Quantum sensing for gravitational cartography

The sensing of gravity has emerged as an important tool in geophysics for applications such as engineering and climate research 1,2,3 where it provides the capability to probe otherwise inaccessible features under the surface of the Earth. Examples include the monitoring of temporal variations such as those found in aquifers 4 and geodesy 5 . However, resolving metre scale underground features is rendered impractical by the long measurement times needed for the removal of vibrational noise 6 . Here, we overcome this limitation and open up the eld of gravity cartography by realising a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, as well as thermal and magnetic eld variations, and instrument tilt. The instrument achieves an uncertainty of 20 E (1 E = 10-9 s-2) and is used to perform a 0.5 m spatial resolution survey across a 8.5 m long line, detecting a 2 m tunnel with a signal to noise ratio of 8. The tunnel centre is localised using a Bayesian inference method, determining the centre to within ± 0.19 m in the horizontal direction and nding the centre depth as (1.89 -0.59/+2.3) m. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. This opens new applications such as mapping the water distribution of aquifers and evaluating impacts on the water 14


Abstract
The sensing of gravity has emerged as an important tool in geophysics for applications such as engineering and climate research 1,2,3 where it provides the capability to probe otherwise inaccessible features under the surface of the Earth. Examples include the monitoring of temporal variations such as those found in aquifers 4 and geodesy 5 . However, resolving metre scale underground features is rendered impractical by the long measurement times needed for the removal of vibrational noise 6 . Here, we overcome this limitation and open up the eld of gravity cartography by realising a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, as well as thermal and magnetic eld variations, and instrument tilt. The instrument achieves an uncertainty of 20 E (1 E = 10-9 s-2) and is used to perform a 0.5 m spatial resolution survey across a 8.5 m long line, detecting a 2 m tunnel with a signal to noise ratio of 8. The tunnel centre is localised using a Bayesian inference method, determining the centre to within ± 0.19 m in the horizontal direction and nding the centre depth as (1.89 -0.59/+2.3) m. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. This opens new applications such as mapping the water distribution of aquifers and evaluating impacts on the water table 7 , detecting new features in archaeology 8,9,10,11 , determination of soil properties 12 and water content 13 , and reducing the risk of unforeseen ground conditions in the construction of critical energy, transport and utilities infrastructure 14 , providing a new window into the underground.

