# 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].

This experiment will be performed in collaboration with the University of Heidelberg and University of Groningen.

##### 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

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**Publications**

**1**. 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