1. Detection of 3He with SQUIDs

2. Experimental parameters For B=300 Gauss The expected signal is 220 fT (specific geometry is taken into account), while the sensitivity is 3 fT/Hz 1/2 SQUID pick-up 3He cell 25 mm 70 mm Bp coils He Dewar Cell is shifted, pick-up loop is 7 cm from the center, so Bp field at the pick-up loop is only 200 G, instead of 500 G in the center of Bp coil, and there is also a large gradient Which causes fast (20 s) T1 relaxation 120 mm

3. Taking into account the specific geometry of the cell and the experimental configuration one would expect a total input magnetic flux of 2.0e-16 Wb or ~0.1  0 that corresponds to 220 fT at the lowest two turns of the gradiometer. For this particular configuration M = 7.4e-9 H, L pickup = 1.52e-6 H, and L input = 0.42e-6 H. This corresponds to a magnetic flux at the SQUID of 7.6e-19 Wb or ~380 m  0 at the SQUID.

4. Input coil Pickup coil SQUID Figure Schematic diagram of experimental apparatus showing SQUID-gradiometer coupling, orientation of magnetic fields, and electronics. The actual sample was a 3He cell as described in the text and not a frog. From Matlachov et al., JMR 170 (2004)

5. Observation of 3He NMR 5v/nT FID ampl. 0.75 mV Translates into 190 fT or 1.7e-16 Wb for 48s prepolarization 2 fT floor The signal will be 10% larger for infinite prepolarization time, 209 fT extrapolating from our data. Theory predicts 220 fT at 300 G

6. Due to magnetic field gradients the T2* of the sample was 0.25sec. A detailed calibration of the set-up was performed with a water phantom and agreement between the measured signal and theoretically expected value was better than 5%, which gives us high confidence in our estimations. The total number of atoms in the cell was 4.5e20, or 2e19/cc. The number of polarized atoms in the cell was 0.7e14/cc. Based on these results we have sensitivity to ~0.7e14 atoms/cc with signal-to-noise-ratio (SNR) of 14 in.25 sec. The proposed measurement time for the nEDM is 500 seconds, which would improve the SNR by a factor of ~45. Giving us sensitivity to ~1.5e12 polarized atoms per cc, with the same SNR. From the EDM report, there will be ~ 0.8e12 atoms/cc of polarized 3He in the cell. Based on these crude measurements, even with this simple configuration we are already within a factor of ~2 of required EDM sensitivity. Calibration tests

7. 50.4 mm 30 mm 75 mm 175 mm 30 mm 120 mm 20 mm 39 mm 30 mm Water phantom measurement configuration Bp coil geometry

8. Speculation toward a more realistic nEDM design Experimental data from a 98.5 cm 2 axial gradiometer (112 mm diameter) Predicted input flux 2e-17 Wb (see nEDM proposal, page 113) Peak-to-peak amplitude of the flux at the SQUID to be 5e-20 Wb, or 25 m  0 RMS value of 8.8 m  0 Expected RMS noise at 0.5 K is 0.5 m  0 /sqrt(Hz) (see page 118 of nEDM proposal) SNR in unity band (1 s measuring time) will be ~18. Array of 8 gradiometers of 30 cm 2 Lost factor of 3 in signal due to reduced area (signal scales linearly with diameter or side size) will be compensated for by the array.

9. Formula V.H.4 from the nEDM proposal (page 143) states n = 0.5 m  0 /sqrt(Hz) and A = 8.8 m  0 and T m = 500 s  f 3 ~ 3 mHz. From page 143 of the proposal the required frequency sensitivity is 26 mHz. The final accurate SNR will, of course, depend on actual geometry and size of pick- up coils. One should also note that, as with the assumptions in the nEDM proposal page 143, this calculation assumes the 3He polarization does not decay significantly over the measurement period.

10. Measurement of T 1

11. Dependence of T 1 on B p coils locations When one coil is moved away, T1 shortened 2 times due to larger rel. gradients

12. Magnetic field non-uniformity 2-coil geometry One-coil geometry

13. High field 3He NMR 30 minutes 45 minutes 60 minutes Signal is not calibrated

14. Relaxation due to gradients Two-coil caseOne-coil case D=0.1 cm2/s for 4.2 K These are estimates, and more accurate calculations are under way

15. Detection fraction 1.5x10 14 atoms/cm 3 are detected with SNR 14 per 0.25 sec Or 5x10 12 with SNR 1 per 1 sec, and this constitute Relative fraction in liquid (2x10 22 cc) X=2.5x10 -10 In nEDM experiment the fraction X=10 -10 To detect this amount using the same detectors and geometry We need 6.25 sec In nEDM experiment geometry differs and detector can be also optimized In current 3He experiment we have 2 fT/Hz 1/2 sensitivity, However, by using larger pick up loops sensitivity can be improved To the level 0.5 fT/Hz 1/2 and better. Time of measurement is also much longer, so the fraction X=10 -10 should be readily detectable

16. Geometry of nEDM Pick-up coil is 6 by 5 cm Pick-upFlux Wb 1-1.70892e-018 2-2.80175e-018 3-3.14763e-018 4-3.2402e-018 5-3.2402e-018 6-3.14762e-018 7-2.80173e-018 8-1.70907e-018 In the middle, 1 fT signal Magnetic dipoles in the 3He cell, blue color, are oriented upward Sensors, pink, are gradiometers of first order Volume magnetization is 5e-9 A/m, which corresponds to X=1E-10

17. SQUID sensitivity for different loops By applying simple scaling that the SQUID sensitivity improves with Square root of pick-up area, we obtain 0.84 fT/Hz^1/2 We can make a big loop instead of a number of small loops, So 6 cm dimension is replaced by 30 cm to give 0.4 fT/Hz^1/2