EDMs of stable atoms and molecules outline Introduction EDM - PowerPoint PPT Presentation

W.Heil EDMs of stable atoms and molecules outline • Introduction • EDM sensitivity • Recent progress in -EDMs paramagnetic atoms/molecules -EDMs diamagnetic atoms • Conclusion and outlook Solvay workshop „ Beyond the Standard model with Neutrinos and Nuclear Physics“ Brussels, Nov. 29th – Dec. 1st, 2017

Our world is composed of matter ... and not antimatter n   400/cm 3 (CMB) n b  0.2 protons/m 3  n n      b 10 b 6 10 n  SM prediction based on observed flavor-changing CP-violation (CKM-matrix)  n n    10  b 18 b n 

SM CP-odd phases  10    10 ~ O ( 1 ) CKM QCD constrained experimentally (d n , d Hg ) explains CP in K and B meson (strong CP problem) mixing and decays Electric dipole moments (EDMs) of elementary particles (flavor-diagonal CP ) EDM measurement free of SM background  10     38 32 34 d e e cm d n ~ 10 10 e cm fourth order Khriplovich, Zhitnitsky 86 electroweak

Fundamental theory TeV Wilson coefficients QCD Low energy d , n d parameters p Nucleus 3 d , t , He level nuclea r EDMs of paramagnetic EDMs of Atom/molecule atoms and molecules diamagnetic atoms level atomic (Tl,YbF,ThO ,…) (Hg,Xe,Ra.Rn,..) Atoms in traps (Rb,Cs,Fr) Solid state

Atomic EDM + + 𝐹 𝑓𝑦𝑢 𝐹 𝑗𝑜𝑢 Ԧ 𝑒 𝐹𝐸𝑁 - - 𝐹 𝑓𝑔𝑔 = 𝐹 𝑓𝑦𝑢 + 𝐹 𝑗𝑜𝑢 = 𝜁 ⋅ 𝐹 𝑓𝑦𝑢 = 0 complete shielding: ⇒ Δ𝐹 𝐹𝐸𝑁 = − Ԧ 𝑒 𝐹𝐸𝑁 ⋅ 𝐹 𝑓𝑔𝑔 = − Ԧ 𝑒 𝐹𝐸𝑁 ⋅ 𝜁 ⋅ 𝐹 𝑓𝑦𝑢 = 0 L.I.Schiff ( PR 132 2194,1963) : EDM of a system of non-relativistic charged point particles that interact electrostatically can not be measured : 𝜁 = 0

Relativistic violation of Schiff screening (requires the use of relativistic electron radial wavefunctions) Paramagnetic EDMs – „Schiff enhancement “ Atoms Polar molecules

Finite size violation of Schiff screening Diamagnetic EDMs – „Schiff suppression “ For a finite nucleus, the charge and EDM have different spatial distributions S- Schiff moment: Schiff moment is dominant CP-odd N-N interaction for large atoms   S     17   d k 10 e cm ( k Hg ~ -3 ) A A 3   e fm (low energy parameters)    2  2 3 d ~ 10 Z R / R d ~ O ( 10 ) d A N A nuc nuc  Nuclear deformation can enhance heavy atom EDMs (e.g., 225Ra, 223Rn )

 Heavy atoms (relativistic treatment) + finite size:   0  d e  0  d atom  0 ~ Z 3  2 d e  P,T-odd eN interaction Tensor-Pseudotensor ~Z 2 G F C T ~Z 3 G F C S Scalar- Pseudoscalar  Nuclear EDM – finite size Schiff moment induced by P,T-odd N-N interaction ~10 -25  [ecm] 𝜃 𝑒 𝑜 , 𝑒 𝑞 , ҧ 𝑕 0 , ҧ 𝑕 1 , ҧ 𝑕 2  General finding: ഥ Θ 𝑅𝐷𝐸 Paramagnetic EDMs: „Schiff enhancement “ (  >> 1) Diamagnetic EDMs: „Schiff suppression “ (  << 1)  Diamagnetic atoms: Phys. Rep. 397 (04) 63; Phys. Rev. A 66 (02) 012111. 𝑒( 129 𝑌𝑓) = 10 −3 𝑒 𝑓 + 5.2𝑦10 −21 𝐷 𝑈 + 5.6𝑦10 −23 𝐷 𝑇 + 6.7𝑦10 −26 𝜃 ≈ 6.7𝑦10 −26 𝜃

EDM precision experiments (upper limits) Xe 

EDM search: Ramsey type phase measurements   ො 𝑭, 𝑪 𝑭, 𝑪 𝒜 𝒜 ො EDM sensitivity (FOM)      shift dS / d           E 2 d ( E ) N / resolution noise   1    d   ˆ ˆ      x x E SNR ext   ˆ               x 2 B 2 d E / B E noise dS  N  Signal d 𝑂  Precession phase magnetic EDM phase bias phase (  B ) shift (  E )

