We outline the experimental concept and key scientific capabilities of AION (Atom Interferometer Observatory and Network), a proposed experimental programme using cold strontium atoms to search for ultra-light dark matter, to explore gravitational waves in the mid-frequency range between the peak sensitivities of the LISA and LIGO/Virgo/ KAGRA/INDIGO/Einstein Telescope/Cosmic Explorer experiments, and to probe other frontiers in fundamental physics. AION would complement other planned searches for dark matter, as well as probe mergers involving intermediate-mass black holes and explore early-universe cosmology. AION would share many technical features with the MAGIS experimental programme, and synergies would flow from operating AION in a network with this experiment, as well as with other atom interferometer experiments such as MIGA, ZAIGA and ELGAR. Operating AION in a network with other gravitational wave detectors such as LIGO, Virgo and LISA would also offer many synergies.

In this work, we analyze the dynamical properties of periodically driven band models. Focusing on the case of Bose-Einstein condensates, and using a mean-field approach to treat interparticle collisions, we identify the origin of dynamical instabilities arising from the interplay between the external drive and interactions. We present a widely applicable generic numerical method to extract instability rates and link parametric instabilities to uncontrolled energy absorption at short times. Based on the existence of parametric resonances, we then develop an analytical approach within Bogoliubov theory, which quantitatively captures the instability rates of the system and provides an intuitive picture of the relevant physical processes, including an understanding of how transverse modes affect the formation of parametric instabilities. Importantly, our calculations demonstrate an agreement between the instability rates determined from numerical simulations and those predicted by theory. To determine the validity regime of the mean-field analysis, we compare the latter to the weakly coupled conserving approximation. The tools developed and the results obtained in this work are directly relevant to present-day ultracold-atom experiments based on shaken optical lattices and are expected to provide an insightful guidance in the quest for Floquet engineering.

The sensing of gravity has emerged as a tool in geophysics applications such as engineering and climate research1–3, including the monitoring of temporal variations in aquifers4 and geodesy5. However, it is impractical to use gravity cartography to resolve metre-scale underground features because of the long measurement times needed for the removal of vibrational noise6. Here we overcome this limitation by realizing a practical quantum gravity gradient sensor. Our design suppresses the effects of micro-seismic and laser noise, thermal and magnetic field variations, and instrument tilt. The instrument achieves a statistical uncertainty of 20 E (1 E = 10−9 s−2) and is used to perform a 0.5-metre-spatial-resolution survey across an 8.5-metre-long line, detecting a 2-metre tunnel with a signal-to-noise ratio of 8. Using a Bayesian inference method, we determine the centre to ±0.19 metres horizontally and the centre depth as (1.89 −0.59/+2.3) metres. The removal of vibrational noise enables improvements in instrument performance to directly translate into reduced measurement time in mapping. The sensor parameters are compatible with applications in mapping aquifers and evaluating impacts on the water table7, archaeology8–11, determination of soil properties12 and water content13, and reducing the risk of unforeseen ground conditions in the construction of critical energy, transport and utilities infrastructure14, providing a new window into the underground.

We experimentally investigate the effects of parametric instabilities on the short-time heating process of periodically-driven bosons in 2D optical lattices with a continuous transverse (tube) degree of freedom. We analyze three types of periodic drives: (i) linear along the x-lattice direction only, (ii) linear along the lattice diagonal, and (iii) circular in the lattice plane. In all cases, we demonstrate that the BEC decay is dominated by the emergence of unstable Bogoliubov modes, rather than scattering in higher Floquet bands, in agreement with recent theoretical predictions. The observed BEC depletion rates are much higher when shaking both along x and y directions, as opposed to only x or only y. We also report an explosion of the decay rates at large drive amplitudes, and suggest a phenomenological description beyond Bogoliubov theory. In this strongly-coupled regime, circular drives heat faster than diagonal drives, which illustrates the non-trivial dependence of the heating on the choice of drive.

We study the localization of collective pair excitations in weakly-interacting Bose superfluids in one-dimensional quasiperiodic lattices. The localization diagram is first determined numerically. For intermediate interaction and quasiperiodic amplitude we find a sharp localization transition, with extended low-energy states and localized high-energy states. We then develop an analytical treatment, which allows us to quantitatively map the localization transition into that of an effective multiharmonic quasiperiodic system. PACS numbers: 03.75.-b, 05.30.Jp, 05.70.Ln,Quasiperdiodic systems, which are formed of a small number of incommensurate sinusoidal components, constitute an appealing intermediate between disordered and periodic systems. Such structures are basic models for a wide variety of physical systems. They appear naturally in the growth of certain crystals [1] or as a result of charge-density waves [2]. They also describe twodimensional lattice electrons in perpendicular magnetic fields [3]. Moreover, they can be created on purpose in solid crystals [4], photonic crystals [5], and ultracoldatom optical lattices [6][7][8]. In quasiperiodic systems, the lack of translation invariance can induce localization of linear waves, similarly as the phenomenon of Anderson localization in disordered systems [9]. In quasiperiodic systems, however, the quasi-repetition of finite patterns radically changes the localization picture. For instance, in a one-dimensional disordered system, any quantum particle is localized with an energy-dependent localization length [10,11]. In contrast, for a quasiperiodic system made of a single incommensurate sinusoidal modulation of a main periodic lattice, there is a localization transition for some critical strength of the quasiperiodic component beyond which the states are localized with a localization length that is independent of the energy [12].The extension of the concept of localization to interacting quantum systems is attracting a considerable attention as regards phase diagrams [13], many-body localization transitions [14], and localization of collective excitations [15][16][17]. These issues have been first investigated for purely disordered systems and extensions to quasiperiodic systems are just starting. So far, most studies focused on the phase diagram of one-dimensional bosons in quasiperiodic lattices at zero temperature [18][19][20], finite temperature [21], and infinite temperature [22]. Conversely, the localization of collective excitations remains largely open. This issue is particularly important because the transport of collective excitations governs many dynamical effects in correlated quantum systems [23], for instance the propagation of correlations in recently-developed quench experiments [24].Here we study the localization of collective pair excitations in weakly interacting Bose superfluids subjected to a one-dimensional quasiperiodic lattice. We first determine the localization diagram numerically and show that, for intermediate interaction and quasiper...