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Physical Review A

Using experimental measurements of three-level avoided crossings to determine the quantum defect for the Stark map of highly excited cesium Rydberg atoms

Limei Wang, Changyong Li, Hao Zhang, Linjie Zhang, Yonggang Yang, Yuan Man, Jianming Zhao, Suotang Jia

Published Mar 23, 2016• 3 citations
Publisher

Abstract

The spectra of Rydberg atoms in the domain of three-level avoided crossings formed by the Rydberg $49{S}_{1/2}$ state and high-$l$ states in the $n=45$ manifold are observed in the standard magneto-optical trap of cesium. We develop a highly accurate method which uses the spectroscopic results in order to refine the quantum defect of the $49{S}_{1/2}$ state from the previous value $4.0495\ifmmode\pm\else\textpm\fi{}0.0001$ extrapolated from $n=6--30\phantom{\rule{0.16em}{0ex}}S$ states [K. H. Weber and C. J. Sansonetti, Phys. Rev. A 35, 4650 (1987)] to the new value $4.049\phantom{\rule{0.16em}{0ex}}78\ifmmode\pm\else\textpm\fi{}0.000\phantom{\rule{0.16em}{0ex}}03$. For this purpose, we determine two characteristic properties of the avoided crossings: (i) the minimum gap between the upper and the lower levels, and (ii) the value of equal gaps between the upper and the middle levels and between the middle and the lower levels. The experimental results for the avoided crossing near 4 V/cm are (i) $(111.7\ifmmode\pm\else\textpm\fi{}1.3)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $(57.0\ifmmode\pm\else\textpm\fi{}2.1)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$. For comparison, quantum mechanical simulations based on the published quantum defect yield (i) $109.52h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $56.04h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$. The refined quantum defect is adjusted such that it yields (i) $111.50h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, and (ii) $56.98h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, in even better agreement with the experimental results. The theoretical values of the electric fields for (i) and (ii) differ by 0.03 V/cm, in perfect agreement with the experimental results. The refinement also improves the agreement of their absolute values. The remaining \ensuremath{\sim}1.5% difference is attributed to effects of stray fields.

