Improved limit on the ${}^{225}\mathrm{Ra}$ electric dipole moment

Background: Octupole-deformed nuclei, such as that of ${}^{225}\mathrm{Ra}$, are expected to amplify observable atomic electric dipole moments (EDMs) that arise from time-reversal and parity-violating interactions in the nuclear medium. In 2015 we reported the first “proof-of-principle” measurement of the ${}^{225}\mathrm{Ra}$ atomic EDM.

Purpose: This work reports on the first of several experimental upgrades to improve the statistical sensitivity of our ${}^{225}\mathrm{Ra}$ EDM measurements by orders of magnitude and evaluates systematic effects that contribute to current and future levels of experimental sensitivity.

Method: Laser-cooled and trapped ${}^{225}\mathrm{Ra}$ atoms are held between two high-voltage electrodes in an ultrahigh-vacuum chamber at the center of a magnetically-shielded environment. We observe Larmor precession in a uniform magnetic field using nuclear-spin-dependent laser light scattering and look for a phase shift proportional to the applied electric field, which indicates the existence of an EDM. The main improvement to our measurement technique is an order-of-magnitude increase in spin-precession time, which is enabled by an improved vacuum system and a reduction in trap-induced heating.

Results: We have measured the ${}^{225}\mathrm{Ra}$ atomic EDM to be less than $1.4\times {10}^{-23}e$ cm ($95\%$ confidence upper limit), which is a factor of 36 improvement over our previous result.

Conclusions: Our evaluation of systematic effects shows that this measurement is completely limited by statistical uncertainty. Combining this measurement technique with planned experimental upgrades, we project a statistical sensitivity at the $1\times {10}^{-28}e$ cm level and a total systematic uncertainty at the $4\times {10}^{-29}e$ cm level.

Figure 1

A diagram of the experimental apparatus with important sections labeled. Atoms exit the $\approx 500{}^{\circ }\mathrm{C}$ oven through a narrow nozzle where they are transversely cooled and collimated, longitudinally slowed, and trapped in a 3D MOT using laser light at 714 nm. One of every ${10}^6$ atoms exiting the oven is trapped in the MOT. The MOT is overlapped with the focus of a 50-W 1550-nm laser which forms an ODT. The focusing lens for the ODT is translated by $\approx 1$ m to transfer the atoms between copper electrodes in the center of a glass tube with a vacuum below ${10}^{-11}$ torr. We start with $\approx 10000 {}^{225}\mathrm{Ra}$ atoms in the MOT and trap $\approx 1000$ atoms between the electrodes. After the atoms Larmor precess for 20 s in a B field along $\widehat{z}$, we detect $\approx 500$ atoms. An E field of 65 kV/cm is applied either parallel or antiparallel to the B field during spin precession.

Figure 2

A level diagram including the lowest nine energy levels of radium. The frequency axis is plotted to scale for the upper eight levels. States with orbital angular momentum $L=2$ ($D$ states) are offset horizontally for clarity. Colored arrows represent the atomic transitions we drive with laser light in our experiment. Transitions at 714, 1429, and 483 nm are used for cooling and trapping, repumping, and detection, respectively. Insets (a), (b), and (c) show the isotope shift between ${}^{226}\mathrm{Ra}$ and ${}^{225}\mathrm{Ra}$ and the hyperfine structure present in ${}^{225}\mathrm{Ra}$ resulting from the nuclear spin $I=1/2$. Dotted lines are the ${}^{226}\mathrm{Ra}$ energy levels. Dashed lines are offset from the ${}^{226}\mathrm{Ra}$ levels by the isotope shift between ${}^{225}\mathrm{Ra}$ and ${}^{226}\mathrm{Ra}$. The isotope shift represents the frequency difference between a ${}^{226}\mathrm{Ra}$ state and the center of gravity of the corresponding ${}^{225}\mathrm{Ra}$ hyperfine states, indicated by the solid lines. The upper left corner of each inset is labeled with the energy level it describes. The vertical axes in all three insets have a consistent scale such that the plotted separations accurately represent relative level separation between hyperfine states. Frequency values in (a) and (c) are taken from Ref. [25] and values in (b) are taken from Ref. [27].

Figure 3

(a) A cross-sectional diagram of the copper electrodes used in the apparatus. Measurements are labeled in mm. The solid circle represents a hole for connecting to a 3.2-mm-diameter copper lead through which the electrodes are connected to the high-voltage power supply. The rounded edges have a 4-mm radius of curvature. (b) A picture of one of the copper electrodes used in this work.

Figure 4

A diagram of the polarizing and detection pulse sequence used in this measurement. Wider blue bars represent polarizing pulses and the narrow blue bars are detection pulses. The red trapezoid designates when the E field is ramped on. The label $\mathrm{\Delta }{T}_i$ is used to denote the time between the end of the polarization pulse and the start of the detection pulse for image $i$. For images 1, 3, and 5, $\mathrm{\Delta }{T}_{1,3,5}=17.4$ ms and for images 2 and 4 $\mathrm{\Delta }{T}_{2,4}=20000+\delta$ ms. After an image is taken, we wait 300 ms before applying another polarizing pulse to allow enough time for the camera to read out all captured pixels and become available for the next image.

Figure 5

A collection of four images that demonstrate the effectiveness of background subtraction. (a) An average of 8 ${}^{226}\mathrm{Ra}$ images atoms taken during the first detection image. Periodic fluctuations are visible in the blue laser beam intensity owing to interference fringes that are caused by optical elements whose surfaces create reflections that copropagate with the input beam. (b) An average of the same images after background subtraction. (c) An average of 63 images of ${}^{225}\mathrm{Ra}$ atoms taken during the first detection image. (d) An average of those same images after background subtraction. We account for the nontrivial shape of the atom cloud image by weighting each ${}^{225}\mathrm{Ra}$ image with a corresponding ${}^{226}\mathrm{Ra}$ image before integrating the image.

Figure 6

Nuclear spin-precession data for three E-field conditions: E field parallel to B field, E field antiparallel to B field, and E field off. The plot shows population fraction in the bright state versus $\delta$, where $\mathrm{\Delta }{T}_{2,4}=20000+\delta$ ms. Lines represent a simultaneous fit of all the data to Eqs. (1) using a ${\chi }^2$ minimization fitting program.