  The celebrated anti-de Sitter/conformal field theory (AdS/CFT)
correspondence1-3, also known as the gravity/gauge duality, posits a dual
relationship between the quantum gravity in an AdS spacetime and the CFT
defined on its lower-dimensional boundary. This correspondence not only offers
profound insights into the enigmatic nature of quantum gravity but also shows
mighty power in addressing strongly-correlated systems. However, despite its
importance in contemporary physics, the AdS/CFT correspondence remains a
conjecture, and further experimental investigation is highly sought after.
Here, we present the first experimental exploration of this conjecture by
testing its core corollary: the leading-order effects of a strongly-coupled CFT
can be exactly described by a weakly-coupled classical field in a
higher-dimensional AdS spacetime. Through measuring the bulk entanglement
entropy (BEE) and boundary-boundary correlation function (BBCF) of scalar
fields in both conventional type-I and previously overlooked type-II hyperbolic
lattices, serving as the discretized regularizations of spatial geometries of
pure AdS2+1 spacetime and AdS2+1 black hole, respectively, we experimentally
confirm that BEE exhibits a logarithmic scaling with the subsystem size,
following the Ryu-Takayanagi (RT) formula, while BBCF showcases an exponential
law dependence on the boundary separation, the scaling dimension of which
conforms to the Klebanov-Witten (KW) relation, both of which align remarkably
well with the established CFT outcomes. This heuristic experimental effort
opens a new avenue for in-depth investigations on the gravity/gauge duality and
extensive exploration of quantum-gravity-inspired phenomena in classical
systems.
