Tailoring Multiloop Atom Interferometers with Adjustable Momentum Transfer

Multiloop matter-wave interferometers are essential in quantum sensing to measure the derivatives of physical quantities in time or space. Because multiloop interferometers require multiple reflections, imperfections of the matter-wave mirrors create spurious paths that scramble the signal of interest. Here, we demonstrate a method of adjustable momentum transfer that prevents the recombination of the spurious paths in a double-loop atom interferometer aimed at measuring rotation rates. We experimentally study the recombination condition of the spurious matter waves, which is quantitatively supported by a model accounting for the coherence properties of the atomic source. We finally demonstrate the effectiveness of the method in building a cold-atom gyroscope with a single-shot acceleration sensitivity suppressed by a factor of at least 50. Our study will impact the design of multiloop atom interferometers that measure a single inertial quantity.

Figure 1

(a) Schematics of the cold-atom gyroscope sensor. The angular tilt $\mathrm{\Delta }\theta$ of the top collimator allows for adjusting the effective momentum transfer of the $\pi$ pulses. (b) Space-time diagram (not to scale) of the time-symmetric four-pulse interferometric sequence in the original equal-$k_{\mathrm{eff}}$ (thin half-transparent lines) and AMT (thick full lines) cases. Red (blue) color labels $F=3$ ($F=4$) internal state of the atoms. Solid (dashed) trajectories correspond to the main (spurious) interferometers. For equal-$k_{\mathrm{eff}}$ (AMT) sequence: the vertical dashed gray (black) lines indicate the timings of the pulses; light- (dark-) gray areas highlight the two loops of the main interferometer. Gray ovals mark the spatial separation of the spurious wave packets at the last pulse in the AMT sequence. For clarity, we show only the output ports labeled by the $F=4$ state.

Figure 2

(a) Space-time diagram of the interferometer to introduce the definitions of the fixed $\mathrm{\Delta }T=40\mu \mathrm{s}$ and the variable $\mathrm{\Delta }{T}_3$. (b) Peak-peak contrast of the spurious interferometers (blue dots) as a function of the third pulse delay $\mathrm{\Delta }{T}_3$, for a set of angles $\mathrm{\Delta }\theta$, and Gaussian fits (solid red lines) to the corresponding data. (c) Fitted values of $\mathrm{\Delta }{T}_3$ yielding maximum contrast for the probed values of $\mathrm{\Delta }\theta$. Dashed black line is the expectation of $\mathrm{\Delta }{T}_3=2\epsilon (T+t_1)$, solid red line is the fit to the data accounting for initial angular offsets $\mathrm{\Delta }{\theta }_{0z}$, $\mathrm{\Delta }{\theta }_{0y}$. (d) Normalized fitted peak contrast for the probed values of ${\epsilon }_{\mathrm{corr}}=\frac{1}{2}[(\mathrm{\Delta }\theta -\mathrm{\Delta }{\theta }_{0z}{)}^2-\mathrm{\Delta }{\theta }_{0y}^2]$. The solid red line is the fit with Eq. (5) with ${\sigma }_r$ and $C_0$ as free parameters (see text). Inset: contrast decay for $\mathrm{\Delta }{T}_3=0$. The solid red line is the expectation for the measured value of ${\sigma }_v$ and the fitted value of ${\sigma }_r$.

Figure 3

(a) Contrast of the main interferometer in the AMT configuration as a function of symmetric time shift $\mathrm{\Delta }{T}_s$, for two values of the angle $\mathrm{\Delta }\theta$. The solid blue and dashed orange lines are empiric Gaussian fits to the data. The vertical dashed lines mark the expected center positions. (b) Phase shift as a function of induced acceleration (see text), in the AMT case with $\mathrm{\Delta }\theta =20\mathrm{mrad}$ and $\mathrm{\Delta }{T}_s=42.9\mu \mathrm{s}$ (blue dots), and in the asymmetric case with $\mathrm{\Delta }{T}_a=\pm 40\mu \mathrm{s}$ (orange squares and green triangles). Solid blue, dashed orange, and dash-dotted green lines are linear fits to the data.