If Baryon Asymmetry of the Universe (multiverse?) is due to CP violation

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2 If Baryon Asymmetry of the Universe (multiverse?) is due to CP violation 6 x 10^-28 e-cm <dn <2 x 10^-25 e-cm BUT Standard Model (without theta problem) 10^-33 e-cm < dn < 10^-31 e-cm Theta problem: edm is very large prop to unkown parameter theta which must be set to ~10^10. To avoid this Axions were invented => small industry of Axion searches

3 H = μσ B ex E n σ edm T σ σ E E B B P σ σ B B E E Ko decay violates CP, T Not understood Edm can select between ----eliminate proposed explanations

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7 SNS goal

8 SNS edm experiment based on -Production of UCN in superfluid He4 with Polarized He3 as: -Polarizer - Co- Magnetometer -Polarization Analyzer --Detector Plus FREE Gift from nature Handle on geometric phase systematic

9 Ultra-Cold Neutrons (UCN) E<Vc critical energy for total refelction UCN totally reflected for all angles of incidence E 2 ~ 10 nev o ~ 500 A λ T~1mK h~1m (mgh~e) B~2 Tesla (ub~e) V Material Wave fn penetrates material -> wall losses limit storage time

10 Superthermal Production of UCN 8.9 Å (12 K or 0.95 mev) neutrons can scatter in liquid helium to near rest by emission of a single phonon. Upscattering (by 12 K phonon absorption) ~ Population of 12 K phonons ~ e 12 K/Tbath

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14 Shows edm

15 Dressed Spin when Brf >> B0 (1-10 mg) so Brf ~ 1 G, ωrf /2π ~ 3 khz. RF field must be homogeneous at the 0.1 1% level. Heating and gradients due to eddy currents present design challenges. Eliminates need for SQUID magnetometers and may increase the sensitivity of the experiment.

16 Boston U MIT Yale Old Miss

17 Measurement Cells 2 acrylic cells with inner dimensions of 7.62 cm (width) cm (height) 50 cm (length)

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20 ( ) E B c v c v E B c v E B c v E B B o o motion motion o eff r r r r r r r r r r r r r = = σ σ σ Vanishes for E B ~sin \theta v x E effect

21 R = ω / ω n μ / μ n Hg Hg B z z Δz

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23 Rotation of the Earth!!!! edm 2.5x10^-26 e-cm

24 Magnetic field v c E Perpendiculat to v Rotates with v However If B r ~ r BLOCH-SIEGERT Frequency shift ~ B^2 then ( + v E) E B r 2 Important systematic effect δω ~ B z z v E Discovered by Cummins molecular beam edm experiment

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27 x ω r Bo, E z y ω = ω xy ± ω E v ωe = γ E c Bz ωxy = r z v ω = 1 r [( ) ] 2 2 ω ω ω 1/ 2 ω ω = + r o ωo ω r r 1 r ωo ωr + 2 ω ( ω ω ) o 2 1 r Bloch-Siegert Average over +/- v δω ~ 2 ω xy ( ω ω ) ( ω m ω ) o 2 1 r ± ω o v c E r

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29 B o Geometric Phase Picture +v -v r o E abv ω ω δω = γ ω ω c E b ar r v xy r = = = abr abv o = = ω o r r o ω ω ω ω >> >>

30 Motion of Spins t dρ = dτ 1 dt 0 = Γρ( t) [ H () t,[ H ( t τ ) ρ() t ] 1, Or Bloch equation d M dt ω ω x y = M ω () t () t = ax + bv y () t = ay bv x

31 z sinω o t cosω o t ω o t θ σ ω y CREATE θ ω x. θ = ω θ = t 0 x () t sinω t ω () t dt' cosω t [ ω ( t' ) sinω t' ω ( t' ) cosω t' ] x o y o y o o

32 Once θ Builds up it produces a change in φ sinω o t cosω o t ω o t θ φ sinω o t σ ω x. φ = θ ()[ t ω cosω t + ω sinω t] x o ( t' ) ~ ω ) t dt' ω cosω t cosω t' x y y o o o

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35 ( ) ( ) ( ) ( ) ( ) ( ) () ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = = = = = τ τ ψ τ τ τ τ τ τ τ τ ω τ τ δω ' ' ' 2 ' ' cos 2 t dt t v t v dt h h R t v dt t r t v t r t v t r R R d ab t t o Velocity autocorrelation function ( ) ( ) = 2 2 ω ω ω ψ ω δω o d ab BLOCH SIEGERT (again)

36 ψ (x) = Velocity autocorrelation function Bloch-Siegert again

37 EXAMPLE Circular orbit ψ ψ 2 ( τ ) = v xy cos ω rτ 2 ( ω ) = v xy δ ( ω ω ) r δω = ω abv o 2 2 xy ω r 2 Bloch Siegert result Short correlation times high frequencies ψ ( τ ) = v 2 e τ / τ c δω = ab ω v 2 o 2 1 [ 1+ 1/ ω τ ] o c

38 Long correlation times low frequencies Diffusion limit bounded diffusion G ( r, t) S( q. ω) ψ 2 ω 2 q ( ω) = lim 2 S( q, ω) q0 Egelstaff, de Gennes Physical content ψ 2 2 τ ( τ ) = r () t r ( t τ )

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40 He3 UCN

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49 3 He

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53 Design optimization at PULSTAR UCN source, NCSU, Ra;eigh, NC An apparatus based on an existing dilution fridge and large cryostat containing a single full size measuring cell without E field Will allow studies of all questions relating to double magnetic resonance (He3-UCN). Because of the complexity and long cooling cycle of the full edm apparatus these measurements will be extremely difficult and time-consuming on that apparatus

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56 Questions to address UCN storage and depolarization studies to optimize cell materials and Fabrication techniques Test bed for new cell designs and trouble shooting cells that don t work on main apparatus. Measure scintillations due to relative He3-UCN precession for the first time!!! Demonstrate the concept of critical dressing constant scintillation rate Detection of He3 psuedomagnetic field..possible double resonance effects Study techniques for reversing σ(3), σ(ucn) and Bo Measurement of trajectory correlatonfunction for systematic error Develop techniques for nmr imaging of He3

57 Diffusion in a rectangle

58 Measurement of Correlation Function(s)

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