Progress towards a precision measurement of atomic recoil frequency using an echo interferometer

We discuss progress toward a precision measurement of the atomic recoil frequency in $^{85}$Rb using an echo-type atom interferometer and a new technique [Phys. Rev. A \textbf{79}, 021605(R) (2009)]. At time $t = 0$, a standing wave pulse (swp) creates a superposition of momentum states. The coherence of these $p$-states decays quickly due to the velocity distribution of the laser cooled sample. At $t = T$, a 2nd swp diffracts the $p$-states again and a density grating associated with the interference of $p$-states differing by multiples of the 2-photon recoil momentum ($n \hbar q = 2 n \hbar k$) is formed in the vicinity of $t = 2T$. A traveling wave readout pulse Bragg scatters light only from the grating with spatial periodicity $\lambda/2$ (associated with interfering $p$-states differing by $\hbar q$). The backscatterd light is detected as the signal. A 3rd swp (applied at $t = 2T - \delta T$) converts the difference between interfering $p$-states from $n\hbar q$ to $\hbar q$. All interfering orders of $p$-states contribute to the signal at $t = 2T$. As a function of $\delta T$, the signal shape exhibits narrow fringes that revive periodically at the 2-photon recoil period, $\pi/\omega_q$. We have achieved a single measurement precision of $\sim 500$ ppb on a timescale of $2T \sim 48$ ms. Further improvements are anticipated by extending the timescale and narrowing the fringe width. This work is supported by CFI, OIT, NSERC, OCE, and York University.