Measurement of the permanent electric dipole moment of the ${}^{129}\mathrm{Xe}$ atom

We report on a measurement of the $CP$-violating permanent electric dipole moment (EDM) of the neutral ${}^{129}\mathrm{Xe}$ atom. Our experimental approach is based on the detection of the free precession of co-located nuclear spin-polarized ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ samples. The EDM measurement sensitivity benefits strongly from long spin coherence times of several hours achieved in diluted gases and homogeneous weak magnetic fields of about 400 nT. A finite EDM is indicated by a change in the precession frequency, as an electric field is periodically reversed with respect to the magnetic guiding field. Our result $(-4.7\pm 6.4)\times {10}^{-28}e\mathrm{cm}$, is consistent with zero and is used to place a new upper limit on the ${}^{129}\mathrm{Xe}$ EDM: $|d_{\text{Xe}}|<1.5\times {10}^{-27}e\mathrm{cm}$ (95% C.L.). We also discuss the implications of this result for various $CP$-violating observables as they relate to theories of physics beyond the standard model.

Figure 1

Schematic view of the EDM experiment setup. The central part of the experiment, i.e., the SQUID gradiometer (1) and the EDM cell (2), is placed inside a two-layer magnetically shielded room (MSR) with an additional mu-metal cylinder (4) to reduce magnetic field gradients. A coil assembly consisting of a cosine-coil (5) and an axial multicoil system (6) generates a homogeneous magnetic guiding field in transverse and longitudinal directions, respectively. Four additional shimming coils (shown in the top-left corner) are used to compensate gradients. A fiber-reinforced plastic tube (7) acts as a rigid mounting structure for all components inside the MSR. The gas mixture with the hyperpolarized noble gases ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ and additional buffer gases is provided outside the MSR (8). By means of a gas-transfer system the gas mixture is expanded into the pre-evacuated EDM cell. Solenoidal coils along the transfer line with decreasing winding number density (3) ensure an adiabatic spin transfer from the outer holding field of a few $100\mu \mathrm{T}$ to the low field region inside the MSR. Demagnetization coils around the MSR and the mu-metal cylinder (not displayed) are used to obtain reproducible low field gradients. A more detailed view of the EDM cell is given in Fig. 2.

Figure 2

Schematic view of the spherical EDM cell in the homogeneous electric field of two plate-capacitor electrodes. The setup itself is inside a T-shaped enclosure which is flooded with ${\mathrm{SF}}_6$ for dielectric insulation. Double-shielded cables serve as $+/-$ HV supply lines (details see text). Leakage currents are measured by insulated pA meters put on the respective $+/-$ potentials. The HV supply itself is positioned outside the MSR. Funnel-shaped electrodes at the same potential as the inner $+/-$ HV supply lines further prevent leakage currents to the grounded conductive walls (carbon coated) of the glass T piece. By means of a SQUID gradiometer (on top) the transverse magnetization of the precessing spin sample is monitored. The hyperpolarized gas mixture enters the cell volume through a pneumatically driven valve.

Figure 3

Top: The SQUID gradiometer raw signal with the prominent beating of the ${}^3\mathrm{He}$ and ${}^{129}\mathrm{Xe}$ precession signal at the Larmor frequencies $\approx 13$ and $\approx 5$ Hz (this corresponds to an applied $B_0$ field of about 400 nT). Bottom: The raw signal after subtraction of the fitted model in Eq. (6) (residuals).

Figure 4

The spectrum (amplitude spectral density) of the gradiometer data (black). The prominent sharp peaks at around 5 and 13 Hz correspond to the precession frequencies of ${}^{129}\mathrm{Xe}$ and ${}^3\mathrm{He}$ at $B_0\approx 400$ nT. The narrow peaks at 50 and 16.6 Hz are caused by power line interference, whereas the peak at 26 Hz is a harmonic component of the strong ${}^3\mathrm{He}$ line. For frequencies above 2 Hz we find a white noise level of the gradiometer signal slightly above $\rho \approx 10$ fT/$\sqrt{\text{Hz}}$. Without an inner mu-metal shield (reduced Johnson noise) the system noise drops by about a factor of 10, reaching $\approx 1$ fT/$\sqrt{\text{Hz}}$ which is close to the intrinsic SQUID noise of 0.7 fT/$\sqrt{\text{Hz}}$.

