Ground-state hyperfine spectroscopy of ⁸⁷Rb atoms in a 1D optical lattice

We report our theoretical and experimental study on how the motional states of an atom trapped in a 1D optical lattice modify its hyperfine transition. We calculate and measure the inhomogeneously broadened line shape of a transition from the state to the state of ⁸⁷Rb atoms in a lattice with various elliptic polarizations, and find excellent agreement. The atoms are at a temperature below 10 μK, and the well depth at an antinode is 100 μK. For the line shape calculation, we develop an efficient formula that allows us to evaluate the Franck-Condon factor from the 3D motional states accurately with a motional quantum number of as high as 1600. Precise spectroscopic measurements are conducted using evaporatively cooled atoms in a 980 nm lattice formed by a Fabry-Perot cavity placed inside a two-layer magnetic shield. Our results show how the broadening and decoherence of a ground hyperfine transition are related with the motional states. Inversely, our results can be applied to develop schemes to manipulate the motional states by using an inhomogeneously broadened hyperfine transition. As an example, we discuss the radio-frequency induced evaporative cooling in an optical lattice with a fixed well depth.