Measurement method for the nuclear anapole moment of laser-trapped alkali-metal atoms

Weak interactions within a nucleus generate a nuclear spin dependent, parity-violating electromagnetic moment, the anapole moment. We analyze a method to measure the nuclear anapole moment through the electric dipole transition it induces between hyperfine states of the ground level. The method requires tight confinement of the atoms to position them at the antinode of a standing wave Fabry-Perot cavity driving the anapole-induced microwave $E1$ transition. We explore the necessary limits in the number of atoms, excitation fields, trap type, interrogation method, and systematic tests necessary for such measurements in francium, the heaviest alkali.

Figure 1

Anapole moment effective constant for different isotopes of francium.

Figure 2

Schematic setup of the proposed apparatus. The microwave cavity axis is along the $y$ axis. The microwave electric field inside the cavity oscillates along the $x$ axis. The two Raman laser beams are polarized along the $x$ axis and $z$ axis, respectively. The microwave magnetic field and the static magnetic field are both directed along the $z$ axis. A dipole trap (not shown) holds the atoms at the origin that coincides with an antinode of the microwave electric field.

Figure 3

Suppression mechanisms of the $M1$ transition. (a) Trapped atoms would sit at the magnetic field node, where the magnetic field is zero. (b) Schematic of the ground hyperfine levels showing a $\mid \Delta m\mid =1$ transition such as the one for the anapole moment and the $\Delta m=0$ out of resonance transition such as that induced by the $M1$ field. The level spacing as well as the spin do not correspond to any particular atom. (c) Trapped atoms would oscillate around the microwave magnetic field node and would sample a zero time-averaged magnetic field.