Pushing towards parallelism in Casimir experiments

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1 Pushing towards parallelism in Casimir experiments R. Sedmik A. Almasi K. Heeck D. Iannuzzi

2 Parallelism why would we want that? Which problems would demand for accurate experiments? Casimir effect at K the Drude vs. plasma debate Clearly Distinctive measurement at d > 3 µm with accuracy < 0.1 % (1 pn/cm2) Sushkov et al, Nature Physics 7 (2011), 230, Klimchitskaya et al, arxiv: (2011) Limits on hypothetical non-newtonian forces (Chameleon, Galileon,...) Distinctive measurement at d > 10 µm with accuracy < 1% (0.1 pn/cm2) Brax et al, Phys Rev. D 76 (2007), Comparison: Where do we stand now? micromachined oscillators, plate sphere: 0.19 % (2.12 pn/cm2) at d = 164 nm Decca et al, Phys. Rev. D75 (2007), torsional balances, plate vs. spherical lens: 1% at d ¼ 3 µm, Masuda and Sasaki, Phys. Rev. Lett. 102 (2009), % at d = 7.29 µm Sushkov et al, Nature Physics 7 (2011), 230 Need a factor ~10 increase in sensitivity at large distance to make unambiguous statements. 2

3 Parallelism why would we want that? The situation in current experiments: Most work performed in geometries featuring inherent symmetry R d No difficulties of alignment but small opposing areas limited sensitivity Established measurement methods (AFM, SFA, capacitance bridges) Direct comparison to theory possible? Theory: which Results for parallel plates can be translated to curved objects only approximative limited distance or via the Proximity Force Approximation Error limited accuracy Numerical schemes available for almost arbitrary geometries Do our approximations sufficiently capture all relevant effects of curved geometries? So far, this does not sound bad! We have seen excellent results. 3

4 Q: Parallelism why would we want that? Can parallel plates fulfill the task? Sensitivity: better than 0.1 % at d > 3 µm, 1% at 10 µm? scales with area (freely) adjustable Accuracy: BASICALLY, YES uncorrugated flat surfaces technically feasible. no approximations regarding geometry (only minor edge effects) What obstacles could be expected? Control of parallelism < 1µrad? DEMONSTRATION IN THIS TALK? THE SOLUTION IS... Flatness of surfaces (large scale < 10 nm) Disturbing other forces Hydrodynamic damping Electrostatic forces A: Parallel plates experiments potentially allow for very high sensitivity and accuracy 4

5 Overview of the talk A status report what is possible now? Review: Amsterdam method Current setup Experiments: Recent measurements Crossed cylinders Really parallel plates what will be possible shortly? A completely new setup: Design, features and specifications Status of construction: proof of principle Active control of parallelism Upcoming experiments 5

6 Part 1: A status report 6

7 Our method experimental challenges Want to measure the Casimir force (sphere vs. plate): Strong dependence on distance Measure AC Susceptible for drifts not DC Accurate and synchronous distance measurement necessary Extremely short ranged in comparison with other forces What forces? Electrostatic force Hydrodynamic damping Compensate phase-shifted w.r.t. Casimir Amsterdam Method: Separate all forces in frequency space and measure each independently. KEY PUBLICATION: de Man, Heeck, Wijngaarden, Iannuzzi, Phys. Rev. Lett. 103 (2009)

8 Our method experimental challenges Typical AFM setup S Photodetector Laser T const. Cantilever Problem: arbitrary potential V0 that changes with distance, time, temperature,... d Example: Substrate z piezo V V 100 mv 0 dpz static Solution: measure and compensate FES at all times (synchronously to data acquisition) 8

9 Current setup V0 compensation S Laser Lock-in amp. (!1) Lock-in amp. (2!1) Photodetector T const. Cantilever VAC cos(!1t) VDC d Data acquisition and control PC Substrate zpiezo dpz static V0 compensation VAC setting AFM Signal: 9

10 Current Setup V0 compensation Frequency spectrum Bonus: 2w1 data gives: known residual term Amplitude S VDC= V0 0!1 2!1!r! Contact-less distance measurement Amplitude calibration Measure the w1 component with lock-in amplifier Feed back via voltage generator Replace unknown force by a small known component 10

11 Current setup force measurement S Laser Lock-in amp. (!1) Lock-in amp. (2!1) Lock-in amp. (!2) Photodetector T const. Cantilever VAC cos(!1t) VDC d Data acquisition and control PC Substrate z stick-slip piezo d cos(!2t) z piezo dpz static V0 compensation VAC setting 11

12 Current setup force measurement Frequency spectrum y ' Amplitude S x quadrature lock-in 0!1!2 2!1!r! Casimir and hydrodynamic force are 90 degree out of phase. Simultaneous measurement by a quadrature lock-in amplifier Problem: Casimir signal but hydrodynamic signal at large distance, 12

13 Current setup force measurement Phase calibration y ' x quadrature lock-in Error 1 degree How is it done? Accurate phase calibration is of highest importance! 13

Current experiments example Hydrodynamics at short separations Force between a sphere and a plate solid Classical Stokes solution: fluid velocity Is of interest because it.

