Rb $nf$ quantum defects from millimeter-wave spectroscopy of cold ${}^{85}\mathrm{Rb}$ Rydberg atoms

Millimeter-wave resonance spectroscopy has been used to measure the $(n+2)d_{5∕2}$ to $n{f}_{5∕2,7∕2}$ transition frequencies of cold ${}^{85}\mathrm{Rb}$ atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb $nf$ quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of ${\mathrm{Rb}}^{+}$.

Figure 1

(a) Energy-level diagram. The $780\mathrm{nm}$ trap laser excitation of the $5p_{3∕2}$ state and the $480\mathrm{nm}$ dye laser excitation of the $(n+2)d$ state are shown by the upward arrows, and the mm wave transitions to the $n{f}_{5∕2}$ and $n{f}_{7∕2}$ states are shown by the downward bold arrows. (b) Timing diagram. The dye laser pulse is followed by the $5\text{−}\mu \mathrm{s}$-long mm wave pulse and the field-ionization ramp.

Figure 2

The $32d_{5∕2}–30f_{7∕2}$ resonance observed with a $5\text{−}\mu \mathrm{s}$-long mm wave pulse (∎). Calculated resonance assuming a $36\mathrm{mG}$ magnetic field and a $10\mu \mathrm{V}∕\mathrm{cm}$ microwave field amplitude (———). Calculated resonance with zero magnetic field and a $10\mu \mathrm{V}∕\mathrm{cm}$ microwave field amplitude (----).

Figure 3

The $n^{*3}$ scaled fine-structure intervals of the Rb $nf$ state vs $1∕n^{*2}$. The two low $n$ points are from Ref. 12.

Figure 4

Plot of the left-hand side of Eq. (8) vs $⟨r_{n\ell }^{-6}⟩∕⟨r_{n\ell }^{-4}⟩$. Assuming there to be no core penetration in the $nf$ states leads to the solid line with slope and intercept ${\alpha }_q$ and ${\alpha }_d$, the quadrupole and dipole polarizabilities of ${\mathrm{Rb}}^{+}$. Assuming that the $nf$ quantum defect is larger than the $ng$ quantum defect only because of core polarization leads to an upper limit to ${\alpha }_d$ shown by the broken line.