DOI
10.1103/physreva.93.033416

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The spectra of Rydberg atoms in the domain of three-level avoided crossings formed by the Rydberg 49S1/249{S}_{1/2}49S1/2​ state and high-lll states in the n=45n=45n=45 manifold are observed in the standard magneto-optical trap of cesium. We develop a highly accurate method which uses the spectroscopic results in order to refine the quantum defect of the 49S1/249{S}_{1/2}49S1/2​ state from the previous value 4.0495\ifmmode±\else\textpm\fi0.00014.0495\ifmmode\pm\else\textpm\fi{}0.00014.0495\ifmmode±\else\textpm\fi0.0001 extrapolated from n=6−−30Sn=6--30\phantom{\rule{0.16em}{0ex}}Sn=6−−30S states [K. H. Weber and C. J. Sansonetti, Phys. Rev. A 35, 4650 (1987)] to the new value 4.04978\ifmmode±\else\textpm\fi0.000034.049\phantom{\rule{0.16em}{0ex}}78\ifmmode\pm\else\textpm\fi{}0.000\phantom{\rule{0.16em}{0ex}}034.04978\ifmmode±\else\textpm\fi0.00003. For this purpose, we determine two characteristic properties of the avoided crossings: (i) the minimum gap between the upper and the lower levels, and (ii) the value of equal gaps between the upper and the middle levels and between the middle and the lower levels. The experimental results for the avoided crossing near 4 V/cm are (i) (111.7\ifmmode±\else\textpm\fi1.3)hMHz(111.7\ifmmode\pm\else\textpm\fi{}1.3)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}(111.7\ifmmode±\else\textpm\fi1.3)hMHz, and (ii) (57.0\ifmmode±\else\textpm\fi2.1)hMHz(57.0\ifmmode\pm\else\textpm\fi{}2.1)h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}(57.0\ifmmode±\else\textpm\fi2.1)hMHz. For comparison, quantum mechanical simulations based on the published quantum defect yield (i) 109.52hMHz109.52h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}109.52hMHz, and (ii) 56.04hMHz56.04h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}56.04hMHz. The refined quantum defect is adjusted such that it yields (i) 111.50hMHz111.50h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}111.50hMHz, and (ii) 56.98hMHz56.98h\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}56.98hMHz, in even better agreement with the experimental results. The theoretical values of the electric fields for (i) and (ii) differ by 0.03 V/cm, in perfect agreement with the experimental results. The refinement also improves the agreement of their absolute values. The remaining \ensuremath{\sim}1.5% difference is attributed to effects of stray fields.
The Stark effect of ultra-cold Cs Rydberg atom is investigated in a magneto-optical trap, and the avoided crossing between nS state and (n-4) manifold is observed. The ion spectrum near the avoided crossing is obtained by using state-selective field pulse ionization technique. By changing the intensity of the applied electric field, we find that the relative intensities of two Stark states near the avoided crossing exchange obviously. Furthermore, state transfer from nS Rydberg state to high-l state due to the avoided crossing is also obtained.
Transitions between high Rydberg states of 133{}^{133}133Cs 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=100n=100n=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 $\ensuremath{\mu}$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of nSnSnS and nPnPnP Rydberg states of Cs beyond n=90n=90n=90. The analysis of the line shapes of transitions to Rydberg states with $n\ensuremath{\approx}230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high nnn values. The analysis also revealed that the initial polarization of the atomic sample (F=4F=4F=4, MF=4{M}_{F}=4MF​=4) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.
A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths frF{f}_{r}^{F}frF​ are derived in terms of matrices HF{\mathit{H}}^{F}HF and hF{\mathit{h}}^{F}hF, which represent the hydrogenic density of states in a Stark field FFF. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements dl0{d}_{l}^{0}dl0​. Normalized oscillator strengths f‾rF{\overline{f}}_{r}^{F}f​rF​ are defined which are independent of all dl0{d}_{l}^{0}dl0​ for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with m=0and1m=0 \mathrm{and} 1m=0and1 are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields F<13n5F<\frac{1}{3{n}^{5}}F<3n51​ level positions are given analytically with respect to H levels of fixed nnn; m=0m=0m=0 intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At F>13n5F>\frac{1}{3{n}^{5}}F>3n51​, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at m=1m=1m=1 anticrossings in Li, as observed in ZLKK. For m=0m=0m=0 the lower levels usually vanish instead. A full Stark map of calculated intensities f‾rF{\overline{f}}_{r}^{F}f​rF​ is presented for Li (m=0m=0m=0) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include ls\mathrm{ls}ls coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].
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.
We have measured the avoided crossings between the Cs (n+4)s states and the lowest three members of the adjacent n Stark manifold for 20<or=n<or=24 using a novel technique based on the differences in the pulsed field ionization of the states under study. The measured positions of the avoided crossings are in excellent agreement with values calculated by matrix diagonalization, and the experimentally determined widths of the avoided crossings, which range from 29 to 78 MHz, are in reasonable agreement with the calculated values.
Two-photon Doppler-free spectroscopy has been used to measure Stark shifts of n2Sn^{2}Sn2S Rydberg states of 85Rb^{85}\mathrm{Rb}85Rb (for n=15to80n=15 \mathrm{to} 80n=15to80). Scalar polarizabilities ${\ensuremath{\alpha}}_{0}$ were found to obey the relation ${\ensuremath{\alpha}}_{0}[\mathrm{in}\mathrm{MHz}/{(\mathrm{V}/\mathrm{cm})}^{2}]=2.202(28)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}{n}^{*6}+5.53(13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{n}^{*7}$, in good agreement with theoretical values. Avoided crossings were also determined, and first avoided crossings (with the $n\ensuremath{-}3$ manifold of levels) fitted the relation $E(\mathrm{in}\mathrm{V}/\mathrm{cm})=4.638(6)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{8}}{{n}^{*5}}+1.528(18)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{10}}{{n}^{*7}}$.