Determining the Three-Dimensional Position of an Atomic Cloud in an Atom Interferometer Using One Laser Beam

Abstract

Accurately measuring the three-dimensional position of an atomic cloud is essential for improving the precision of atom interferometers. In the work presented here, the three-dimensional position of an atomic cloud in an atom interferometer is measured with only one laser beam, generated by a phase modulator. The vertical position is determined from the change in the additional-sideband effect with the time interval $T$ between adjacent Raman pulses in the atom interferometer. Based on this method, the vertical position of the atomic cloud is measured with an uncertainty of 0.2 mm; therefore, the uncertainty in a gravity measurement contributed by the gravity gradient is not limited by the uncertainty in the measurement of the vertical position at the level of $0.1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. Furthermore, a method of measuring Rabi oscillations at different horizontal positions to determine the horizontal position of the atomic cloud is proposed and is demonstrated experimentally. With this method, the horizontal position can be determined with an uncertainty of less than 0.1 mm, and the horizontal velocity of the atomic cloud can also be deduced. The methods demonstrated in this paper are helpful for evaluating systematic errors in atom interferometers, and also useful in precision measurements based on an atomic fountain.