Main Text
The quantum gravity gradient sensor uses atom interferometry 15 , which has been used in laboratory based experiments to provide sensitive measurements of gravity 16 , to investigate the equivalence principle 17 , the ne-structure constant 18 and Newton's gravitational constant 19 , prompting the desire to transition these sensors into practical devices for use in real-world environments 20 . For example, gravity sensors have been created which can be used on volcanoes and mountain environments 21,22 , and for measurements by air 23 , sea 24 , and on rockets 25 . A typical approach in these devices is to employ light pulses to drive two-photon stimulated Raman transitions in atoms and use these to create a superposition of matter waves in different momentum and energy states. The resulting atomic wave packets move along two spatially separated trajectories, before being recombined and interfered. This creates the matter-wave analogue of a Mach-Zehnder interferometer. The phase difference in the resulting interference pattern is proportional to the local gravitational eld. However, such devices, as with any gravimeter, are fundamentally limited in their measurement time due to the need to average out micro-seismic vibration 26 . This presents a major barrier to realising gravity maps with high spatial resolution.
In order to enable gravity cartography, and operation in application-relevant conditions, we implement a novel "hourglass" con guration cold atom gravity gradiometer 27 . This enables robust coupled differential measurements upon two clouds of atoms, separated by a vertical baseline 28 . Two counter-orientated single beam magneto-optical traps (MOTs) allow passage of common Raman beams to perform interferometry (Fig. 1a). The measurement axis is aligned to measure the vertical component, G zz , of the (3x3) gravity gradient tensor, which is the largest and most relevant component for gravity cartography. Differential operation suppresses primary noise sources (vibration and micro-seismic), systematic shifts (such as tilt), and changes in the optical path-length between the beams used to drive the Raman transitions 29 . The commonality of laser intensity noise for the cooling beams of the single-beam MOTs 6 enables cloud temperature uctuations to be stable to within a few 100 nK (Fig. 1b, upper), limiting the impact of AC Stark shifts, and reduces cloud centre-of-mass motion by an order of magnitude when compared to conventional 6-beam approaches (see Methods). The resulting baseline stability is 50 ppm (Fig. 1b, lower), which corresponds to a systematic error of less than 0.1 E.
The hourglass con guration provides several practical bene ts (see Methods). Avoiding the need for offaxis beams creates a robust and compact optical delivery arrangement, allowing months of operation in the eld with no need to correct alignment. The con guration also provides a radially compact form factor, enabling compact magnetic shielding with 25 dB attenuation that suppresses effects due to external magnetic elds, preventing these from affecting the atom cloud generation. The beam con guration, in combination with a robust all-bre laser system, enables independent control of the counter-propagating Raman beams, facilitating reversal of the light pulse directions 31 . Interleaving measurements in each direction suppresses several systematic effects, including reducing those due to residual magnetic elds to below measurement precision. Furthermore, phase shifts and contrast loss from parasitic Raman transitions 32 are prevented through independent delivery of the Raman beams for each direction, without the need for a phase lock.
To measure the gravity gradient (see Methods), each MOT is loaded for 1 to 1.5 seconds with 87 Rb atoms before sub-Doppler cooling is used to reduce the cloud temperatures to the micro-Kelvin regime. The clouds are then dropped and simultaneously subjected to an atom interferometry sequence. The output of each interferometer is measured using uorescence to detect the ratio of the populations of the two relevant atomic ground states, with approximately 10 5 atoms participating in each atom interferometer, for a typical measurement rate of 0.7 Hz. A Lissajous plot of the upper versus lower atom interferometer outputs is then used to extract the differential phase, from which the gravity gradient is determined (Fig 2, inset) 33 . The calibration of the sensor was veri ed under laboratory conditions by modulating the position of known test masses near to the sensor to vary G zz (Fig. 1c). This resulted in a measured change of (205 ± 13.1) E, compared to a modelled signal of 202 E.
Similarly, the sensitivity and stability of the instrument were evaluated in an outdoor environment. The Allan deviation 34 of the phase data (Fig. 2) showed an average short-term sensitivity of (466 ± 8) E/√Hz and an uncertainty of 20 E within 10 minutes of measurement.
To demonstrate the potential for gravity cartography, a 0.5 m spatial resolution survey was performed along an 8.5 m survey line on a road surface above a tunnel (see Methods). A site model using an air/soil contrast in nite cuboid void, and taking into account local buildings and terrain, produced an estimated peak signal of 150 E. The parameters for the model were informed using auxiliary data from on-site measurements such as topography scanning and ground penetrating radar. The measurement data in Fig. 3a shows a gravity gradient anomaly consistent with this site model and the expected location and size of the tunnel (Fig. 3b).
