Experimental realization of the classical Dicke model

Abstract

We report the experimental implementation of the classical description of the Dicke model whose quantum version describes a large number of two-level atoms interacting with a single-mode electromagnetic field in a perfectly reflecting cavity. This is performed by employing two nonlinearly coupled active, synthetic LC circuits, implemented by means of analog electrical components. The simplicity and versatility of our platform allows us not only to experimentally explore the coexistence of regular and chaotic trajectories in the classical Dicke model, but also to directly observe the so-called ground-state and excited-state “quantum” phase transitions. In this analysis, the trajectories in phase space, Lyapunov exponents, and the finite-time Lyapunov exponent are used to identify the different operating regimes of our electronic device. Moreover, with this technology, we measure the classic analog of the fidelity-out-of-time-order-correlator (FOTOC). Exhaustive numerical simulations are performed to show the quantitative and qualitative agreement between theory and experiment.