# Presentation: 374973

## An Electron EDM Search using Trapped Molecular Ions

- Russell Stutz

- JILA, NIST, and University of Colorado

- Funding: W.M. Keck Foundation & NSF

- Laura Sinclair, Aaron E. Leanhardt, and Eric A. Cornell
- Theory: Edmund R. Meyer and John L. Bohn

## Motivation for e- EDM Searches

-  Direct observation of T-violation (and P-violation).
-  Constraints on extensions to the standard model.

- S.M. Barr, Int. J. Mod. Phys. A **8**, 209 (1993)

- Supersymmetry:

- Multi-Higgs:

- Left-Right:

- Standard Model:

- SUSY

- Multi-Higgs

- Left-Right

- Std. Mod.

- de [e*cm]

- 10-24

- 10-38

- 10-26

- 10-28

- 10-30

- 10-32

- 10-34

- 10-36

- |de| < 1.6 x 10-27 e*cm
- E.D. Commins Tl Exp. Limit [PRL **88**, 071805 (2002)]

## Why Use Molecular Ions?

- Why use molecules?
-  Large internal electric fields.
-  Molecules have closely spaced levels of opposite parity  they can be fully polarized with E~100 V/cm.
-  Molecules containing heavy atoms give large relativistic enhancement to the electron EDM signal.
- Why use ions?
-  Ions are easy to trap.
-  Potential for long spin coherence times.

## Candidate Molecular Ions

- HfH+ and PtH+
-  3 ground states  ~100 V/cm to fully polarize
-  strong atomic 6s orbital character  large Eeff

- Khriplovich & Lamoreaux, *CP Violation without Strangeness*, (1997).

## Candidate Molecular Ions

- HfH+ and PtH+
-  3 ground states  ~100 V/cm to fully polarize
-  strong atomic 6s character  large Eeff

- 23/2

- 23/2

- 21/2

- a31

- 31

- 33

- literature values [arXiv:physics/0506038 and refs. therein]
- 1st order estimate

- ?

- 1010 V/cm

- 21/2

- 21/2

- 21/2

## Experimental Procedure

- HfH+ 31 J=1 ground state
-  -doublet splitting ~ 200 MHz

- m = -1

- m = 0

- m = +1

- -doublet splitting
- ~ 200 MHz

- Energies not to scale.
- Nuclear spin of 1⁄2 excluded for clarity.

## Experimental Procedure

- HfH+ 31 J=1 ground state
-  Electric field mixes states of opposite parity.

- m = -1

- m = 0

- m = +1

- elElab

- elElab

- elElab

- elElab

- Energies not to scale.

- Elab

- Elab

## Experimental Procedure

- HfH+ 31 J=1 ground state
-  Magnetic field lifts degeneracy between |m|=1 levels.

- m = -1

- m = 0

- m = +1

- mB

- mB

- mB

- mB

- Energies not to scale.

- B

- s

- s

- B

- s

- s

## Experimental Procedure

- HfH+ 31 J=1 ground state
-  Electron EDM shifts the |m|=1 levels in opposite directions in the two -doublet levels.

- m = -1

- m = 0

- m = +1

- deEeff

- deEeff

- deEeff

- deEeff

- 2mB + 2deEeff

- 2mB - 2deEeff

- Energies not to scale.

- s

- s

- s

- s

## Experimental Procedure

- HfH+ 31 J=1 ground state
-  Perform electron spin resonance (ESR) frequency measurement via the Ramsey Method.
-  Photodissociate one spin state and count HfH+ and Hf+ ions.

- m = -1

- m = 0

- m = +1

- Energies not to scale.

- Hf+

- H

- Hf+

- H

- deEeff

- deEeff

- 2mB - 2deEeff

- deEeff

- deEeff

- 2mB + 2deEeff

## Experimental Setup

-  Discharge or laser ablation creates molecular ions.
-  Expansion cools ions to rovibrational ground state (T ~ 1 K).

- ion source

## Experimental Setup

- ion lens

-  Discharge or laser ablation creates molecular ions.
-  Expansion cools ions to rovibrational ground state (T ~ 1 K).
-  Mass selective ion lens focuses only one isotope into trap.

