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arXiv:1808.04987 · New Journal of Physics

Transmission spectroscopy of a single atom in the presence of tensor light shifts

Matthias Steiner, Yue-Sum Chin, Christian Kurtsiefer

Published Feb 4, 2019• 2 citations
arXivHTMLPDF

Abstract

We investigate the interplay between Zeeman and light shifts in the transmission spectrum of an optically trapped, spin-polarized Rubidium atom. The spectral shape of the transmission changes from multiple, broad resonances to a single, narrow Lorentzian with a high resonant extinction value when we increase the magnetic field strength and lower the depth of the dipole trap. We present an experimental configuration well-suited for quantum information applications that enables not only efficient light-atom coupling, but also a long coherence time between ground state hyperfine levels.

DOI
10.1088/1367-2630/ab0431

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We investigate the interplay between Zeeman and light shifts in the transmission spectrum of an optically trapped, spin-polarized Rubidium atom. The spectral shape of the transmission changes from multiple, broad resonances to a single, narrow Lorentzian with a high resonant extinction value when we increase the magnetic field strength and lower the depth of the dipole trap. We present an experimental configuration well-suited for quantum information applications that enables not only efficient light-atom coupling, but also a long coherence time between ground state hyperfine levels.
We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 52S1/2,F=1{5}^{\phantom{\rule{0.16em}{0ex}}2}{S}_{1/2},\phantom{\rule{0.222222em}{0ex}}F=152S1/2​,F=1 hyperfine ground level of a single optically trapped 87{}^{87}87Rb atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum-state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field, we achieve transverse and longitudinal dephasing times of ${T}_{2}^{*}=75\ensuremath{-}150\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and T1>0.5ms,{T}_{1}>0.5\phantom{\rule{0.28em}{0ex}}\mathrm{ms},T1​>0.5ms, respectively. We derive the light-shift distribution of a single atom in the approximately harmonic potential of a dipole trap and show that the measured atomic spin coherence is limited mainly by residual position- and state-dependent effects in the optical trapping potential. The improved understanding enables longer coherence times, an important prerequisite for future applications in long-distance quantum communication and computation with atoms in optical lattices, or for a loophole-free test of Bell's inequality.
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.
We demonstrate that the differential ac-Stark shift of a Zeeman-sensitive ground hyperfine transition in an optical trap can be eliminated by using properly polarized trapping light. We use the vector polarizability of an alkali-metal atom to produce a polarization-dependent ac-Stark shift that resembles a Zeeman shift. We study a transition from the $|2{S}_{1/2},F=2,{m}_{F}=\ensuremath{-}2⟩$ to the $|2{S}_{1/2},F=1,{m}_{F}=\ensuremath{-}1⟩$ state of 7Li^{7}\mathrm{Li}7Li to observe $0.59\ifmmode\pm\else\textpm\fi{}0.02\text{ }\text{ }\mathrm{Hz}$ linewidth with interrogation time of 2 s and $0.82\ifmmode\pm\else\textpm\fi{}0.06\text{ }\text{ }\mathrm{s}$ coherence time of a superposition state. Implications of the narrow linewidth and the long coherence time for precision spectroscopy and quantum information processing using atoms in an optical lattice are discussed.
We describe the implementation of a system for studying light-matter interactions using an ensemble of 106{10}^{6}106 cold rubidium 87 atoms trapped in a single-beam optical dipole trap. In this configuration the elongated shape of the atomic cloud increases the strength of the collective light-atom coupling. Trapping all optically allows for long storage times in a low decoherence environment. We are able to perform several thousands of measurements on one atomic ensemble with little destruction. We report results on paramagnetic Faraday rotations from a macroscopically polarized atomic ensemble. Our results confirm that strong light-atom coupling is achievable in this system which makes it attractive for single-pass quantum information protocols.
Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali-metal atoms and alkaline-earth-metal ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications.
Many precision measurements (e.g., in spectroscopy, atomic clocks, quantum-information processing, etc.) suffer from systematic errors introduced by the light shift. In our experimental configuration, however, the tensor light shift plays a positive role enabling the observation of spectral features otherwise masked by the cancellation of the transition amplitudes and creating resonances at a frequency unperturbed either by laser power or beam inhomogeneity. These phenomena occur thanks to the special relation between the nonlinear Zeeman and light shift effects. The interplay between these two perturbations is systematically studied and the cancellation of the nonlinear Zeeman effect by the tensor light shift is demonstrated.