# Experimental search for the electric dipole moment of Xe-129

In our new project we propose to measure the permanent electric dipole moment (EDM) of the isotope ^{129}Xe, which would imply a breakdown of both parity *P* and time-reversal symmetry *T* and, through the *CPT* theorem, a breakdown in *CP*, the combined symmetries of charge conjugation *C* and parity *P*. Historically, the non-observation of EDMs of particles and atoms has ruled out more speculative models (beyond the Standard Model) than any other single experimental approach in particle physics. The most precise EDM limit was measured in the diamagnetic atom ^{199}Hg (d_{Hg} < 3.1·10^{-29} e∙cm). To get more stringent limits, we propose a ^{3}He/^{129}Xe clock comparison experiment with the detection of free spin precession of gaseous, nuclear polarized ^{3}He or ^{129}Xe samples with a SQUID as magnetic flux detector. We recently described the design and operation of the two-species ^{3}He/^{129}Xe co-magnetometer [1]. The precession of co-located ^{3}He/^{129}Xe nuclear spins can be used as ultra-sensitive probe for non-magnetic spin interactions of type *Δω* ~ **d**_{Xe}∙**E**, since the magnetic dipole interaction (Zeeman-term) drops out in the weighted frequency difference *Δω* of their Larmor frequencies. Compared to spin masers, the detection of free spin precession with spin coherence times T > 1 day does not have the systematic limitations of a feedback loop necessary to sustain coherent spin precession.

Our goal is to improve the present experimental limit (d_{Xe} < 3·10^{-27} e∙cm [2]) significantly by about four orders of magnitude (proposed).

Let the ^{3}He and ^{129}Xe atoms of nuclear spin-½ precess around the combined electric and magnetic fields (assuming both the fields are either parallel or antiparallel to each other). In this case we have a shift in the Larmor precession frequency associated with the application of the electric field (provided we have a finite EDM). If we compare the measured Larmor frequencies with electric field E parallel and antiparallel to the applied magnetic field (see Fig.1), we get

Since an atomic EDM tends to scale as Z^{2} or Z^{3}, we can set d_{He} ≈ 0 << d_{Xe}. In our clock comparison experiment, the observable is the weighted frequency- or phase difference that will result in

From that it follows for the Xe EDM measurement sensitivity

where *δν* is the error in frequency determination, *E* is the electric field strength, and *γ*_{He}/ *γ*_{Xe} ≈ 2.75 is the ^{3}He/^{129}Xe gyromagnetic ratio

##### Fig.1: Spin ½ level scheme in presence of static magnetic and electric fields (finite EDM assumed)

With the frequency statistical error of δν = 0.2 nHz, obtained in the previous measurements at PTB after 1 day and assuming a moderate electric field strength of 2 kV/cm, we get a Xe-EDM senstitvity of d_{Xe} < 4·10^{-29} e∙cm after one day. This is already a factor of 80 better than the published Xe-EDM sensitivity limit [2].

Our current prototypes of the EDM-glass-cells have a T_{1} relaxation time of about 10 hours for ^{129}Xe [3]. To be not restricted due to the gradient relaxation, the magnetic holding field of the experiment (B_{0} ≈ 500nT) has to be as homogeneous as possible. We use a sophisticated cos-coil system that is located inside the magnetic shielded room (MSR) at the research center in Jülich.

The MSR has a two layer mu-metal shield with a shielding factor of ~300 @ 1Hz. The magnetic noise inside the room was measured with our new low-T_{c} SQUID-gradiometer-system to about 1.5 fT/sqrt(Hz) as can be deduced from the spectral power density (Fig.2). We achieve that extremly low noise level even during day time. That allows us to perform Xe-EDM-measurements with a permanent high SNR.

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Fig.2: Spectral power density inside the MSR in Jülich measured with our low-T_{c} SQUID-gradiometer-system

This experiment is performed in collaboration with the University of Heidelberg, the University of Groningen and the research center Jülich

##### Literature

1. C. Gemmel et al., Eur. Phys. Journal D **57** (2010) 303

2. M.A. Rosenberry and T.E. Chupp, Phys. Rev. Lett. **86** (2001) 22

3. M. Repetto et al., J Magn Reson. 2015 Mar;252:163-9

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**Publications**

- Werner Heil, Claudia Gemmel, Sergei Karpuk, Yuri Sobolev, Kathlynne Tullney, Fabian Allmendinger, Ulrich Schmidt, Martin Burghoff, Wolfgang Kilian, Silvia Knappe-Grüneberg, Allard Schnabel, Frank Seifert, and Lutz Trahms "Spin clocks: Probing fundamental symmetries in nature". Annalen der Physik, 525 (2013), 539-549. DOI: 10.1002/andp.201300048

- Tullney K., Allmendinger F., Burghoff M., Heil W., Karpuk S., Kilian W., Knappe-Grüneberg S., Müller W., Schmidt U., Schnabel A., Seifert F., Sobolev Y., Trahms L. "Constraints on spin-dependent short-range interaction between nucleons". Phys Rev Lett. 2013 Sep 6;111(10):100801. Epub 2013 Sep 3.

- F. Allmendinger, W. Heil, S. Karpuk, W. Kilian, A. Scharth, U. Schmidt, A. Schnabel, Yu. Sobolev, and K. Tullney "New Limit on Lorentz-Invariance- and CPT-Violating Neutron Spin Interactions Using a Free-Spin-Precession 3He-129Xe Comagnetometer". Phys. Rev. Lett. 112, 110801 – Published 17 March 2014

- Maricel Repetto, Earl Babcock, Peter Blümler, Werner Heil, Sergei Karpuk, Kathlynne Tullney "Systematic T1 Improvement for Hyperpolarized 129Xenon". J Magn Reson. 2015 Mar;252:163-9. doi: 10.1016/j.jmr.2015.01.015. Epub 2015 Jan 31.