Experimental Demonstration of Shaken-Lattice Interferometry

We experimentally demonstrate a shaken-lattice interferometer. Atoms are trapped in the ground Bloch state of a red-detuned optical lattice. Using a closed-loop optimization protocol based on the dcrab algorithm, we phase-modulate (shake) the lattice to transform the atom momentum state. In this way, we implement an atom beam splitter and build five interferometers of varying interrogation times $T_{\mathrm{I}}$. The sensitivity of shaken-lattice interferometry is shown to scale as $T_{\mathrm{I}}^2$, consistent with simulation (C. A. Weidner, H. Yu, R. Kosloff, and D. Z. Anderson, Phys. Rev. A 95, 043624 (2017).). Finally, we show that we can measure the sign of an applied signal and optimize the interferometer in the presence of a bias signal.

Figure 1

Top view of the experimental setup. The optical lattice beam (dark red) propagates through a lens (L) and focuses on the atoms in the center of the vacuum cell. The lattice beam then passes through a cat’s eye system placed after the atoms that focuses the beam through an EOM and onto the retroreflecting mirror. The imaging beam (magenta) images the atoms’ momentum state after being dropped from the lattice and falling for 20 ms time-of-flight.

Figure 2

Two example shaking functions. (a) Splitting and recombination shaking protocols. (b) Protocol from (a), but with 4 propagation steps added after splitting. We optimize the interferometer so that the atoms remain split after each propagation step. In both cases the second half of the shaking protocol is simply the reflection of the first half.

Figure 3

Percent error in the (a) splitting and (b) recombination protocols as a function of (a) the splitting time $T_{\mathrm{I}}/2$ and (b) the total interrogation time $T_{\mathrm{I}}$. (a, inset) An image from optimized splitting of the atoms evenly into the $\pm 2\hslash k_{\mathrm{L}}$ momentum states and (b, inset) recombining the atoms into the ground Bloch state. The colorbar represents optical density (OD).

Figure 4

Minimum detectable effective acceleration $\delta a$ plotted as a function of interrogation time for each of the five interferometers optimized for this work (black) and fit (red) to $f(T_{\mathrm{I}})=a{T}_{\mathrm{I}}^b+c$. The scaling value $b$ is consistent with the expected $T_{\mathrm{I}}^2$ scaling, and the offset $c$ arises due to imaging noise and is measured experimentally. (inset) Data taken with no atoms present (blue) and no shaking applied to the atoms (red) showing no signal other than imaging noise. Blue data is scaled by the ratio of the relative atom numbers as explained in the text.

Figure 5

Here and in Fig. 6, the momentum population of the atoms after the $T_{\mathrm{I}}=2\mathrm{ms}$ interferometer sequence as a function of the applied acceleration signal. Atoms in the $2n\hslash k_{\mathrm{L}}$ state are denoted by open blue circles ($n=-2$), blue crosses ($n=-1$), black dots ($n=0$), red plus signs ($n=1$) and red asterisks ($n=2$). As the applied signal is varied away from zero, we can distinguish positive and a negative signals. The dotted lines are cubic spline fits to guide the eye.

Figure 6

Plot of the momentum state variation as a function of applied acceleration with the biased interferometer, showing variation of the final state as the acceleration is varied around the optimized bias value of $a_{\mathrm{bias}}=-0.71\mathrm{m}/{\mathrm{s}}^2$ (black dashed line). Data points and splines colored as in Fig. 5. (inset) An experimental image of the optimized split state in the biased interferometer. OD is indicated by the colorbar on the right.