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Micromechanical oscillators in the Casimir regime: A tool to investigate the existence of hypothetical forces. Ricardo S. Decca Department of Physics, IUPUI. Collaborators. Daniel López Argonne National Labs Ephraim Fischbasch Purdue University

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slide1

Micromechanical oscillators in the Casimir regime:

A tool to investigate the existence of hypothetical forces

Ricardo S. Decca

Department of Physics, IUPUI

slide2

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

slide3

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?

slide4

Attractive force!

  • Dominant electronic force at small (~ 1 nm) separations
  • Non-retarded: van der Waals
  • Retarded: Casimir

2a

No mode restriction on the outside

slide5

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”
slide6

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)

slide7

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

slide10

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

slide11

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

slide13

Comparison with theory

AFM image of the Au plane

vi: Fraction of the sample at

separation zi

slide15

Al2O3

Al2O3

Al2O3

“Casimir-less” experiments

Au

Au

Ge

Si MTO

slide16

“Casimir-less” experiments

Signal optimization:

Work at wo!!!

Heterodyne

Oscillate plate at f1, sphere at f2

such that f1 + f2 = fo

slide17

z = 500 nm

1 sec

10 sec

100 sec

1000 sec

slide18

“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

slide19

Sanity check: more samples!

“Casimir-less” experiments

slide21

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

slide22

-Improve signal

-Reduce background

What next?

slide24

About five orders of

magnitude improvement

Two orders of magnitude

improvement

slide25

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
slide26

Separation measurement

Electrostatic force calibration

… and time

Vomust be constant as a function of separation…

slide27

Comparison with theory

PRD 75, 077101

  • Dark grey, Drude model approach
  • -Light grey, Leontovich impedance approach
slide28

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

slide29

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

slide30

w

t

Experimental setup

w, t = 2mm

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