Towards a Mg Lattice Clock: Observation of the ${}^1{S}_0\text{−}{}^3{P}_0$ Transition and Determination of the Magic Wavelength

We optically excite the electronic state $3s3p$ ${}^3{P}_0$ in ${}^{24}\mathrm{Mg}$ atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, $-206.6(2.0)\mathrm{MHz}/{\mathrm{T}}^2$, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.

Figure 1

Optical transitions in ${}^{24}\mathrm{Mg}$ relevant for optical lattice spectroscopy. Atoms are continuously loaded into the long-lived electronic state ${}^3{P}_0$ in an optical dipole trap (ODT) at 1064 nm using a dual MOT [23]. Atoms trapped in a MOT using the ${}^1{S}_0\text{−}{}^1{P}_1$ transition are optically transferred with 457 nm light to the ${}^3{P}_1$ state and then to ${}^3{P}_2$. The atoms are further cooled in a MOT with 383 nm light that excites the ${}^{3}D$ manifold, and cold atoms are permitted to accumulate in ${}^3{P}_0$ in the ODT. These atoms are optically depumped to the ground state via ${}^3{P}_1$, and the magic-wavelength optical lattice is adiabatically turned on. The dipole trap and the optical lattice laser beams are depicted by the bold arrows. The 458 nm light interrogates the magnetic-field-enhanced clock transition.

Figure 2

(a) Measured and fit line profiles for three depths of a 466.97 nm optical lattice. Two sets of measurements (red and blue dots) are shown with their corresponding Gaussian fits (red and blue solid lines). (b) The observed linear ac Stark shift versus the optical lattice depth for several lattice wavelengths. The frequencies of the line center (dots) from Gaussian fits as in (a) and their corresponding linear regression (solid lines) are depicted. For each measurement set at a lattice wavelength, a single frequency offset accounts for the drift of our ultrastable cavity.

Figure 3

Quadratic Zeeman shift of the clock transition versus magnetic field strength (black squares), a parabolic fit (black curve), and the theoretical prediction of Ref. [12] (red curve). The predicted dependence on the magnetic field is $-217(11)\mathrm{MHz}/{\mathrm{T}}^2$, which agrees with the experimental result of $-206.6(2.0)\mathrm{MHz}/{\mathrm{T}}^2$.