Sagnac Interferometry with a Single Atomic Clock

The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology.

Figure 1

Experimental sequence. The situation is depicted in an inertial frame. Starting with atoms prepared in $|\downarrow ⟩$ located at $\theta =0$, a $\pi /2$ pulse generates a superposition of two nondegenerate internal states. Atoms in $|(\uparrow )\downarrow ⟩$ are then transported along a circular path in (anti-)clockwise direction. After a half revolution, a second pulse converts any phase shift into population difference, which is measured in the elementary sequence (black arrows). An extended Ramsey sequence (green arrows) can be used to achieve full common path operation. Here, the $\pi /2$ pulse at time $T$ is extended to a $\pi$ pulse, fully inverting the atomic states. Transport is continued such that all atoms complete a full revolution before converting and measuring the phase difference at time $2T$.

Figure 2

Interferometer scale factor. Results for the two-dimensional case are shown with $R=10$ and flat-top speed profile ${\mathrm{\Omega }}_P(\tau )=\pi /\omega T$ for $0<\tau <\omega T$. Plots for ${\mathrm{\Omega }}_S=0,0.1,0.2$ are shown in black, blue, and red. The inset shows the same data for $0<\omega T<50$.