For use in practical applications, it will be important to interpret the data in an accessible way that produces information upon which a user can make decisions or act. For this purpose, we have developed a Bayesian inference method to make quantitative predictions of the depth and spatial extent of the anomaly. This was applied to the gradiometer data with a data-generated model of a buried cuboid 35 assumed a priori. The prior distribution of the cuboid density contrast is taken to be Gaussian, with a mean of -1.80 g/cm 3 , to represent a void in surrounding soil, and standard deviation of 0.10 g/cm 3 . The inference process produces distributions for the position, depth and cross-sectional area of the tunnel using the probability of excavation (POE) metric 36 (Fig. 3c). The observed spread of the POE is expected, due to measurement uncertainty and the ambiguity that exists between model parameters specifying depth, area, and density, typical of inference from potential eld data 37 . A signal to noise ratio of 8 for the detection is estimated from the data, nding the deduced horizontal position of the tunnel centre at (0.19 ± 0.19) m along the survey line and a depth to the centre of (1.89 -0.59/+2.3) m (see Methods).
Furthermore, by assuming a priori knowledge of the tunnel geometry, the focus of the inference was switched to infer the soil density (Fig. 3d). This results in a near Gaussian posterior distribution for the density parameter, with a mean of -1.80 g/cm 3 and standard deviation of 0.15 g/cm 3 .
The uncertainty demonstrated by the prototype instrument during static operation surpasses the reported performance of commercial gravimeters for survey applications by a factor of 1.5-4 38,39 . In this rst demonstration of sub-metre resolution mapping with quantum gravity sensors, the repeatability of the prototype during the survey was similar to commercial gravimeters and limited by systematic effects (see Methods), such as due to the Coriolis effect, which can be addressed through further engineering.
Furthermore, the sensor could be moved from one spatial position to another within 75 seconds, including alignment to the vertical to within 1 millidegree. If addressing these aspects, such as through operation on a rail or vehicle, the current instrument performance would in principle allow detection of the tunnel, or similar anomaly, with a 10-point line scan and a signal to noise ratio of 3 within 15 minutes of total measurement time.
The detection of the tunnel allows the assessment of the instrument performance for a range of potential applications. Fig. 4a shows a range of typical signal sizes for a variety of application areas in comparison to the sensor uncertainty, with features in the range above the sensor uncertainty being detectable with the current instrument. In civil engineering applications, this performance could provide a reduction in the uncertainty of ground conditions and be used to inspect brown eld sites, to search for tunnels and large or near-surface utilities, and to detect erosion features before they become sinkholes. This performance is also relevant to archaeological applications, for example enabling the detection of tombs or hidden chambers and investigating how previous civilisations used underground infrastructure. Furthermore, the sensor could be of particular use in the mapping of aquifers, in order to better understand and optimise the use of water and its impact on the environment. It could also be used to measure density distributions within the ground. Based upon the inferred standard deviation, the soil density extraction method is currently sensitive to 10% level changes in the mean, meaning that in principle this could distinguish between soil that is either dry or saturated, or used to investigate localised soil compaction, e.g. in precision agriculture. Typical anticipated signals for these applications, with the 20 E noise our sensor achieves within a 10 min measurement time, are illustrated in Fig. 4b.
The removal of vibration noise means, in contrast to gravimeters, that future improvements in instrument sensitivity can be directly translated into reductions in measurement time or improved uncertainty. Implementation of further scienti c enhancements to the sensor, including, for example, the use of large momentum beam splitters 40,41 , has the potential to provide a further 10-100 fold improvement in instrument sensitivity, allowing faster mapping or detection of smaller and deeper features. It is expected that such performance will be achieved in practical instruments within the next 5-10 years.   .181 (1991). a) Hourglass gradiometer using two counter-orientated single beam magneto-optical traps, realised using mirror assemblies (blue). The initial atom clouds (green)are dropped before being subjected to light pulses separated by time T to realise the atom interferometers (purple clouds). The beam delivery is shown in red, with the beams transiting through the mirror assembly indicated by the smaller arrow. Each interferometer is operated simultaneously, with a vertical baseline separation of 1 m. b) Temporal variation of atom cloud temperatures from each trapping region, measured using time of ight , and baseline drift, determined from time of arrival, with the sigma range represented by the shaded region. c) Calibration measurement of gravity gradient variation caused by movement of a test mass between two positions (black -mass close, grey -mass displaced) from the sensor (blue tube), with the modelled projection of the change in gravity gradient signal, ΔGzz, shown in red.

Figure 2
Allan deviation with overlapping averages of the instrument output during outdoor operation. Insettypical Lissajous gure of the output signal of the upper and lower interferometers, which is used to extract the gradiometric phase.

Supplementary Files
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