High-resolution spectroscopy of 162Dy Rydberg levels

Abstract

Highly excited Rydberg states of lanthanides are a promising, yet largely unexplored, playground for quantum studies. Here, we report on the first high-resolution spectroscopy of 162Dy obtained by two-color trap depletion spectroscopy in a magneto-optical trap. The absolute excitation frequency of over 700 states with effective principal quantum number n between 21 and 130 is measured with an accuracy of 20 MHz. Most states are assigned to the 8 different series converging to the first 4f10(5I8)6s(2S1/2) J = 17/2 ionization potential. This energy is measured at EIP = 47901.8265 +/- 0.0008 cm-1, improving the precision of the literature value by over an order of magnitude. A multichannel quantum defect theory approach is used to benchmark and refine the assignments and to characterize six observed perturbing states belonging to higher ionization limits. These results pave the way for using dysprosium in Rydberg-based quantum architectures, leveraging the unique properties arising from its complex electronic structure. They also represent a compelling benchmark for ab-initio calculations of open-shell atomic systems.

Figures (5)

• Figure 1: (a) Two-photon excitation scheme to the Rydberg levels. The first photon, nearly resonant with the intermediate $4f^{10}(^5I_8)6s6p(^1P^\circ_1)$$J=9$ level, corresponds to the transition used for MOT operation. The two arrows indicate the two different excitation pathways employed (see main text). Owing to selection rules, Rydberg states with $J = 8, 9,$ and $10$ can be accessed, as highlighted by the three arrows originating from the intermediate state. (b) Relevant Rydberg series: black lines denote Rydberg levels converging to the first ionization threshold, while gray lines correspond to those associated with the second ionization threshold. The blue-shaded area indicates the range of frequencies we explored. (c) Sketch of the core of the experimental platform. The two lasers used to operate the MOT are labeled $\mathrm{MOT}_V$ and $\mathrm{MOT}_H$, respectively. The laser exciting the atoms to the Rydberg states is labeled as Probe, and the MOT fluorescence is detected by a phototube (PT). (d) Typical spectroscopic signal for $n=90$. Over a frequency span of approximately 6GHz, eight distinct features corresponding to the expected transitions are clearly visible and marked by vertical dashed lines. Each feature exhibits a doublet structure arising from the two different MOT laser frequencies (see main text). $\Delta f_{\text{Probe}}= 0$ corresponds to 1435.657500(20)THz.
• Figure 2: (a) Measured energies of all observed Rydberg levels (b) Plot of the corresponding quantum defects, $\delta$, as a function of the effective integer quantum number $n$. Quantum defects are calculated from Eq. \ref{['eq:Ryd-Ritz']} using the estimated value of $E_{\mathrm{IP}}$. For both panels, gray points represent the full experimental dataset, while red points indicate the Rydberg levels used to extract the ionization potential $E_{\mathrm{IP}}$. The black line in (a) is the best fit used to extract $E_{\mathrm{IP}}$. (c) Residuals ($\Delta$) obtained from the best fit, expressed in units of the experimental uncertainty of 20MHz (d) Dependence of the $\chi^2$ value on $E_{\mathrm{IP}}$. The zero of the horizontal axis corresponds to 47901.8265cm^-1, which is our estimated value of $E_{\mathrm{IP}}$. The black dashed line shows a parabolic fit to the $\chi^2$ dependence on $E_{\mathrm{IP}}$, used to determine the uncertainty in $E_{\mathrm{IP}}$. Error bars in (a) and (b) are within the pointsize while in (c) they are 1 by definition, and thus they are not plotted.
• Figure 3: Quantum defects of assigned Rydberg levels, divided in series for different values of J. Red points correspond to J=8, blue to J=9 and green to J=10. The colored-shaded areas indicate the position of the perturbers used for series grouping (see main text). The black line represents the quantum defect $\delta_{15/2}$ calculated from Eq. (\ref{['eq:Ryd-Ritz']}) using the first excited ionization threshold; the discontinuity occurs when $n^{*}_{15/2}$ becomes equal to 11.
• Figure 4: Panels (a), (b), and (c) show the results of MQDT calculations compared with the experimental data for the Rydberg series with $J=8$, 9, and 10, respectively. The fitting routine is also used to assign a total angular momentum $J$ to each experimental data point. The dashed vertical lines represent the position of the perturbers reported in Tab. \ref{['tab:perturbers']}. The $J=9$ case possesses a perturber not shown in the Figure, located above $E_{\mathrm{IP}}$. (d) Experimental data points that remain unassigned. Red and blue points indicate points suspected to correspond to J=8 and 9, respectively, because they are quite near a quantum defect line from the fit, but a physical constraint disqualifies it for that $J$. Yellow points represent experimental data having either J=9 or J=10. Gray points may belong to a Rydberg g-series, as suggested by their small quantum defect. Black points are not assigned either because theoretical predictions for different series are nearly indistinguishable or because the experimental values deviate too strongly from the theoretical expectations.
• Figure 5: In (a) quantum defects of all the 8 observed Rydberg series as a function of $n$. In red the unperturbed $J=8$, and in green the perturbed $J=10$ Rydberg series reported in the next panel. In (b) amplitude of the depletion signals for the two $J=8$ and $J=10$ Rydberg series. Dashed lines are best fit functions (see text).