Search for spin-mass interactionTwo ways to search for SMIS/C accelerometer experimentExperimental designConstruction of the apparatusNoise and error reductionExpected resolution of SMILEStatus of G measurementPrinciple of the experimentDesign of the experimentAbsolute length measurementError budget and expected resolutionPaik-1Lecture 21Search for Spin-Mass Interactionand Precision Measurement of GHo Jung PaikUniversity of MarylandMay 10, 2007 Physics 798G Spring 2007Paik-2Search for spin-mass interaction• The Standard Model predicts a violation of CP symmetry in strong interaction, which has not been observed.⇒ To solve this “strong CP puzzle,” the axion has been proposed (Peccei and Quinn, 1977; Weinberg, 1978; Wilczek, 1978).• The axion mediates spin-mass interaction (SMI).⇒ Potential between an electron and an unpolarized nucleon:where θ≤ 3 × 10−10and λis in meters.• The axion is a strong candidate for cold dark matter.• Search for SMI complements the cavity search for the axion.⇒ Unlike the cavity experiment, these experiments do not assume any population of the axion.,106,11)ˆˆ(8332/22−−××≈⎟⎠⎞⎜⎝⎛+⋅=λθλσπλpsrepsaggerrrmggVhPaik-3Two ways to search for SMI• Modulate σand search for effect on r using a motion sensor.Ritter et al. (1993): Torsion balance with a modulated spin source ⇒ |gsgp| ≤ 5 × 10–27, λ≥ 10 cm• Modulate r and search for effect on σusing a susceptometer.Ni et al. (1994, 1999):SQUID susceptometer with a moving source mass ⇒ |gsgp| ≤ 7 × 10–29, λ≥ 3 cm.Paik-4U. Wash. experimentPaik-5Experimental limits on SMIHeckel et al. (2006):Paik-6S/C accelerometer experiment• Torque between a polarized source with an electron spin density ρsand a test mass of nucleon density ρN:⇒ Problem: I = 0 identically for any closed loop of spin.• Spin source: A toroid with alternating sections of two high-μmaterialswith spin contrast (e.g., A: Magnifer 7904, B: NdNi). Due to quenching of L, σis always parallel to J in transition metals. whereasσcan be anti-parallel to J in rare-earth magnets.⇒ Problem: All rare-earth magnets are hard.• Force sensor: A superconducting differential angular accelerometer with magnetically levitated test masses. ,)mks(107712θρρλθddINNsa−××=.11)ˆˆ(81/2NsrdVdVerrrIλλσπ−⎟⎟⎠⎞⎜⎜⎝⎛+⋅=∫∫Paik-7Experimental design11+θ13θ11θ1411+12+12+12+12+11+11+Spin sourceθ12Driving coilTantalumNiobiumTest massAB49.7 mmTestmass 211+11+11−12−12+11−Testmass 1Spinsource12+12−Vertical cross sectionHorizontal cross sectionPaik-8Construction of the apparatusPaik-9Noise and error reduction• Intrinsic noise: Perform a resonance experiment to suppress the SQUID noise limit:• Common-mode balance and axis alignment:By adjusting currents in the sensing and alignment circuits, angular and linear accelerations are rejected to 10−5and 5 × 10−8m−1.• Dynamic error compensation:Angular and linear accelerometer outputs are used to compensate the residual acceleration sensitivity to 10−8and 5 × 10−11m−1.• Nonlinearity noise: This noise is reduced to ≤ 10−5by stiffening the translational modes by applying feedback to the test masses.τωωωα0eff0eff0,88)( =≈⎥⎦⎤⎢⎣⎡+= QQTkIQTkQTkIfSBNBBPaik-10Expected resolution of SMILE10-4010-3510-3010-25COUPLING gs gpNi et al. (1999)Ground ExperimentSMILEDisallowed by Cosmological ArgumentsDisallowed by Astrophysical ArgumentsAxion LimitFree Flyer10-410-310-210-1RANGE λ (m)• Soft rare-earth material is assumed.⇒ Without it, a factor of 100 loss in sensitivity.⇒ Experiment shelved in favor of the 1/r2law test.Paik-11Status of G measurement6.66 6.67 6.68 6.69 6.70 6.71 6.722000 E-Wash1986 CODATAPTB 1995MSL 1999U. Wuppetal 1999TR&D 1998LANL 1997U. Zurich 1999JILA 1998HUST 1999BIPM 19991998 CODATA G (10-11m3kg-1s-2)Paik-12Principle of the experiment• Planetary system of the source and test masses: GM/r3= ω2. ⇒ The differential accelerometer is used as a null detector.⇒ Straightforward to measure M and ωto <10−6.• Superconducting levitation of the test masses.⇒ No anelasticity associated with a suspension fiber.• Superconducting differential accelerometer.⇒ Low thermal (T = 4.2 K) and amplifier (SQUID) noise.⇒ Both linear and angular acceleration are rejected to ≥105.• Optical interferometry for distance measurement.⇒ Test mass separation is measured to <100 nm in situ at low temperature.Paik-13Design of the experimentTop view of the experimentPaik-14Absolute length measurement• Multi-frequency interferometry (3~5 frequencies).⇒ With tunable CW dye laser, ±8.8 nm accuracy demonstrated between up to 1 cm distance.• Frequency scanning interferometry, developed for alignment of ATLAS tracker.⇒ ~250 nm accuracy demonstrated for 0.2~1.5 m distances.• Null detection with frequency scanning interferometry.21221)1(4λλλλλ−=⇒+===ΔnnnRdPaik-15Error budget and expected resolutionError source Error (m s−2)ΔG/GInstrument 2.5 × 10−153.4 × 10−81.4 × 10−71.2 × 10−74.9 × 10−71.1 × 10−72.1 × 10−72.1 × 10−7< 10−9< 10−10< 10−71.4 × 10−8< 10−86.2 × 10−7Seismic 1 × 10−14Source mass metrology8.5 × 10−15Source mass position3.6 × 10−14Test mass metrology8.1 × 10−15Gradiometer baseline1.5 × 10−14Mass calibration1.5 × 10−14Turntable wobble < 10−16Source driven acceleration < 10−17Angle measurement < 10−16Temperature fluctuations1 × 10−15Others < 10−15Total4.5 ×