Quantum tiltmeter with atom interferometry

Matter-wave sensors with cold atoms have progressed tremendously over recent decades. We report a sensitive tilt sensor based on quantum technology employing cold atoms. This quantum tiltmeter is constructed with the configuration of a Ramsey-Bordé atom interferometer, achieving an improvement of nearly three orders of magnitude for tilt measurements with a short-term sensitivity of $1.3\mu {\mathrm{rad}/\mathrm{Hz}}^{1/2}$, with resolution down to $55\mathrm{nrad}$ at an integration time of 1000 s. The deformation of the Earth's surface has been monitored in a continuous run of 31 h, showing that a quantum tiltmeter can be applied to record tilt tides and can be an valuable sensor in geophysics and various scientific facilities.

Figure 1

(a) The space-time diagram of the RB interferometer. Only the lower interferometer is shown since the atoms in $F=2$ are cleaned after the second Raman pulse. (b) Schematic diagram of the quantum tiltmeter based on AI. A single pair of Raman beams is used here to simplify the modulation experiment, a commercial bubble tiltmeter is fixed on the mount of the mirror (not shown in the figure) to monitor the tilt variations.

Figure 2

Rabi oscillation at different positions. The black squares refer to the Rabi oscillation of the atom cloud located in the mid of the Raman beam, the Rabi oscillations in the position of the first $\pi$/2 pulse (the red circles), the second $\pi$/2 pulse (the green upper triangles), the third $\pi$/2 pulse (the blue lower triangles), and the fourth $\pi$/2 pulse (the cyan diamonds) are also shown in the figure when $T_1=8.6\mathrm{ms}$. The insert is the relative position of the atom cloud and the Raman beam when the $i\mathrm{th}$ Raman pulse is switched on.

Figure 3

[(a) and b)] Identifying the central fringe by modulate the chirp rate $\alpha$ with different $T_1$ for $\pm k_{\mathrm{eff}}$. The data points corresponding to the gray circles, red squares, and blue diamonds are for 4.6 ms, 6.6 ms, and 8.6 ms. The royal blue arrows head to the central fringe. (c) Modulating the tilt angle of the Raman beam. The relative angle ${\beta }_{\mathrm{Re}}$ of the mirror is monitored by the commercial tiltmeter. The tilt in the direction of Raman beams $\beta$ is measured by our quantum tiltmeter.

Figure 4

Allan deviation of the quantum tiltmeter. It gives a short-term sensitivity of 1.$3\mu {\mathrm{rad}/\mathrm{Hz}}^{1/2}$ for tilt measurements; the detection noise limitation (gray dash-dot line) is shown in the figure.

Figure 5

The vibration noise spectroscopy (black line) and the transfer function (red line) of the symmetric RB interferometer.

Figure 6

A continuous tilt measurement is carried out for 31 h. (a) Red circles: Continuous tilt measurements of 31 h operated by the quantum tiltmeter between 22 and 24 January 2017. Each data point represents an average of 1760 s. The royal blue line is the monitored temperature near the reflection mirror, and the dash-dot line is the temperature shifted with a 2-h delay. The linear correlation of the tilt and temperature from 11 h to 15 h is shown in the inset. (b) The experiment tilt tide (blue squares) after temperature compensation, the black line is the theory model of the Earth tilt tide.