Intense, Narrow Atomic-Clock Resonances

We present experimental and theoretical results showing that magnetic resonance transitions from the “end” sublevels of maximum or minimum spin in alkali-metal vapors are a promising alternative to the conventional 0-0 transition for small-size gas-cell atomic clocks. For these “end resonances,” collisional spin-exchange broadening, which often dominates the linewidth of the 0-0 resonance, decreases with increasing spin polarization and vanishes for 100% polarization. The end resonances also have much stronger signals than the 0-0 resonance, and are readily detectable in cells with high buffer-gas pressure.

Figure 1

Energy sublevels of the ground state of an alkali-metal atom in a small magnetic field (not to scale). The nuclear spin quantum number in this illustration is $I=3/2$. The three insets show examples of observed resonance curves (signal intensity vs frequency) for the 0-0 resonance, a microwave end resonance, and a Zeeman end resonance, all in ${}^{87}\mathrm{Rb}$ at 140 °C. The corresponding linewidths are $\Delta \nu =8.6$, 2.6, and 1.1 kHz. Spin exchange causes the 0-0 resonance to be broader and have a hundred times poorer signal-to-noise ratio (SNR) than the end resonances.

Figure 2

The apparatus for magnetic resonance studies.

Figure 3

The ${}^{87}\mathrm{Rb}$ linewidth of a microwave end resonance measured as a function of laser-light intensity at 140 °C, $[{\mathrm{N}}_2]=0.96\mathrm{amg}$, using the frequency-scanning method. The solid curve is the fit of $\Gamma /\pi$ from Eq. (1) to the experimental data, using a fixed estimate ${\Gamma }_d=111{\mathrm{s}}^{-1}$ [21]. The fitting parameters ${\Gamma }_{\mathrm{sd}}$ and ${\Gamma }_{\mathrm{ex}}$ are consistent with the measurement of Walter et al. [13]. ${\Gamma }_0$ is the sum of contributions from ${\Gamma }_{\mathrm{C}}$ and ${\Gamma }_{\mathrm{in}}$. The insets show experimental resonance curves at the two light-intensity points indicated.

Figure 4

Dependence of the microwave and Zeeman end resonance linewidths on the nitrogen buffer-gas density at 60 °C, obtained using the transient method. The $[{\mathrm{N}}_2]$-independent baseline is due to ${\Gamma }_{\mathrm{ex}}$ and residual inhomogeneity ${\Gamma }_{\nabla B}$. The hatched areas bounded by dashed lines show the linewidth predictions for the two resonances, based on the data of Walter et al. [13]. Compared to the microwave resonance, the Zeeman linewidth shows much less broadening, since it is not affected by the Carver rate ${\Gamma }_{\mathrm{C}}$.