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arXiv:1805.05704 · Physical Review A

Observation of vector and tensor light shifts in Rb87 using near-resonant, stimulated Raman spectroscopy

Qingqing Hu, Christian Freier, Yuan Sun, Bastian Leykauf, Vladimir Schkolnik, Jun Jie Yang, Markus Krutzik, Achim Peters

Published Jan 29, 2018• 26 citations
arXivHTMLPDF

Abstract

We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the $^{87}\mathrm{Rb}$ atom $5s$ ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the $5s$ ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum $J$ is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

DOI
10.1103/physreva.97.013424

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We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb^{87}\mathrm{Rb}87Rb atom 5s5s5s ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the 5s5s5s ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum JJJ is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.
Abstract We present the polarization‐ and orientation‐dependent characteristics of the differential light shifts (DLSs) in 87Rb using the near‐resonant, stimulated Raman spectroscopy with an atomic fountain clock. Simulation and experimental results demonstrate that the Raman resonant frequencies would shift sinusoidally as the rotation of the laser's polarization vector due to the polarization‐dependent vector and tensor DLSs, and the total DLS is counteracted in some elliptically polarized laser configurations. What is more, this paper provides an alternative method to measure the effective magnetic field vector and the absolute scalar, vector, and tensor (SVT) DLSs and to verify the theoretically calculated SVT dynamical polarizabilities. These results will facilitate the evaluation and elimination of the light shift‐related systemic errors in the atomic optics‐based quantum sensors, including the atomic magnetometer, atomic interferometer, atomic clock, and quantum register.
We employ doubly resonant two-photon excitation into the 74S74S74S Rydberg state to spectroscopically measure the dynamic scalar polarizability, ${\ensuremath{\alpha}}_{0}$, and tensor polarizability, ${\ensuremath{\alpha}}_{2}$, of rubidium 5P3/25{P}_{3/2}5P3/2​. A cavity-generated 1064-nm optical lattice allows us to reach intensities near $2\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{m}}^{2}$, where the atom field is larger than the hyperfine interaction, and magnetic sublevels are well resolved. In the evaluation of the data we use a self-referencing method that renders the polarizability measurement largely free from the intensity calibration of the laser light field. We obtain experimental values ${\ensuremath{\alpha}}_{0}=\ensuremath{-}1149(\ifmmode\pm\else\textpm\fi{}2.5%)$ and ${\ensuremath{\alpha}}_{2}=563(\ifmmode\pm\else\textpm\fi{}4.2%)$, in atomic units. Methods and results are supported by simulations. The results provide an experimental test of atomic-structure calculations used to determine systematic shifts in atomic clocks and to interpret fundamental-physics experiments.
We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the D1D1D1 and D2D2D2 transition frequencies, with the size of the detuning from the D2D2D2 resonance twice that from the D1D1D1 resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.
We report a precision measurement of a tune-out wavelength for 87Rb^{87}\mathrm{Rb}87Rb using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.
Characterizing the trap-light-induced frequency shifts of optical Zeeman transitions is essential for the precise control of the interacting dynamics between optically trapped single atoms and external light fields. The closed hyperfine transition, for example, 6 S 1/2 | F = 4〉 → 6 P 3/2 | F ′ = 5〉 of the cesium (Cs) atom, is commonly used because of its high transition strength. However, within this hyperfine transition line, different Zeeman transitions experience distinct light shifts due to diverse susceptibilities to the light field, which are usually sorted as dynamic scalar, vector, and tensor polarizabilities. Here, we report an efficient method for measuring the light shifts of optical Zeeman transitions using single neutral atoms confined in an optical tweezer (OT). The method employs a weak probe beam together with an auxiliary optical pumping beam to manipulate the atomic population in ground states. In this way, population changes in a specific Zeeman state are mapped onto a different ground-state hyperfine manifold, allowing the optical spectrum of the Zeeman transition to be reconstructed through standard state-detection techniques. By using the method, we demonstrate the spectrum measurement of the open Zeeman transition 6 S 1/2 | F = 4, m F = 4〉 → 6 P 3/2 | F ′ = 5, m F ′ = 3〉 for a single Cs atom trapped in a π polarized OT. We further perform a systematic characterization of the tweezer-induced light shifts for both this open transition and the closed Zeeman transition 6 S 1/2 | F = 4, m F = 4〉 → 6 P 3/2 | F ′ = 5, m F ′ = 5〉 over a wide range of trap depths. The influence of the tensor polarizability in deep trap depths is experimentally observed.
The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of 87,85Rb^{87,85}\mathrm{Rb}87,85Rb have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the 5s1/2,F=1,25{s}_{1/2},F=1,25s1/2​,F=1,2 states of 87Rb^{87}\mathrm{Rb}87Rb are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the 5s1/2,F=25{s}_{1/2},F=25s1/2​,F=2 state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the 5s1/2,F=2,35{s}_{1/2},F=2,35s1/2​,F=2,3 states of 85Rb^{85}\mathrm{Rb}85Rb are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels MF{M}_{F}MF​ of each hyperfine level FFF are also determined by considering the contributions of tensor polarizabilities.