Probing P & T-violation Beyond the Standard Model. Aaron E. Leanhardt

Transcription

1 An Electron EDM Search in HfF + : Probing P & T-violation Beyond the Standard Model Aaron E. Leanhardt Experiment: Laura Sinclair, Russell Stutz & Eric Cornell Theory: Ed Meyer & John Bohn JILA, NIST, and University of Colorado March 21, 2007

2 e - EDM JILA

3 e - Energy Levels H B r S r B H E r S r E P-even,T-even P-odd,T-odd d e E S r + d r B E μ B B _ m = 1 2 e _ m = +1 2 μ + B B S r d r e d e E Frequency Shift: Δω = 2d e E h Frequency Resolution: Δω = 1 τ N

4 Advantages of Molecules 1. Large internal electric fields. Effective E-field seen by e -, E eff ~ V/cm. Compared to maximum E lab ~ 10 5 V/cm. 2. Accessible internal electric fields. Easy to polarize, need only E lab ~ 1 V/cm. 3. Rejection of systematic errors. Magnetic field insensitive transitions. E eff independent of E lab. Advantages of Ions 1. Easy to trap. 2. Long spin coherence times.

5 Molecular Ion of Choice: HfF + HfF + Theory Meyer et. al., PRA 73, (2006). Petrov et. al., arxiv:physics/ (2006).

6 Polar Molecules Molecules do not have permanent electric dipole moments. Molecules do have closely spaced levels of opposite parity. Ω-doubling ~10 6 Hz vs. s/p splitting ~10 14 Hz in atoms. Ω = projection of e - angular Ω = +1 Ω = -1 momentum along molecular axis Hz rotation rotation

7 HfF + in the 3 Δ 1 State Net e - spin: Σ =1 Small magnetic moment: μ m << μ B Hf nucleus: I=0 & I=1/2 isotopes 3 Δ1 spin: Σ = ±1 orbital: Λ = ±2 spin + orbital: Ω = Λ + Σ = ±1 + = Λ Σ Ω Ω-doublet splitting m = 1 m = 0 m = + 1

8 Intramolecular Electric Fields E lab mixes states of opposite parity inducing a net molecular dipole moment in the lab frame. Sign of E eff is set by sign of induced molecular dipole moment. E eff > 0 2d e E eff E lab μ el E lab μ el E lab m = 1 m = 0 m = + 1 μ el E lab μ el E lab E eff < 0 2d e E eff

9 Systematic Checks Measure frequency splitting in both Ω-doublet levels. Zeeman shift is common mode. Vary magnitude of E lab. Linear Stark shift implies fully mixed states of opposite parity and E eff nominally independent of E lab. E eff > 0 2μ m B + 2d e E eff B E lab μ el E lab μ el E lab m = 1 m = 0 m = + 1 μ el E lab μ el E lab E eff < 0 2μ m B - 2d e E eff

10 Ion-Ion Collisions & Decoherence Electric field between two ions during a collision tips the quantization axis and generates a geometric phase shift. Sets limits on ion number, N~100, and interrogation time, τ~1s. Δϕ Ω T 4

11 Envisioned Experimental Sequence 1. Apply rotating E lab. 2. Raman π pulse. 3. Ramsey π/2 pulse. 4. Coherent evolution. 5. Ramsey π/2 pulse. 6. Raman π pulse. 7. Photodissociation: HfF + Hf + + F. 8. Separately detect Hf + and HfF +. r E ( t) E cos( ω t) xˆ + sin( ωt) yˆ lab lab [ ]

12 e - EDM Sensitivity Estimate d e < 1.6 x e*cm [~10-18 Debye] E.D. Commins Tl Exp. Limit [PRL 88, (2002)] d e [e*cm] SUSY Left-Right Multi-Higgs d e < e*cm / day 1/2 d e < 2E Projected sensitivity: d e < e*cm / day 1/2 Theoretical calculations: E eff ~ 2 x V/cm Expected spin coherence time: τ ~ 1 second Expected counting statistics: N ~ 3 x 10 6 ions / day eff h τ N Std. Mod. Systematic Checks Change Ω-doublet levels. Vary E lab while E eff remains constant.

13 Experimental Setup Laser Ablation in a Supersonic Jet Fluorescence Spectroscopy Mass Spectrometry Ion Beam Imaging Create HfF +. Cool rotational, vibrational, and translational motion. Measure rotational temperature of neutral HfF molecular beam. Trap Hf +, HfF +, HfF 2+, and HfF 3+. Measure translational temperature of ion beam.

14 Mass Spectrometry 20 cm Exothermic Chemical Reactions ~100,000 ions Hf + + SF 6 HfF + + SF 5 Hf + + SF 6 HfF 2+ + SF 4 Hf + + SF 6 HfF 3+ + SF 3

15 Ion Beam Imaging N = 600 ions/shot T = 2 K

16 LIF Spectroscopy v =2 v =1 v =0 [14.2] Ω=3/2 J =11/2 J =9/2 J =7/2 J =5/2 J =3/2 3 transitions per J level. Count lines to measure rotational temperature. P J =J -1 Q J =J R J =J +1 X 2 Δ 3/2 v =2 v =1 v =0 J =11/2 J =9/2 J =7/2 J =5/2 J =3/2

17 New Neutral HfF Spectroscopy [14.2] Ω=3/2 X 2 Δ 3/2 (0 0) Theory Experiment & Theory T~5 K T=1 K T=5 K T=5 K T=25 K Difference in rotation constants gives chirp in line spacing. B = cm -1 B = cm -1 See also: J. Mol. Spect. 225, 1 (2004).

18 Traditional Discharge Spectroscopy Neutral and ionic atomic lines. Neutral moleclar lines. Unassigned lines well above noise. Hf Ar HfF

19 Novel Ion-Sensitive Spectroscopy Near resonance, optical potential from pulsed standing wave has: ~10 K depth. ~300 GHz power broadened linewidth. Microchannel plate only detects ions. Test idea on known Yb + transition at 370 nm.

20 e - EDM Search Outlook d e < 1.6 x e*cm [~10-18 Debye] E.D. Commins Tl Exp. Limit [PRL 88, (2002)] d e [e*cm] SUSY Left-Right Multi-Higgs d e < e*cm / day 1/2 Created & trapped HfF + molecular ions. Characterized temperature of supersonic beam. Projected sensitivity: d e < e*cm / day 1/2 Theoretical calculations: E eff ~ 2 x V/cm Expected spin coherence time: τ ~ 1 second Expected counting statistics: N ~ 3 x 10 6 ions / day Std. Mod. Currently searching for HfF + electronic transitions Next, begin measuring spin coherence times

21 e - EDM JILA d e < 1.6 x e*cm [~10-18 Debye] E.D. Commins Tl Exp. Limit [PRL 88, (2002)] d e [e*cm] SUSY Left-Right Multi-Higgs d e < e*cm / day 1/2 Aaron Leanhardt Russell Stutz Std. Mod. Laura Sinclair Eric Cornell