Sauerwein, NickOrsi, FrancescaUhrich, PhilippBandyopadhyay, SoumikMattiotti, FrancescoCantat-Moltrecht, TigranePupillo, GuidoHauke, PhilippBrantut, Jean-Philippe2023-06-052023-06-052023-06-052023-05-0410.1038/s41567-023-02033-3https://infoscience.epfl.ch/handle/20.500.14299/198095WOS:000981353200005Random spin models play a key role in our understanding of disorder and complex many-body systems. Two all-to-all interacting, disordered models have now been realized using a cavity quantum electrodynamics platform.All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics over holographic duality in high-energy physics to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realizations in nature. Here we realize an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark-state manifold cross over to a random distribution of weakly mixed light-matter, 'grey', states. In the Lipkin-Meshkov-Glick model, the ferromagnetic finite-sized ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localized eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present substantial steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.Physics, MultidisciplinaryPhysicsquantum phase-transitionmany-body localizationanderson localizationultracold atomssimulationsgastext::journal::journal article::research article