14 Current experiments example Hydrodynamics at short separations Force between a sphere and a plate solid Classical Stokes solution: fluid velocity Is of interest because it... has immediate applications in lab-on-a-chip devices is even after several decades of research not entirely understood we have the ability to perform relevant measurements with unprecedented accuracy fluid sl i p Sto If surface separations are comparable to the mean free path f: slip flow s 0 f s ti olu s ke s on ti u l o on distance 14

15 Current experiments example Hydrodynamics at short separations Force between a sphere and a plate We have found that... The Vinogradova theory for f v (used since 15 years) in many investigations is self-inconsistent We proposed... A new heuristic model that is suitable for practical application Submitted to PRL 15

16 Current experiments example Crossed cylinders Experiment at is geometrically equivalent to sphere vs. plate Measurement: Ederth, Phys. Rev. A62 (2000) Recent theoretical results for Rodriguez-Lopez and Emig, Casimir interaction between inclined cylinders, arxiv: (2012) AFM measurement of the Casimir gradient between inclined cylinders Cantilever 12 4 μ 00 measured last week preliminary data m 5μ m Au-coated optical fiber 16

17 Part 2: A new approach. Parallel plates 17

18 How to keep things parallel assume: parallel plates n(t) plates with relative tilt! n(t)! 0 Capacitance bridge time,modulatedangle Signal C d0 Signal C 0 time,modulatedangle Idea: Use feedback circuit to compensate 18

19 How to keep things parallel A feedback circuit d0 setting + + sin (Y) +!m Ref. 3Á Compensation of electrostatic potentials Piezos!e Capacity Measurement Y error 2Á X X error!m cos (X) + X Coordinate conversion Lock-in amp.!c C(t)!c Ref. ModulationCapacitance bridge Lock-in amp. C cos(!ct)!e Ref. Lock-in amp. VDC 19

20 How to keep things parallel Proof of principle Step response under very bad conditions First test - in air - without anti-vibration - with rough surfaces 6 µm single-sided step nominal distance 90 µm plate area 1 cm2 Long-term stability Same conditions 3 µrad(rms) Target Assumptions: good surface quality, vacuum, anti-vibration 0.1 µrad (~1 nm total tilt) 20

21 Force measurement Idea: Implementation: Measure capacitively the deformation of a membrane... Upper plate d0 {F/k F Membrane Lower plate Cap. bridge /F Custom-fabricated Silicon membrane Force constant 0.3 N/m Eigenfrequency 19 Hz 21

22 Design: core elements upper plate (Kelvin capacitor) membrane lower plate (Kelvin capacitor) 22

23 Design: core elements Membrane clamped to holder of lower plate... mounted on 3 piezo columns 23

24 Design: core elements Fixed on a temperature-controlled base plate.. 24

25 Design: core elements Top plate fixed on three rigid columns. 25

1%) (at 6 µm distance) Plate area: 1 cm2, surfaces: Aucoated mono-crystalline wafers

26 Design: Setup Core placed in a high-vacuum capable chamber Specifications Force sensitivity: <0.1 pn (0.1%) (at 6 µm distance) Plate area: 1 cm2, surfaces: Aucoated mono-crystalline wafers Measurement range 300 nm 50 µm Pressure range: mbar ~2 bar (pumps detachable) Temperature stability of core: 1 mk Custom active anti-vibration stage (lower corner frequency 0.1 Hz) 26

27 Status of new setup...core parts are ready and operable 27

28 Experiments Possible geometries:...in any gas at any pressure Possible measurements of: Casimir forces Hydrodynamic forces non-newtonian forces? Force transducer: ferrule-top cantilever instead of membrane 28

29 Hypothetical Yukawa interactions Chameleon fields: Possible explanation for expansion of the universe Scalar field of mass dim. 1 Couples to photons J. Khoury and A.Weltman, Phys. Rev. Lett. 93 (2004) Action: Equation of motion definition of effective potential: Interaction depends on the local mass density (larger density lower interaction) 29

.. If local mass density is changed, only the Chameleon force varies!

30 Hypothetical Yukawa interactions Possible to measure? 3 orders Of magnitude d = 10 μm, A = 1 cm2 Not in the conventional way (as a function of d) but... If local mass density is changed, only the Chameleon force varies! Idea: change pressure New limits on coupling constants at d = 10 µm with sensitivity 0.1 pn KEY PUBLICATION: Brax, van de Bruck, Davis, Shaw, Iannuzzi, Phys. Rev. Lett. 104 (2010)

31 Other hypothetical interactions Galileon model Idea: Vainshtein mechanism. Veinshtein, Phys. Lett. B39 (1972), 393 Coupling between scalar field and matter depends (inversely) on the local mass density. Implementation Coupling to other fields Galileon scalar fields, mass dimension 0 5 Coupling constants with mass dimension (2 -n ) Proposal for experiment Brax et al, arxiv: v2 (2011) DC experiment necessary. Eöt-Wash type gravitation experiment (parallel rotating discs) Static Casimir experiment with varying gas density Constraints could be derived from a Chameleon experiment! 31

32 Conclusions Parallel plate experiments have potentially high accurracy and could end the debate regarding Drude vs. plasma We are using know how from an established Casimir setup to design a new experiment with parallel plates. Such a setup is under construction, core parts are already under test This setup can also be used to find new limits for non-newtonian forces 32

33 Acknowledgments Thank you for your kind attention! S. de M an sa ni A. F. Bo rg he.w at er in g T. v. d ru ca G.G n ha va.c D H. Re ct or J. an.s la m M R. W ijn ga ar de n A. Almasi K. Heeck D. Iannuzzi 33

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