Figure 5

The distribution of the subcut reduced ${\chi }^2$ values ($={\chi }^2/\nu$ with degrees of freedom $\nu =992$). Here the data of run number 4 is shown which has 5743 subcuts.

Figure 6

The measured Larmor frequency of helium ${\omega }_{\text{He}}$ as a function of time for measurement run number 6 lasting about 7 h. The time bin per data point is 40 s and the errors are smaller than the symbol size.

Figure 7

Top: The weighted phase difference according to Eq. (4) for measurement run number 6. Bottom: The weighted phase difference after subtraction of the fitted model in Eq. (20) (residuals). Each data point corresponds to a time bin of 40 s.

Figure 8

An electric field that is periodically switched between $\pm E_z$ with a period $T_a=12000$ s in this example causes a signal in the weighted phase difference that is proportional to a triangular wave $\left[h(t,T_a)\right]$ for a nonzero EDM. Due to the finite high voltage ramping rate of 25 V/s, the edges of the function are smoothed out.

Figure 9

The resulting total (black circles) and uncorrelated (gray squares) EDM uncertainty of a separate test run (without physical $E$-field switching but assuming a hypothetical field of $E_z=800$ V/cm lasting approximately 7 h with $T_{\text{2,}}{\text{Xe}}^{*}=2.9$ h as a function of the $E$-field switching period $T_a$.

Figure 10

Leakage currents monitored during EDM run number 6 with the two pA meters in the high voltage supply lines to the electrodes (see Fig. 2). The pA meters have offsets that slightly drift with time. During polarity reversal a displacement current of $\approx 40$ pA is detected. (Data points are truncated for a better presentability. In Fig. 15 the current during field switching is displayed.) Error bars are smaller than the symbol size.

Figure 11

The extracted EDM mean values and statistical uncertainties (including correlated uncertainties) of the nine single runs. The big difference in the resulting total uncertainty of the single measurement runs (lasting between 5 and 11 h) is striking. The reason is the strong dependence of the statistical uncertainty [Eq. (5)] of a single EDM run on the parameter settings (see Table 1).

Figure 12

ASD of the residual frequency noise which decreases with ${\sigma }_{\text{ASD}}\propto {\tau }^{-3/2}$ as indicated by an according fit (blue). This shows the presence of white noise (with small deviations around $\tau \approx 1000$ s). To fulfill the ASD statistics criteria $N\gg 1$ [51], only data are shown for integration times $\tau <3000$ s.

Figure 13

Sketch of the field mill assembly to measure the effective electric field inside a spherical glass vessel in between two electrodes kept at $+4$ and $-4$ kV, respectively. Two copper plates at its center which form a plate capacitor are rotated by ${180}^{\circ }$ back and forth every 4 s. The displacement currents are monitored by means of an integrator circuit as shown on the bottom left. Opposing electric fields can build up due to charge separation on the inner surfaces of the insulator (glass), which leads to a change in capacitance (see text).

Figure 14

Time course of the electric field [normalized to $E(t=0)]$ inside the spherical glass vessel as recorded by the field mill. The cell was filled with a ${}^3\mathrm{He}$/${}^{129}\mathrm{Xe}$ gas mixture of 30/100 mbar. After an initial field drop, the field stabilizes at $\approx 96\%$ of the field at $t=0$, the value that was measured without glass cell. The externally applied field was 800 V/cm. Each data point with error bar results from an amplitude fit to five rectangular integrator pulses in succession (duration 20 s). The temporal course of the data points show a somewhat higher fluctuation presumably due to environmental electrostatic disturbances. The outliers at about 1200 s are artifacts caused by resets of the integrator circuit (which are needed from time to time in order to keep the integrator output voltage within the dynamic range).

Figure 15

Displacement current measured during an electric field reversal ($-4$ to $+4$ kV) by means of the pA meter in the HV supply lines (see Fig. 2). The voltage ramping rate is 25 V/s with an interruption of 80 s at $V=0$ kV to switch the relays, i.e., a total of 400 s for polarity reversal. A built-in low pass filter causes the double hump structure (the slope of the wings should be the same indicated by the red lines). The exponential relaxation of the displacement current after $t=5800$ s is due to an electric field drop of $\approx 3\%$ which is associated with a capacitance change (for details see text).