Detection of 3He with SQUIDs

Experimental parametersFor B=300 Gauss

The expected signal is 220 fT (specific geometry is taken into account), while the sensitivity is 3 fT/Hz1/2

SQUID pick-up

3He cell

25 mm

70 mm

Bp coilsHe Dewar

6106.5 kT

BP

Cell is shifted, pick-up loop is7 cm from the center, so Bp field at the pick-uploop is only 200 G, instead of500 G in the center of Bp coil, and there is also a large gradientWhich causes fast (20 s) T1 relaxation

120 mm

inputpickuppickupsquid LL

M

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 ~0.10 that corresponds to 220

fT at the lowest two turns of the gradiometer. For this particular configuration M = 7.4e-9 H, Lpickup =

1.52e-6 H, and Linput = 0.42e-6 H. This

corresponds to a magnetic flux at the SQUID of 7.6e-19 Wb or ~380 m0 at

the SQUID.

Inputcoil

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)

Observation of 3He NMRFID results: test06_14_07_11 (06/14/07 17:46:28)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-1

0

1

2

x 10-3

time, s

V

FID

DEF

950 960 970 980 990 1000

2

4

6

8

10

12

14x 10

-5

Freq, Hz

FFT

Lorentz

DECRA: F0 = 978.66 Hz, T

2* = 0.2829 s, DEF: F

0 = 978.37 Hz, T

2* = 0.2386 s

5v/nT

FID ampl. 0.75 mVTranslates into 190 fT or 1.7e-16 Wb for 48s prepolarization

2 fT floor

The signal will be 10% larger for infiniteprepolarization time, 209 fT extrapolating from our data.Theory predicts 220 fT at 300 G

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

50.4

mm

30 mm75

mm

175

mm

30 mm120 mm

20 mm

39 mm

30 m

m30

mm

Water phantom measurement configuration

-0.1

0

0.1

-0.1

0

0.1

-0.1

-0.05

0

0.05

0.1

Bp coil geometry

Speculation toward a more realistic nEDM design

Experimental data from a 98.5 cm2 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 m0

RMS value of 8.8 m0

Expected RMS noise at 0.5 K is 0.5 m0/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 cm2

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.  

Formula V.H.4 from the nEDM proposal (page 143) states

n = 0.5 m0/sqrt(Hz) and A = 8.8 m0 and Tm = 500 s

f3~ 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.

32

22

3

13)(

mTA

nf

Measurement of T1

20

15

10

5

0

NM

R s

igna

l, a.

u.

806040200Time, sec

y0 = 18.561 ± 1.1 A = -17.523 ± 1.45 invTau = 0.049494 ± 0.011

Dependence of T1 on Bp coils locations

10

8

6

4

2

0

403020100

y0 = 9.8532 ± 0.655 A = -9.6441 ± 0.795 invTau = 0.099566 ± 0.0204

One coil is moved away at 15 cm

When one coil is moved away, T1 shortened 2 times due to larger rel. gradients

Magnetic field non-uniformity

x, m

y, m

Bx

-0.01 0 0.01

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

x, m

y, m

By

-0.01 0 0.01

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

2.6

2.8

3

3.2

3.4

3.6

3.8

x 10-4

-4

-2

0

2

4

x 10-5

x, m

y, m

Bx

-0.01 0 0.01

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

x, m

y, m

By

-0.01 0 0.01

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

6.25

6.3

6.35

6.4

6.45

6.5

x 10-4

-1.5

-1

-0.5

0

0.5

1

1.5

x 10-5

2-coil geometry One-coil geometry

High field 3He NMR

30 minutes 45 minutes

60 minutes

Signal is not calibrated

Relaxation due to gradients

Two-coil case One-coil case

20

22

1

)()(1

B

BBD

Tyx

D=0.1 cm2/s for 4.2 K

These are estimates, and more accurate calculations are under way

Detection fraction1.5x1014 atoms/cm3 are detected with SNR 14 per 0.25 secOr 5x1012 with SNR 1 per 1 sec, and this constitute Relative fraction in liquid (2x1022 cc) X=2.5x10-10

In nEDM experiment the fraction X=10-10

To detect this amount using the same detectors and geometryWe need 6.25 sec

In nEDM experiment geometry differs and detector can be also optimized

In current 3He experiment we have 2 fT/Hz1/2 sensitivity, However, by using larger pick up loops sensitivity can be improvedTo the level 0.5 fT/Hz1/2 and better. Time of measurement is also much longer, so the fraction X=10-10 should be readily detectable

Geometry of nEDM

Pick-up coil is 6 by 5 cm

Pick-up Flux Wb1 -1.70892e-0182 -2.80175e-0183 -3.14763e-0184 -3.2402e-0185 -3.2402e-0186 -3.14762e-0187 -2.80173e-0188 -1.70907e-018

In the middle, 1 fT signalMagnetic dipoles in the 3He cell, blue color, are oriented upwardSensors, pink, are gradiometers of first order

Volume magnetization is 5e-9 A/m, which corresponds to X=1E-10

SQUID sensitivity for different loops

By applying simple scaling that the SQUID sensitivity improves withSquare root of pick-up area, we obtain 0.84 fT/Hz^1/2We 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