Atom interferometric techniques for measuring uniform magnetic field gradients and gravitational acceleration

We discuss techniques for probing the effects of a constant force acting on cold atoms using two configurations of a grating echo-type atom interferometer. Laser-cooled samples of $^{85}$Rb with temperatures as low as 2.4 $\mu$K have been achieved in a new experimental apparatus with a well-controlled magnetic environment. We demonstrate interferometer signal lifetimes approaching the transit time limit in this system ($\sim 270$ ms), which is comparable to the timescale achieved by Raman interferometers. Using these long timescales, we experimentally investigate the influence of a homogeneous magnetic field gradient using two- and three-pulse interferometers, which enable us to sense changes in externally applied magnetic field gradients as small as $\sim 4 \times 10^{-5}$ G/cm. We also provide an improved theoretical description of signals generated by both interferometer configurations that accurately models experimental results. With this theory, absolute measurements of $B$-gradients at the level of $3 \times 10^{-4}$ G/cm are achieved. Finally, we contrast the suitability of the two- and three-pulse interferometers for precision measurements of the gravitational acceleration, $g$.