High-resolution spectroscopy of Rydberg states in an ultracold cesium gas

Transitions between high Rydberg states of ${}^{133}$Cs atoms have been studied by high-resolution millimeter-wave spectroscopy of an ultracold sample. The spectroscopic measurements were performed after releasing the atoms from a magneto-optical trap. Switching off all trapping fields and compensating the stray electric and magnetic fields to below 1 mV/cm and 2 mG, respectively, prior to the spectroscopic measurement enabled the recording of millimeter-wave spectra of Rydberg states with principal quantum number beyond $n=100$ under conditions where the inhomogeneous broadening by stray fields is minimal and no dephasing of the Rydberg-atom sample can be detected over measurement times up to 60 $\mu$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of $nS$ and $nP$ Rydberg states of Cs beyond $n=90$. The analysis of the line shapes of transitions to Rydberg states with $n\approx 230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high $n$ values. The analysis also revealed that the initial polarization of the atomic sample ($F=4$, $M_F=4$) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.

Figure 1

(a) Schematic overview of the laser setup for laser cooling of cesium. The frequency of the master-oscillator power-amplifier (MOPA) system (Toptica TA-Pro) is stabilized by frequency-modulation (FM) spectroscopy [17] of a saturated absorption line of atomic cesium. The frequency modulation of the laser light required for the FM scheme is performed by a resonantly driven electro-optical modulator (EOM). Repumping light is provided by an external-cavity diode laser (ECDL, Toptica DL-Pro), which is stabilized to a second saturated absorption line of cesium atoms using a lock-in detection scheme. (b) Overview of the relevant transitions coupling the hyperfine components $F$ of $6S_{1/2}$ and $F^{\prime }$ of 6$P_{3/2}$: (A) light for absorption imaging, (C) light for laser cooling, (R) light for repumping.

Figure 2

(a) Schematic top view of the setup. Pairs of fiber output couplers and retro reflectors deliver the cooling and repumping light (see text for details). UV light excites ground-state atoms into Rydberg states, and millimeter-wave radiation from a backward-wave oscillator (BWO) drives transitions between Rydberg states. Field plates (see Fig. 3) can be used to apply electric fields across the photoexcitation region. (b) Schematic side view of the setup showing how the atom cloud is imaged onto a charge-coupled-device (CCD) chip by a matched pair of achromatic lenses.

Figure 3

Schematic description of the three potential configurations for the eight electrodes generating homogeneous electric fields at the position of the MOT (blue circle). Electrodes with positive potentials are presented in white and electrodes with a negative potential in black. The arrows indicate the direction of the electric field vectors. The configuration on the left-hand side generates an electric field in $z$ direction, the configuration in the middle generates a field in $x$ direction and the configuration on the right-hand side generates a field in $y$ direction.

Figure 4

Millimeter-wave spectrum of Rydberg states around 231$S_{1/2}$ excited from the initial 93$P_{3/2}$ state. The dashed vertical lines are calculated line positions based on the extrapolated quantum defects of Ref. [9]. The appearance of the dipole-forbidden transitions $n{P}_{1/2,3/2}\leftarrow 93P_{3/2}$ and the apparent line broadening are caused by the residual electric fields.

Figure 5

Experimental and simulated spectra of millimeter-wave transitions between $n{P}_{3/2}$ and $n^{\prime }{S}_{1/2}$ Rydberg states of cesium ($49S_{1/2}\leftarrow 45P_{3/2}$, $68S_{1/2}\leftarrow 59P_{3/2}$, $81S_{1/2}\leftarrow 67P_{3/2}$, $90S_{1/2}\leftarrow 72P_{3/2}$). Each point represents an average over 80 laser shots. The error bars show the standard deviation of each measurement. The black line is a simulated spectrum that has been fitted according to the model described in the Appendix.

Figure 6

Millimeter-wave spectrum of the $68S_{1/2}\leftarrow 59P_{3/2}$ transition including a fitted simulation (thick black line) and an assignment of the single hyperfine transitions (black arrows on dashed vertical lines). The inverted stick spectrum, on which the simulation is based, is presented in arbitrary intensity units and shows the splitting of the $F^{\prime }\leftarrow F$ transitions into their $M_F$ components at the residual magnetic field of 2 mG.

Figure 7

Plot of the fitted magnetic dipole constants of the hyperfine structure of $n{S}_{1/2}$ (a) and $n{P}_{3/2}$ (b) Rydberg states of cesium atoms weighted by ${\left(n^{*}\right)}^3$ vs $n^{*}$ (our measurements are shown in black). The gray bar represents the 95$\%$ confidence interval of a weighted average of all four measurements and guides the eye for the comparison with the literature data [9, 22, 23, 24, 25, 26, 27, 28, 29] (shown in gray) at lower principal quantum numbers.

Figure 8

Experimental and simulated spectra of millimeter-wave transitions from the $59P_{3/2}$ Rydberg state to the $66D_{3/2}$ and $66D_{5/2}$ states of cesium.