## Experimental Setup

- Paul trap

-  Linear Paul trap holds ions for measurement.
-  Electric and magnetic fields are applied.
-  Rf applied for ESR via Ramsey Method.
-  Photodissociation laser pulse to detect spin states.

## Experimental Setup

- ion
- counting

-  Linear Paul trap holds ions for measurement.
-  Rotating E-field and quadrupole B-field are applied.
-  Rf applied for ESR via Ramsey Method.
-  Photodissociation laser pulse to detect spin states.
-  Channeltron counts atomic or molecular ions.

## Applying Electric & Magnetic Fields

-  Electric field defines molecular quantization axis.
-  Use a radial electric field that ***rotates***:
-  Fast enough that the ion motion is negligible.
-  Slow enough that the molecular axis adiabatically follows.
-  The magnetic quadrupole field gives rise to a radial magnetic field on the ion’s circular orbit, B=B’R.

## Applying Electric & Magnetic Fields

- quadrupole B-field

- homogeneous B-field

-  Electric field defines molecular quantization axis.
-  Use a radial electric field that ***rotates***:
-  Fast enough that the ion motion is negligible.
-  Slow enough that the molecular axis adiabatically follows.
-  The magnetic quadrupole field gives rise to a radial magnetic field on the ion’s circular orbit, B=B’R.

## Sensitivity Estimate

-  N = 150 ions/shot (107 ions/day)
-  Eeff = 1010 V/cm
-   = 1 second
-  Flip magnetic field direction.
-  Change -doublet levels.
-  Change direction of rotating E-field
-  Increase magnitude of rotating E-field

- Inverts EDM signal 

- Constant EDM signal 

- SUSY

- Multi-Higgs

- Left-Right

- Std. Mod.

- de [e*cm]

- 10-24

- 10-38

- 10-26

- 10-28

- 10-30

- 10-32

- 10-34

- 10-36

- |de| < 1.6 x 10-27 e*cm
- E.D. Commins Tl Exp. Limit [PRL **88**, 071805 (2002)]

- proj. sensitivity: |de| < 6 x 10-29 e*cm with 1 day of data

## Experimental Progress

-  Built a linear Paul trap.
-  Laser ablation of HfO2 target to form Hf+ and HfO+.
-  Photodissociation of CH+ to C+ and H.
-  Laser ablated Hf target in expansion, loaded Hf+ ions into trap
-  Mass spectrometry of Hf+ with ~1 amu resolution.

- 1 cm

- CH+ → C+ + H

- T~1K Hf+ beam

## Summary

-  Proposed an experiment to search for the electron EDM using trapped molecular ions.
-  Expect Eeff ~ 1010 V/cm.
-  Expect spin coherence times ~ 1 second.
-  Projected sensitivity ~ 6 x 10-29 e*cm with 1 day of data.

- SUSY

- Multi-Higgs

- Left-Right

- Std. Mod.

- de [e*cm]

- 10-24

- 10-38

- 10-26

- 10-28

- 10-30

- 10-32

- 10-34

- 10-36

- |de| < 1.6 x 10-27 e*cm
- E.D. Commins Tl Exp. Limit [PRL **88**, 071805 (2002)]

- proj. sensitivity: |de| < 6 x 10-29 e*cm with 1 day of data

## Decoherence Effects

- d<2  d=2d>2

-  Axial electric field tips molecular axis out of radial plane.
-  Rotating spin picks up spatially varying Berry’s phase.
-  Net effect cancels out in the ***absence*** of ion-ion collisions.
-  Collisions lead to phase diffusion and decoherence.

## Paul Trapping Fields

-  Periodic focusing and defocusing leads to a net radial restoring force and a harmonic trap (characterized by a secular oscillation frequency sec).
-  DC voltages on endcaps provide axial confinement.

## Mass Selective Ion Lens

- Choose the (mass-dependent) secular frequency, sec, and the rf drive frequency, , to be commensurate.

- velocity kick: