Experimental and theoretical study of the $6{d}_{3/2}$ polarizability of cesium

Experimental and theoretical study of the $6 d_{3 / 2}$ polarizability of cesium

A. Kortyna, C. Tinsman, J. Grab, M. S. Safronova, and U. I. Safronova

Phys. Rev. A 83, 042511 – Published 20 April 2011

Abstract

We report polarizability measurements of atomic cesium’s $6 d_{3 / 2}$ state. The scalar and tensor polarizabilities are determined from hyperfine-resolved Stark-shift measurements using two-photon laser-induced-fluorescence spectroscopy of an effusive beam. The resulting values are $α_{0} = - 5310 (180) a_{0}^{3}$ and $α_{2} = 8650 (260) a_{0}^{3}$ . In addition, our measurements yield the hyperfine coupling constants $A = 16.36 (15)$ MHz and $B = - 0.7 (8)$ MHz, which agree with previous measurements. We also present relativistic all-order calculations of both scalar and tensor polarizabilities. The resulting theoretical values, $α_{0} = - 5686 (121) a_{0}^{3}$ and $α_{2} = 8750 (82) a_{0}^{3}$ , are in agreement with the present experimental results.

Received 8 February 2011

DOI:https://doi.org/10.1103/PhysRevA.83.042511

Authors & Affiliations

A. Kortyna, C. Tinsman, and J. Grab^*

Department of Physics, Lafayette College, Easton, Pennsylvania 18042, USA

M. S. Safronova

Department of Physics and Astronomy, 217 Sharp Lab, University of Delaware, Newark, Delaware 19716, USA

U. I. Safronova

Physics Department, University of Nevada, Reno, Nevada 89557, USA and Institute of Spectroscopy, Russian Academy of Science, Troitsk, Moscow, Russia

^*Current address: Department of Physics, Cornell University, 109 Clark Hall, Ithaca, NY 14853-2501, USA.

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Vol. 83, Iss. 4 — April 2011

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Figure 1
Relevant hyperfine manifolds. Also illustrated are the laser-excitation and fluorescence-detection schemes of the $6 d_{3 / 2}$ state of cesium. Two single-mode lasers excite the $6 s_{1 / 2} (F^{″} = 4) \to 6 p_{1 / 2} (F^{'} = 3 or 4) \to 6 d_{3 / 2} (F)$ resonant two-photon transition. Absorption of the $876.4$ nm laser beam is monitored in a vapor cell and 852.4 nm fluorescence is detected from an effusive beam.Reuse & Permissions
Figure 2
Apparatus for measuring Stark shifts and hyperfine intervals of the $6 d_{3 / 2}$ state of cesium. Symbols in the diagram have the following meanings: 9.193 GHz EOM: 9.193 GHz electro-optical modulator; 40 MHz AOM: 40 MHz acousto-optical modulator; ADC: 12-bit analog-to-digital converter; Broadband EOM: 1-250 MHz electro-optical modulator; BS: beam splitter; DAC: 12-bit digital-to-analog converter; DL1 and DL2: single-mode external-cavity diode lasers; PD and Lockin: photodiode and phase-sensitive lockin amplifier; PMT: photomultiplier tube; Pol.: high-contrast linear polarizer; Rb Freq. Stnd.: 10 MHz rubidium frequency standard; RF Signal Gen.: 1 kHz to 2 GHz radio-frequency signal generator; Sat. Abs. Spect.: saturated-absorption spectrometer; solid lines: signal paths; short dashed line: laser beam paths; long dashed lines: cesium beam path.Reuse & Permissions
Figure 3
Two-photon spectra of the $6 d_{3 / 2} (F = 3, 4, 5)$ hyperfine states at zero field. The upper plot shows the laser-induced-fluorescence signal from the effusive beam (circles) with the hyperfine sublevels marked. Also shown are fitted Voigt profiles, offset for clarity (blue dotted line), and the aggregate fit (red solid line). The lower plot shows the frequency-calibration spectrum: the absorption signal from the cesium vapor cell collected concurrently with the upper plot. For the calibration spectrum, the laser is phase modulated at $210$ MHz, and the locations of the hyperfine sublevels and sidebands are marked. The least-squares fit of Voigt profiles to the lower plot has been omitted for clarity.Reuse & Permissions
Figure 4
Stark-shifted two-photon spectra of the $6 d_{3 / 2} (F = 3$ , 4, and 5) hyperfine states. The upper plot is the laser-induced-fluorescence signal from the effusive beam taken at $6.86 (9)$ kV/cm. All $(F, m)$ sublevels of the $F = 4$ and $F = 5$ hyperfine manifold are marked. The $| 5, 5 〉$ and $| 5, 4 〉$ states are clearly resolved. Also shown are Voigt profiles fitted to each spectral feature, offset for clarity (blue dotted line), and the aggregate least-squares fit (red solid line). The lower plot shows the frequency-calibration spectrum: the absorption signal from the cesium vapor cell collected concurrently with the upper plot but at zero field. For the calibration spectrum, the scanned laser is phase modulated at $115$ MHz, and the locations of the hyperfine states and the modulation sidebands are marked. The least-squares fit of Voigt profiles to the lower plot has been omitted for clarity.Reuse & Permissions
Figure 5
Equation (7) plotted using our data for the $| 5, 5 〉$ to $| 5, 4 〉$ Stark splitting and the $F = 5$ to $F = 4$ hyperfine splitting for the $6 d_{3 / 2}$ state. A linear least-squares fit gives a slope of $- 2.152 (11) MHz / (kV / cm)^{2}$ or $- 8648 (44) a_{0}^{3}$ .Reuse & Permissions
Figure 6
Net Stark shift of the $| 5, 5 〉$ sublevel of the $6 d_{3 / 2}$ state. A linear least-squares fit gives a slope of $- 0.2499 (68) {MHz/(kV/cm)}^{2}$ or $- 1004 (27) a_{0}^{3}$ .Reuse & Permissions

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