EDMs of paramagnetic atoms and molecules (Tl, YbF, ThO , …) Interaction energy -d e 𝜁 E •  𝜁 d e  E amplification -585 for Tl 𝜁 atom containing electron electric field 𝜻  10 9 for ThO (E lab  100 V/cm)

2. advantage of YbF , ThO : No coupling   v  E to motional magnetic field electron spin is coupled to internuclear axis and internuclear axis is coupled to E    v  E  = 0 no motional systematic error

Experimental setup: general scheme B E beam of atoms or molecules state readout state preparation Spin precession Observable: phase difference = 2 (m B B ± d e 𝜁 E)  / ħ ( ) H ThO:  H ; J 1 metastable state (ground rotational level; J=1), lifetime ~ 2ms M = -1 M = 0 M = +1

 0 E eff N = -1 E lab H N = +1  E 0 eff M = -1 M = 0 M = +1

 0 E eff    B N = -1    E lab B B H    B N = +1    B  E 0 eff M = -1 M = 0 M = +1

 d  e E  0 E eff eff    B N = -1    E lab B  d  e E B eff H    B  d  e E N = +1  d  eff    e E B eff  E 0 eff M = -1 M = 0 M = +1

C P = +1 P = -1 Preparation/Readout Lasers  d  e E  0 E eff eff    B N = -1    E lab B  d  e E B eff H    B  d  e E N = +1  d  eff    e E B eff  E 0 eff M = -1 M = 0 M = +1

    N   N   N         ˆ i i x , , e M 1 , e M 1 , / 2   N          g B d E / B e eff

Results Science 343 (2014) 269                       3 3 2 . 6 4 . 8 3 . 2 10 [ / ] ( ) / 2 . 6 4 . 8 3 . 2 10 [ rad rad / s s ] ( d d E E W C ) / stat sys e eff stat sys e eff S S using E eff = 84 GV/c m , W S (molecule-specific constant) Phys.Rev. A 84 , 052108 (2011) C S = 0             29 29 d 2 . 1 3 . 7 2 . 5 10 ecm d 8 . 7 10 ecm ( 90 % CL ) e stat sys e d e = 0    9 C S 5 . 9 10 ( 90 % CL )

199 Hg EDM experiment PRL 116 , 161601 (2016) 19 cm use of buffer gases: no EDM false effects due to geometric phases systematic effects in units of 10 -32 ecm  E 10 kV / cm

Effective data taking: 252 days

Results: Hg-EDM    30 d Hg 7 . 4 10 ecm (95% CL) Limits on CP-violating observables from 199 Hg EDM limit

Courtesy of B. Santra

Towards long spin-coherence times (T 2 *) SQUID 15 detector 10 5 B SQUID [pT] 0 -5 Motional narrowing regime:  diff <<1/(  B) -10 -15 (G. D. Cates, et al., Phys. Rev. A 37, 2877) 0,0 0,2 0,4 time [s] 1 1 1   12 * T T T 8 2 1 2, field      4 2   1 4 R 4 2 2 2 2   h B SQUID [pT]             4   B B 2 B R p B * T He 60 . 2 0 . 1   1 , x 1 , y 1 , z 0 T 175 D 2 , 2, field -4 * Long T : -8  2  100 h T  1 p ~ mbar , R ~ 5 cm , B ~ T -12 1 0 2 4 6 8 10 time [h]

Comagnetometry to get rid of magnetic field drifts 406.68 drift ~ 1pT/h B [nT] 406.67   10 -5 Hz/h 406.66 0 5 1 0 1 5 2 0 t [h] B 0 3 He (13 Hz) 129 Xe (4,7 Hz)                  He 0 He const .  L , He  L , Xe He Xe Xe Xe

Subtraction of deterministic phase shifts I. Earth‘s rotation  =  He -  He /  Xe   Xe  rem =  -  Earth II. Ramsey-Bloch-Siegert shift He   * t / T self shift ~ S e 2 0   Xe 2 cross-talk ~   * t / T S e 2 0  *  *  *  *               t / T t / T 2 t / T 2 t / T ( t ) c a t a e a e b e b e 2 , He 2 , Xe 2 , He 2 , Xe Earth He Xe He Xe EDM

Measurement sensitivity: 129 Xe electric dipole moment                h h 4 E d   Xe E E B o Rosenberry and Chupp, PRL 86,22 (2001)  E o  E   E         27 0 . 7 3 . 3 0 . 1 10 ecm d Xe Observable: weighted frequency difference                   He , EDM Xe , EDM Xe , EDM ( ) ( )     He Xe He Xe                   He , EDM Xe , EDM Xe , EDM ( ) ( )     He Xe He Xe   h   4 d sensitivity limit:      Xe E He Xe