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arXiv:0912.1528 · Physical Review A

Experimental observation of magic-wavelength behavior of Rb87 atoms in an optical lattice

Nathan E. Lundblad, Malte Schlosser, J. V. Porto

Published Mar 29, 2010• 65 citations
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Abstract

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped $^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

DOI
10.1103/physreva.81.031611

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We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87Rb^{87}\mathrm{Rb}87Rb atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb atoms. Recent progress in metrology exploits so-called “magic wavelengths,” whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.
The precise measurement of transition frequencies of trapped atomic samples is susceptible to inaccuracy arising from the inhomogeneous differential shift of the relevant energy levels in the presence of the trapping fields. We demonstrate near-complete cancellation of the differential ac Stark shift ("light shift") of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in ^{87}Rb atoms trapped in an optical lattice. Up to 95(2)% of the differential light shift is cancelled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology.
In experiments with trapped atoms, atomic energy levels are shifted by the trapping optical and magnetic fields. Regardless of this strong perturbation, precision spectroscopy may be still carried out using specially crafted, "magic" trapping fields. Finding these conditions for particularly valuable microwave transitions in alkali-metal atoms has so far remained an open challenge. Here I demonstrate that the microwave transitions in alkali-metal atoms may be indeed made impervious to both trapping laser intensity and fluctuations of magnetic fields. I consider driving multiphoton transitions between the clock levels and show that these "doubly magic" conditions are realized at special values of trapping laser wavelengths and fixed values of relatively weak magnetic fields. This finding has implications for precision measurements and quantum information processing with qubits stored in hyperfine manifolds.
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.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than 2×10−172\times10^{-17}2×10−17 is feasible, which is of the same accuracy as the expected best optical atomic clock.
Precision measurements and quantum-information processing with cold atoms may benefit from trapping atoms with specially engineered, ``magic'' optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying a magic bias BBB field along a circularly polarized trapping laser field. We map out these BBB fields as a function of trapping laser wavelength for all commonly used alkalis. We also highlight a common error in evaluating Stark shifts of hyperfine manifolds.