Matter-wave velocimeter based on the free-induction decay of atomic lattices

We demonstrate a matter-wave velocimeter that relies on measurements of the free-induction decay of an atomic lattice formed in a laser-cooled sample exposed to an optical standing wave (Carlse et al. Submitted Physical Review (2024)). For atoms falling in a gravitational potential, lattice formation is ensured by changing the relative detuning of the counter-propagating components of the excitation to maintain a standing-wave in the frame of reference of the moving sample. The contrast of the resulting lattice is sensitive to the first order Doppler shift, and it can be probed by back-scattering a near-resonant, traveling-wave read-out pulse. We measure the center-of-mass velocity of the sample by determining the line-center of the Doppler-shifted back-scattered spectrum and infer gravitational acceleration by repeating measurements at varying drop times. We find that improved precsion in both velocity and acceleration determinations can be realized by narrowing the contrast spectrum using two time-separated excitation pulses that imprint a Ramsey fringe pattern on the lattice contrast. We demonstrate these ideas using a sample of rubidium atoms with a temperature of ∼ 10 μK, resulting in a velocity determination with a precision of 600 μm/s and measurements of gravity with a precision of 2 mm/s^2. We show that the primary sensitivity limitation of this velocimeter relates to the thermal coherence length of the sample and describe how the most precise atomic velocity sensor can be realized by applying these techniques to a typical Bose gas.