Measurement of the g factor of ground-state 87Sr at the parts-per-million level using co-trapped ultracold atoms

Abstract

We demonstrate nuclear magnetic resonance of optically trapped ground-state ultracold 87Sr atoms. Using a scheme in which a cloud of ultracold 87Rb is co-trapped nearby, we improve the determination of the nuclear g factor, gI , of atomic 87Sr by more than two orders of magnitude, reaching accuracy at the parts-per-million level. We achieve similar accuracy in the ratio of relevant g factors between Rb and Sr. This establishes ultracold 87Sr as an excellent linear in-vacuum magnetometer. These results are relevant for ongoing efforts towards quantum simulation, quantum computation and optical atomic clocks employing 87Sr, and these methods can also be applied to other alkaline-earth and alkaline-earth-like atoms.

Figures (4)

• Figure 1: Schematic of the experimental setup used to measure $g_I$ of $^{87}$Sr in the electronic ground state. Clouds of Rb and Sr atoms are confined in respective crossed optical dipole traps, where the (near-)vertical dipole trap beam is common to both traps. The microwave radiation is emitted using a dedicated microwave antenna, whereas the radio frequency radiation is emitted using coils carrying alternating current.
• Figure 2: (a) Breit-Rabi diagram for $^{87}$Rb in the electronic ground state. The states are labeled by their total magnetic quantum number $m$, and (at low field) by their total angular momentum $F$. The violet arrow marks the hyperfine transition between the two $m=-1$ states used here for (co)magnetometry. (b) Zeeman splitting of $^{87}$Sr in the electronic ground state. The violet arrows show the transitions between nuclear spin states, labeled by their nuclear magnetic quantum number $m_I$. Note the differences between (a) and (b), particularly regarding energy scale. These are due to the total electron spin being zero in Sr, while it is nonzero in Rb.
• Figure 3: (a) Spectrum of the $^{87}$Rb hyperfine transition from the lower $m=-1$ state to the upper $m=-1$ state at an inferred magnetic field of 500.544 G, with Gaussian fit. (b) $^{87}$Sr nuclear magnetic resonance spectrum measured simultaneously in a comagnetometer-like configuration. Solid lines are Gaussian fits to the data.
• Figure 4: (a) Summary of the $^{87}$Sr $g_I$ data. The measured $^{87}\text{Sr}$ NMR frequency as a function of the magnitude of the magnetic field $B$ as inferred from the $^{87}\text{Rb}$ data. The solid line is a linear fit to the data in Table \ref{['tab:summary']}. (b)-(g) Close-ups on the separate data points including rms widths as error bars, and the linear fit, with the uncertainty range of the fitted slope indicated with a (blue) band.