We demonstrate a matter-wave velocimeter which probes the free-induction decay of an atomic lattice formed by interaction with an optical standing wave in the reference frame of the laser-cooled sample. During the drop time of the atoms in a gravitational field, we ensure lattice formation by changing the relative detuning of counterpropagating components of the standing wave. The contrast of the lattice, which is sensitive to the first-order Doppler shift, is measured by backscattering a near-resonant traveling-wave electric field. We infer the center-of-mass velocity by determining the line center of the backscattered spectrum. By varying the drop time, we also measure the gravitational acceleration of the falling lattice. We find that the spectrum can be considerably narrowed by imprinting a Ramsey fringe using two time-separated excitation pulses. We demonstrate these ideas using a sample of rubidium atoms with a temperature of $\sim 10\mu \mathrm{K}$, achieving a precision of $600\mu \mathrm{m}/\mathrm{s}$ for measurements of velocity and $2\mathrm{mm}/{\mathrm{s}}^2$ for determinations of gravity. Since the primary limitation in precision relates to the thermal coherence length of the sample, we show that the most precise atomic velocimeter can be realized by applying these techniques to a typical Bose gas.

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• Atom interferometry
• Atom optics
• Bose gases
• Cold atoms & matter waves
• Cooling & trapping
• Fermi gases
• Optical transient phenomena
• Velocimetry