Constraints on Spin-Spin Velocity-Dependent Interactions

The existence of exotic spin-dependent forces may shine light on new physics beyond the standard model. We utilize two iron shielded ${\mathrm{SmCo}}_5$ electron-spin sources and two optically pumped magnetometers to search for exotic long-range spin-spin velocity-dependent force. The orientations of spin sources and magnetometers are optimized such that the exotic force is enhanced and common-mode noise is effectively subtracted. We set direct limit on proton-electron interaction in the force range from 1 cm to 1 km. Our experiment represents more than 10 orders of magnitude improvement than previous works.

Figure 1

The experimental setup (not to scale). Two QuSpin OPMs noted as OPM1 and OPM2 are enclosed in a five-layer magnetic shield. Their sensitive axis orientations are antiparallel along the $\widehat{x}$ axis. Two spin sources noted as ${\mathrm{ISSC}}_{1,2}$ are put in the other, four-layer shield. The spin source is driven with a motor to rotate clockwise or counterclockwise. The blue arrows show the direction of net spin in OPMs and ISSCs.

Figure 2

Top: a typical spectrum of two OPMs and the subtraction result. A uniform ac magnetic field of 8 Hz is applied along the $\widehat{x}$ axis. The dashed blue line and the red dot-dashed line are the spectrum of the OPMs on the left-hand and right-hand side, respectively. The yellow solid line is their difference. Bottom: the OPMs’ response to the pseudomagnetic field along the $\widehat{x}$ axis. The blue dotted and red dotted line are the pseudomagnetic field sensed by ${\mathrm{OPM}}_1$ and ${\mathrm{OPM}}_2$, respectively, and the black dashed line is the subtraction result. The subtraction result agrees well with the result from ${\mathrm{OPM}}_1$.

Figure 3

Statistical results of the $f_8^{ep}$. Each data point represents an average of about one 2.7-h-long dataset. The distribution of $f_8^{ep}$ for one dataset is shown in the inset. The result is well fitted with a Gaussian distribution (red line) with ${\overline{\chi }}^2=1.18$.

Figure 4

Limits on the SSVDI coupling coefficients between electron and proton. The black solid line is our constraints. “Hunter2014 e-p” is from Ref. [24] that uses geoelectrons and atomic magnetometer; “Fadeev 2022 e-p” is from Ref. [44] that compares the experimental and theoretical results of hydrogen spectroscopy; “Chu 2020 e-p” [45] propose to use ${}^3\mathrm{He}$ as sensor and dysprosium iron garnet as spin source, the line is based on their sensitivity at $3\times {10}^{-17}\mathrm{T}$ and is rescaled using the fraction of spin polarization ${\zeta }_p^{{}^3\mathrm{He}}=-0.027$ [46].