E. Chalkley, S. Aston, C.Collins, M. Nelson, C.Speake22nd March, 2011

Testing the inverse square law

of gravitation at short range with a

superconducting torsion balance

Outline

Large Extra Dimensions and the Inverse Square Law

A superconducting torsion balance– The levitation system– The instrument housing and cryocooler– The test masses

Limiting systematics What we can achieve

Large Extra Dimensions It can be shown that the observed density of

dark energy leads to a preferred scale for large extra dimensions: ~14μm.

At this length scale, deviations from the gravitational inverse square law could indicate a universe with supersymmetry and large extra dimensions.

Callin, Burgess Nuc. Phys B 752 (2006) 60

A superconducting torsion balance

6 DOF micropositioningsystem for source mass

Cryocooled chamber,

can maintain 4.2 K over long

measurement periods

Torque readout:Angle interferometer(ILIAD) for 6th DOF.

Torque 10-17Nm

Source- and test-masses

comprising radial stripes of density-

modulated material.Separation 14μm,

controlled by 5 DOFcapacitance

measurement

Float structure levitated by superconducting

magnetic bearing,supports test-mass

The test masses 2048 pairs of alternating

Au/Cu stripes on parallel plates.

Produces distinctive phased torque signal as one plate is rotated w.r.t. the other.

Designed and fabricated in partnership with the EuminaFAB collaboration.

Zoom in the stripes

The test masses

Source Mass

Test Mass

80mm80mm

78mm1mm 1mm

10µm1µm15µm

The levitation system Lead superconducting

coils on the bearing, niobium/lead on the float– Side coils: control– Top coils: levitate

Five DOF very stiff – ψ rotation less stiff (resonance at 0.1Hz)

Signal cadence at 0.03Hz – 0.1Hz resonance puts us in DC measurement regime.

The levitation system

Prototype levitation bearing: Al body with 12

hand-wound Pb coils.Science coils to be produced lithographically at Heriot-Watt

Prototype levitation float:Silica panels with

evaporated Pb pads, glued assembly.

Science float all Cu.

ILIAD A cryogenic version of the robust, tilt-immune

EUCLID interferometer. Does not require realignment after initial setup.

Read out displacements due to 10-17Nm gravitationally generated torque on levitated float.

Limiting systematicsSystematic Noise

SourceTorque at 15μm

spacingMitigating factors

Newtonian gravity 2.91 x 10-17 Nm Measure mass distribution in test mass, subtract out

Casimir force -2.68 x 10-18 Nm Vary separation, subtract outMagnetic

contamination-4.97 x 10-18 Nm Process control during

manufacture, mag shielding

Electrostatics -4.12 x 10-18 Nm

Contact potential -1.97 x 10-18 Nm All-over Au coating of test surfaces

Seismic noise 4.16 x 10-17 Nm Long integration period

What we can achieveAt λ = 14 µm, α = 6 can be reached with 1 day of integration.

Full calculation of field using 2 flat toroidal LEDs gives SNR close to unity over same period.

Summary

We are building an instrument that should be capable of testing the LED theory at the preferred length scale of the dark energy limit.

Bringing together technology in cryogenics, interferometry, materials science and nanopositioning.