Constraints on a Spin-Dependent Exotic Interaction between Electrons with Single Electron Spin Quantum Sensors

A new laboratory bound on the axial-vector mediated interaction between electron spins at micrometer scale is established with single nitrogen-vacancy (NV) centers in diamond. A single crystal of $p$-terphenyl doped pentacene-$d_{14}$ under laser pumping provides the source of polarized electron spins. Based on the measurement of polarization signal via nitrogen-vacancy centers, we set a constraint for the exotic electron-electron coupling $g_A^e{g}_A^e$, within the force range from 10 to $900\mu \mathrm{m}$. The obtained upper bound of the coupling at $500\mu \mathrm{m}$ is $|g_A^e{g}_A^e/4\pi \hslash c|\le 1.8\times {10}^{-19}$, which is one order of magnitude more stringent than a previous experiment. Our result shows that the NV center can be a promising platform for searching for new particles predicted by theories beyond the standard model.

Figure 1

(a) Schematic experimental setup. A NV center in diamond, which is labeled as $S$, is used to search for the exotic dipole-dipole interaction between electrons. The source of polarized electrons is provided by laser pumped pentacene doped in a $p$-terphenyl single crystal with the thickness being $h=15\mu \mathrm{m}$. The radius of the laser beam for pumping pentacene is $r_0=35\mu \mathrm{m}$. The distance between the NV center and the surface of the single crystal is labeled by d. An external magnetic field, $B_0=512\mathrm{G}$, was applied along the NV’s axis (labeled by the $z$ axis). (b) The electronic energy diagram of pentacene within a $p$-terphenyl host lattice under external magnetic field $B_0$. A laser with a 520-nm wavelength is used to pump the state of pentacene from the singlet ground state $S_0$ to the first excited single state $S_1$. Then, they decay quickly into the triplet state $T_E$ through spin-selective intersystem crossing (ISC). The population in the state $|0⟩$ is much larger than that in $|\pm ⟩$. A radio-frequency pulse labeled by rf is to engineer the population of states $|0⟩$ and $|+⟩$. The spin polarization will relax back to the ground singlet state by phosphorescence or nonradiative decay. The decay time of states $|\pm ⟩$ is $t_1=7\pm 1\mu \mathrm{s}$ [23].

Figure 2

(a) Pulse sequence for measurement of the polarized electrons by $S$. For the rf pulse, the frequency is 820 MHz, and the pulse length is 80 ns. For MW pulses, the frequency is 1.43 GHz, and the pulse length of $\pi /2(\pi )$ is about 90 ns (180 ns). The pulse lengths of all the laser pulses are $1.5\mu \mathrm{s}$. The delay time between MW pulses is set to $\tau =30\mu \mathrm{s}$. (b) Black circles with error bars are experimental accumulated $\varphi$ due to the polarized electrons, with different distances $d=12$, 23, and $49\mu \mathrm{m}$. The error bars of the data are due to the photon statistics. Red line is the fit for $\varphi$ with Eq. (4) when $\lambda =500\mu \mathrm{m}$.

Figure 3

Upper limit on the axial-vector-mediated dipole-dipole interactions between electrons $g_{\mathrm{A}}^{\mathrm{e}}{g}_{\mathrm{A}}^{\mathrm{e}}/4\pi \hslash c$ as a function of the force range $\lambda$ and mass of the axial-vector bosons $m$. The black solid lines represent upper bounds from Refs. [12, 14]. Our work (the red line) establishes a new laboratory bound in the force range from 10 to $900\mu \mathrm{m}$. The obtained upper bound of the interaction at $500\mu \mathrm{m}$ is $|g_A^e{g}_A^e/4\pi \hslash c|\le 1.8\times {10}^{-19}$, which is one order of magnitude more stringent than a previous experiment.