Improved measurement of atomic recoil frequency using atom interferometry*

We have recently used a single state time domain atom interferometer to make a measurement of atomic recoil frequency in cold $^{85} Rb$ atoms precise to 2.5 ppm. The interferometer involves excitation by off-resonant standing wave pulses applied at $t=0$ and $t=T$. The pulses diffract and recombine a superposition of momentum states corresponding to the same internal state. This results in a population grating ``echo'' in the vicinity of $t=2T$. The grating was detected using an off resonant readout pulse. This pulse results in a backscattered signal detected using a heterodyne technique. Our measurement of the recoil frequency is in excellent agreement with the value of the recoil frequency obtained from previous measurements of the transition wavelength, atomic mass, and Planck's constant. We present improved measurements using PMT detection, reducing the effect of magnetic field gradients, and increasing the spatial extent of our interferometry beams. We also investigate the role of collisions between hot and cold $^{85} Rb$ atoms on the lifetime of our echo signal and discuss the precision that can be achieved using an atomic fountain.