401 $\hbar k$ Atom Interferometry with Floquet Atom Optics

To overcome efficiency limitations due to differential Doppler shifts in large momentum transfer atom interferometry, we implement a periodic atom-light coupling to realize Floquet atom optics. Using the strontium $^1S_0$-$^3P_1$ transition, we use this technique to demonstrate state-of-the-art atom interferometers with momentum separation of 401 $\hbar k$. These Floquet atom optics enable pulse efficiencies greater than 99$\%$ for all Doppler detunings, even under strong driving where the detuning is on the order of the Rabi frequency, and result in symmetric evolution of the two arms of the interferometer. This technique is generally applicable to systems with multiple states with discrete detunings, such as multi-isotope interferometers. Furthermore, this work paves the way for even more sensitive clock atom interferometry with larger momentum transfer, a key ingredient in proposals for gravitational wave detection and dark matter searches.