Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry

We show that light-pulse atom interferometry with atomic point sources and spatially resolved detection enables multiaxis (two rotation, one acceleration) precision inertial sensing at long interrogation times. Using this method, we demonstrate a light-pulse atom interferometer for ${}^{87}\mathrm{Rb}$ with 1.4 cm peak wave packet separation and a duration of $2T=2.3\mathrm{s}$. The inferred acceleration sensitivity of each shot is $6.7\times {10}^{-12}g$, which improves on previous limits by more than 2 orders of magnitude. We also measure Earth’s rotation rate with a precision of $200\mathrm{nrad}/\mathrm{s}$.

Figure 1

(a) Schematic diagram of the apparatus, viewed from the side. The atom cloud (red circle) is cooled and launched from below the magnetically shielded interferometry region. The two interferometer output ports are imaged by both perpendicular cameras (CCD1 and CCD2). All interferometry pulses are delivered from the top of the tower and are retroreflected off a mirror [at angle $\theta (t)$] resting on a piezoactuated tip-tilt stage. (b) Image of the ensemble after a beam splitter pulse showing the separation between two halves of the atomic wave packet. For this shot we launched the atoms with extra velocity to reach CCD3. (c) Top view of the tip-tilt stage and lower cameras with the direction and magnitude of Earth rotation ${\mathbf{\Omega }}_{\mathbf{E}}$ and an (arbitrary) applied counterrotation ${\mathbf{\Omega }}_{\mathrm{C}}$. In our apparatus, ${\varphi }_E\approx 105°$.

Figure 2

Spatial fringes on the atom population observed on CCD2 versus rotation rate offset $\delta {\Omega }_x$. Alternating (blue versus red) regions show anticorrelation in atom population. The second output port, with fringes $\pi \mathrm{rad}$ out of phase, is not shown. Each image is the second-highest variance principle component arising from a set of 20 measurements [19].

Figure 3

Fringe spatial frequency (blue squares, solid line) and contrast versus applied rotation for the data in Fig. 2. The fitted slope of the fringe spatial frequency is consistent with term 2 of Table  to $<10\%$. Fringe contrast is observed over a wide range of rotation rates (red triangles, dotted line), while the contrast from integration detection decays rapidly (black circles, dashed line). Both Gaussian fits are constrained to be centered at the observed point of zero phase gradient ($\delta {\Omega }_x\approx 0\mu \mathrm{rad}/\mathrm{s}$), and the fringe contrast fit is further constrained to have the same peak value as the integrated contrast fit, since the methods should agree in the large wavelength limit.

Figure 4

Images of the interferometer output ports using (a) 3 nK and (b) 50 nK atom sources with rotation compensation (${\mathbf{\Omega }}_{\mathrm{C}}=-{\mathbf{\Omega }}_{\mathbf{E}}$). The upper (lower) port consists of $N_1$ ($N_2$) atoms in state $|F=1⟩$ ($|F=2⟩$). Each pair of images represents the two extremes in the observed population ratio, $N_1/(N_1+N_2)$ [open circles in (c) and (d)]. Population ratio variations between trials reflect interferometer phase variations caused by vibration of the retroreflection mirror. Also shown in (a) and (b) are the atom densities integrated horizontally for the two images (black and red curves), with the shaded regions used to determine the port atom numbers, $N_i$. The lower port has been optically pushed, resulting in a hotter cloud with fewer peak counts. Both ports are heated by a 5 ms imaging pulse. This heating is most evident for 3 nK clouds.

Figure 5

(a) PSI dual-axis gyroscope. We extract the differential phase $\Delta {\Phi }_{LR}$ between the left and right sides of the ensemble as a function of the rotation rate $\delta {\Omega }_E$, as measured on cameras CCD1 (black, dashed line) and CCD2 (red, solid line). (b) Sample ellipses emerging from the right-versus-left population ratios of CCD2 (upper) and CCD1 (lower), corresponding to the open circles of part (a).