New $CP$-Violation and Preferred-Frame Tests with Polarized Electrons

We used a torsion pendulum containing $\sim 9\times {10}^{22}$ polarized electrons to search for $CP$-violating interactions between the pendulum’s electrons and unpolarized matter in the laboratory’s surroundings or the Sun, and to test for preferred-frame effects that would precess the electrons about a direction fixed in inertial space. We find $|g_{\mathrm{P}}^e{g}_{\mathrm{S}}^N|/(\hslash c)<1.7\times {10}^{-36}$ and $|g_{\mathrm{A}}^e{g}_{\mathrm{V}}^N|/(\hslash c)<4.8\times {10}^{-56}$ for $\lambda >1\mathrm{AU}$. Our preferred-frame constraints, interpreted in the Kostelecký framework, set an upper limit on the parameter $|{\tilde{\mathit{b}}}^e|\le 5.0\times {10}^{-21}\mathrm{eV}$ that should be compared to the benchmark value $m_e^2/M_{\mathrm{Planck}}=2\times {10}^{-17}\mathrm{eV}$.

Figure 1

Scale drawing of the spin pendulum. The light green and darker blue volumes are AlNiCo and Sm ${\mathrm{Co}}_5$, respectively. Upper left: top view of a single “puck”; the spin moment points to the right. Lower right: the assembled pendulum with the magnetic shield shown cut away to reveal the 4 pucks inside. Two of the 4 mirrors (light gold) used to monitor the pendulum twist are prominent. Arrows with filled heads show the relative densities and directions of the electron spins; open-headed arrows show the directions of $\mathit{B}$. The 8 tabs on the shield held small screws that we used to tune out the pendulum’s residual $Q_{21}$ and $Q_{22}$ moments.

Figure 2

Data from a set of runs at ${\varphi }_{\mathrm{d}}=22.5\mathrm{deg}$. The turntable offset (determined from data at all 4 ${\varphi }_{\mathrm{d}}$ values shown in Fig. 3) is subtracted from the vertical axes. The dashed curves show the signal from a hypothetical ${\tilde{\mathit{b}}}^e=(5\times {10}^{-20}\mathrm{eV})\widehat{\mathit{x}}$ which gives out-of-phase sine waves in ${\beta }_{\mathrm{N}}$ and ${\beta }_{\mathrm{W}}$. The solid curves show the best sidereal fit, which yields ${\tilde{b}}_x=(-0.2\pm 1.9)\times {10}^{-21}\mathrm{eV}$, ${\tilde{b}}_y=(-0.1\pm 1.9)\times {10}^{-21}\mathrm{eV}$. The data set spanned a duration of 118 h.

Figure 3

Extraction of lab-fixed signals from one of the complete sets of 4 ${\varphi }_{\mathrm{d}}$ values. The sine and cosine waves result from turntable-fixed effects while solid horizontal lines are the lab-fixed signals; the gyrocompass effect is shown by the dashed line. The data in Fig. 2 yielded the ${\varphi }_{\mathrm{d}}=22.5°$ points.

Figure 4

Upper limits on $|g_{\mathrm{P}}^e{g}_{\mathrm{S}}^N|/(\hslash c)$ as a function of interaction range $\lambda$; the shaded region is excluded at $2\sigma$. Our results and previous work by Youdin et al. [7], Ni et al. [8], and Wineland et al. [6] are indicated by solid, dash-dotted, dotted, and dashed lines, respectively. Our work does not provide constraints for $10\mathrm{km}<\lambda <{10}^3\mathrm{km}$ because integration over the terrestrial surrounding is not reliable in this regime [see Ref. 15 ].