) (10 x 10  m 2 ) ~ 20 nm pp

32. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Sample characterization

33. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 -  vs T and spectroscopic ellipsometry (190 nm to 830 nm) used to determine optical properties. -Both methods indicate a rather good Au sample Sample characterization

34. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 -Measured real and imaginary parts of the dielectric functions (red circles) are similar to published values (Palik, black squares) -It was checked that either can be used, given the same results. Sample characterization

35. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Sample characterization

36. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Both samples on the left panel. Difference between them on the right one Sample characterization

37. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 v i : Fraction of the sample at separation z i Roughness corrections Roughness corrections are ~0.5% to the Casimir interaction at 160 nm Comparison with theory

38. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Finite conductivity and finite temperature Comparison with theory

39. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Comparison with theory Bentsen et al., J. Phys. A (2005)

40. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 -Dark grey, Drude model approach -Light grey, plasma model approach PRD 75, 077101 Comparison with theory

41. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Effects of environment: V o For the residual effects of the patch potentials, it has been noted that their influence does not average to 0, since. Hence in the effective area of separation, there could be a residual electrostatic force. For the size of our sphere, at large separations, we do not see it. Is it possible for it to be there at short separations? Why do we see V o constant? (Many others don’t) We can give an answer to the first question:

42. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Effects of environment: V o The capacitance is measured as arising from a contribution from the sphere and the plate plus a small, constant parasitic capacitance.

43. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Low temperature measurement Setup schematic LHe can Springs Low pressure He can Magnet Experimental space (with positioning stage) Also at T = 0K dissipation will be reduced

44. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Low temperature measurement Characterization When compared with previous measurements, the error in frequency is ~ 30 times larger at 1.5 K and ~ 40 times larger at 4.2 K and 77 K, yielding an increased error in P C LC =(1240 +/-  ) nm CW 1550 nm x  x = z i Readout Measured error is ~ 5 nm. Mechanical vibrations And problems with the interferometer

45. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Room temperature Frequency shifts, Q increases, 77K f(Hz) … Noise increases! Low temperature measurement

46. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Low temperature measurement Results Measurements at 1.5 K seem to have the lowest noise All data seem to coincide with the room temperature measurements The error on the low T measurement, e l (400 nm) = 5 mPa is larger than the difference between the Drude and plasma models of 2.4 mPa This statement holds true at all temperatures and separations investigated

47. PASI- Frontiers on Casimir Physics Ushuaia, Argentina, 10/7/2012 Summary Measurement of the Casimir force, done with different mechanical transducers Our MTO used as example for minimum detectable force, SNR, etc Description on system characterization Possibilities for the future?