CP-violating magnetic moments of atoms and molecules. $$$ National Science Foundation $$$ NIST Precision Measurement Grant

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1 -violating magnetic moments of atoms and molecules $$$ National Science Foundation $$$ NIST Precision Measurement Grant EDM/V INT/U.Washington, Seattle, Mar 22,

2 Collaborators Boris Ravaine Misha Kozlov UNR Theoretical Atomic Physics group with visitors, Basque restaurant, Apr

3 Outline 3

4 electron EDM and supersymmetry courtesy of D. DeMille Present limit d e < 1.6 ä e cm Our proposal 4

5 -violating polarizability D = α E μ? =?β E b 0 implies P and T violation (or -violation) T-reversal: T μ μ T E + E μ I μ = β E Baryshevskii 2004 I will relate this to eedm 5

6 Measuring b 8π B= nβ E 3 Signal number density and E-field Liquid Xe: high number density high E-field breakdown strength 0 M. Romalis (Princeton) b (LXe) =? ä d e 6

7 Coupling V electron EDM and b V is a pseudo-scalar = d E = d σ E d e i Z 2 r σ rˆ even 0 μ i i DEext 0 μ = 2 = 0 ΔE e i0 odd The strongest E-field is near the nucleus μ 0 μ j j V i i DEext 0 = ij even odd odd ( ΔE )( ΔE ) i0 j0 Third order ab initio relativistic Hartree-Fock calculations 7

8 Dirac-Hartree Hartree-Fock Results Closed-shell atoms Third-order calculations ab initio relativistic Z 5 B. Ravaine, M. Kozlov and A. Derevianko, Phys. Rev. A 72, (2005) 8

9 Projected EDM sensitivity of LXe setup d e B 3 β < ne0 8π de 1 n~ /cm 3 E 0,max ~4ä10 5 V/cm β 2 ( ) LXe a.u. d e Weakest measurable B-field sensitivity B min ~ 3ä10-15 G Hz -1/ days of averaging Lamoreaux (2004) Projected d e (b,lxe) < 6ä10-26 e cm but Present limit d e (b,tl) < 1.6ä10-27 e cm Can we save the idea? 9

10 Permanent molecular -violating magnetic moment Z=83 Magnetic moment of diamagnetic molecules (Λ=0 Σ=0) is identically zero Yet, T and P violation lead to magnetic moments A. Derevianko and M. Kozlov, Phys. Rev. A 72, (R) (2005). 10

11 Polar molecules (BiF( BiF) P μ = β C E0 increase the E-field Huge internal molecular fields Z=83 E e mol 2 Re V cm P ( if) β ( Bi ) Emo B 0.3 d 17 e C + μ = l vs μ ( ) 6 ( ) BiF < 10 μb LXe 10 de Electron magnetic moment g/2= (76) Five orders of magnitude enhancement due to stronger fields and higher Z 11

12 Thermally-induced molecular µ Gaining even more orders Kozlov & Derevianko Phys. Rev. Lett. 97, (2006). 12

13 Thermalized sample of spins in E-field E de n de e E-field exp e n kt But external E 0, B=0 d = deσ μ = μ σ = μ e B Misbalance in the spin up/down population => macroscopic magnetization=> ultraweak magnetic field B d d e B n work with solid state 1. Shapiro idea Proof of principle experiment Vasiliev & Kolycheva Lamoreaux 2002: recent advances in magnetometry => competitive schemes 13

14 -violating magnetization B dee 2 kt eff E eff For solid-state samples E eff E applied 10 5 V cm Can we increase E-field acting on eedm? How about molecules? Eeff 10 cm 11 V Potentially SIX orders of magnitude improvement Kozlov & Derevianko Phys. Rev. Lett. 97, (2006). 14

15 Thermally-induced molecular µ µ per molecule is directed along the molecular axis μ = μ B de e kt eff nˆ For rotating molecules nˆ = 0 μ = 0 We need to polarize the sample nˆ E ext μ E ext This link violates Time and Parity 15

16 Effective E-field E in the molecules polar molecules radicals (unpaired electron) Heavy constituents E eff ~Z 3 Molecule E, V / cm eff BaF 8 10 YbF 3 10 HgH Problem: How to make a solid out of highly reactive species? 16

17 Matrix isolation (manufacturing a designer solid) Developed in 1950 s. ESR spectroscopy, Cold substrate ~ 4 K Hosts: Ne, Ar, Xe, SF 6, Matrix ratios as high as 1:100 => n guests ~ /cc Samples are typically small ~ 1mm thickness x 1cm 2 area 17

18 Upper limit on the number density Dipole-Dipole interaction b/w the molecules Possible phase transitions To avoid alignment VDD < kt n kt D max 2 Molecule DD ( ) n,1/ cm max BaF YbF HgH Corresponding matrix ratio ~ 1:100 18

19 Molecule in a matrix cage To the first approximation molecules are free HFS constants for trapped and free molecules differ by a few % For our densities ε=2 => E=E ext /2 * H D E 2deEeff + Ω * E = Eext / ε μ = μ B de e kt eff n z ( ) n E* 1 degree of polarization z 19

20 z n Degree of polarization For rotating molecules n z = 0 External E-field couples to the molecular dipole moment In a thermal sample DE/kT ~ E ~ 10 5 V/cm Breakdown strength for LXe 4 x 10 5 V/cm Molecular axis evolves in a complex multi-valley potential -hindered rotations -librations -Some evidence of rotations for HXeBr and Hydrates -molecules are small (1.7 A vs 4.3 A) 20

21 Permanent vs thermally-induced µ μ = μ B de e kt eff n z For the present limit on eedm μ 12 ( HgH) < n z μ B The largest permanent µ ( ) 17 μ BiF < 3 10 n z μ B For low T μ μ 21

22 Schematics & sensitivity B = 4πγ nμ Weakest measurable B-field Signal-to-noise ratio 22

23 Weakest measurable B-fieldB Demonstrated (atomic magnetometer, Princeton) Projected ( SQUID, Lamoreaux) G/ Hz G/ Hz The present limit on eedm can be recovered within t t demostrated projected = = sec 8 10 sec For t=1week the limit on eedm can be improved by factors ( ) ( ) demostrated T=4K Dillution fridge T->mK Assumptions: γ=1, <n z >~1 23

24 Signal-to to-noise Radicals have traditional magnetic moments μ = 2μ Ωn Random magnetization of the sample => B-field noise Noise is not correlated with E ext mol B z S N = 3 μ μ B N t τ integration time correlation time number of molecules τ h 2 D n dipolar interactions (Strong spin-axis coupling) Budker, Lamoreaux, Sushkov & Sushkov PRA (2006) 24

25 S/N numerical estimate V=10-3 cm 3 matrix ratio 1:100 S/N =1 + present limit on eedm => t =10-5 sec If t= 1week, the present limit can be improved by 2x10 5 These estimates are consistent with the B-field estimates For permanent µ we deal with diamagnetic molecules => noise is strongly suppressed 25

26 electron EDM and supersymmetry courtesy of D. DeMille Present limit µ 26

27 Artificial vacuum footnote Phys. Lett B 194, 137 (1987) matrix isolated Cs atoms 27

28 Summary Concepts of β and µ μ = β E D = β B H = β E B Permanent molecular µ (closed-shell μ=0) Thermally-induced µ promising technique? Other techniques? Systematics? 28