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

Abstract

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.

Motion-selective coherent population trapping by Raman sideband cooling along two paths in a $Λ$ configuration

“…δ p R , δ q R , and hence, δ CPT (0) are referenced to the differences, ω 3 − ω 1 and ω 3 − ω 2 , which are measured by 6.8-GHz rf spectroscopy. However, in a circularly polarized lattice, the rf lineshape is asymmetric and broad [13], and extracting the difference by fitting a theoretical curve to a lineshape is susceptible to errors. We estimate the uncertainty to be 1 kHz.…”

Motion-selective coherent population trapping for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime

“…In Appendix B, we also include the case of k p = 0 for a transition by an rf field. As a model system, we use a 1D optical lattice in our apparatus [13]. Its wavelength λ OL is 980 nm, at which α = −873 and β = −25 in atomic units for 87 Rb.…”

“…In our previous publication on rf spectroscopy [13], we used a series expansion of H n (a i x) in terms of (a i − ā)/ā with ā = a 2 for i = 1, 3 to speed up the evaluation of F(n, l). The recursion relation, Eq.…”