Circulating pulse cavity enhancement as a method for extreme momentum transfer atom interferometry

Large scale atom interferometers promise unrivaled strain sensitivity to midband (0.1 - 10 Hz) gravitational waves, and will probe a new parameter space in the search for ultra-light scalar dark matter. These atom interferometers require a momentum separation above 10^4 \hbar k between interferometer arms in order to reach the target sensitivity. Prohibitively high optical intensity and wavefront flatness requirements have thus far limited the maximum achievable momentum splitting. We propose a scheme for optical cavity enhanced atom interferometry, using circulating, spatially resolved pulses, and intracavity frequency modulation to overcome these limitations and reach 10^4 \hbar k momentum separation. We present parameters suitable for the experimental realization of 10^4 \hbar k splitting in a 1 km interferometer using the 698 nm clock transition in 87Sr, and describe performance enhancements in 10 m scale devices operating on the 689 nm intercombination line in 87Sr. Although technically challenging to implement, the laser and cloud requirements are within the reach of upcoming cold-atom based interferometers. Our scheme satisfies the most challenging requirements of these sensors and paves the way for the next generation of high sensitivity, large momentum transfer atom interferometers.