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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.

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We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted Y configuration in an alkali-metal atom. It consists of a Λ formed by two Raman transitions between the ground hyperfine levels and the D transition, allowing RSC along two paths and formation of a CPT dark state. Using statedependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the Λ to make only the motional ground state a CPT dark state. We call this scheme motionselective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a 87 Rb atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss on application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.

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