Upper limit on the magnetic dipole contribution to the $5p\text{−}8p$ transition in Rb by use of ultracold atom spectroscopy

We report on hyperfine-resolved spectroscopic measurements of the electric-dipole-forbidden $5p_{3/2}\to 8p_{1/2}$ transition in a sample of ultracold ${}^{87}\text{R}\text{b}$ atoms. The hyperfine selection rules enable the weak magnetic dipole $\left(M1\right)$ contribution to the transition strength to be distinguished from the much stronger electric quadrupole $\left(E2\right)$ contribution. An upper limit on the $M1$ transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the $M1$ matrix element and find that it is less than the upper limit extracted from the experiment.

Figure 1

Hyperfine transitions used to separate the $M1$ and $E2$ contributions to the ${}^{87}\text{R}\text{b}$ $5p_{3/2}\left(F^{\prime }\right)\to 8p_{1/2}\left(F^{″}\right)$ transition at 587.6 nm. Starting in $F^{\prime }=0$, the transitions to $F^{″}=1$ (dashed line) and $F^{″}=2$ (solid line) are $M1$ allowed and $E2$ allowed, respectively. The indicated hyperfine splittings are not drawn to scale.

Figure 2

Level diagrams showing the transitions used for state preparation and $5p_{3/2}\left(F^{\prime }\right)-8p_{1/2}\left(F^{″}\right)$ spectroscopy. (a) The trap (solid) and repump (dashed-dotted) lasers provide an ultracold sample of ${}^{87}\text{R}\text{b}$ atoms which are optically pumped into $5s_{1/2}\left(F=1\right)$ using the depletion laser (dashed) and spontaneous emission (dotted). (b) The preparation laser [either pulsed or cw (dashed)] provides excitation to $5p_{3/2}\left(F^{\prime }=0\right)$, and the tunable dye laser at 587.6 nm (solid) further excites to $8p_{1/2}\left(F^{″}=1,2\right)$. Atoms in $8p_{1/2}$ are detected by pulsed photoionization at 1064 nm (dotted).

Figure 3

Timing diagram for the $5p_{3/2}\left(F^{\prime }\right)-8p_{1/2}\left(F^{″}\right)$ spectroscopy. The case of pulsed preparation ($5s_{1/2}-5p_{3/2}$ excitation) is shown. Fractional populations in the $5p_{3/2}\left(F^{\prime }=0\right)$ (solid line) and $8p_{1/2}\left(F^{″}=2\right)$ (dashed line) levels, calculated by rate equations, are also shown. The preparation and excitation intensities are $5.2\text{mW}/{\text{cm}}^2$ and $62\text{W}/{\text{cm}}^2$, respectively.

Figure 4

(a) Solid line: typical spectrum of the $5p_{3/2}\left(F^{\prime }=0\right)\to 8p_{1/2}\left(F^{″}=1,2\right)$ transition. As shown in the inset, no signal is observed for $F^{″}=1$ (near $-64\text{MHz}$), setting a limit on the relative $M1$ transition strength. Dashed line: best fit to a pair of Gaussians as described in text. Dotted line: residuals from the fit offset by seven units for visibility. (b) Spectrum of the $5p_{3/2}\left(F^{\prime }=2\right)\to 8p_{1/2}\left(F^{″}=1,2\right)$ transition (solid line), with best fit to a pair of Gaussians (dashed line), and residuals offset by seven units (dotted line). In this case, allowed $E2$ transitions to both $F^{″}=1$ and 2 are observed.