  The exponential growth of the out-of-time-ordered correlator (OTOC) has been
proposed as a quantum signature of classical chaos. The growth rate is expected
to coincide with the classical Lyapunov exponent. This quantum-classical
correspondence has been corroborated for the kicked rotor and the stadium
billiard, which are one-body chaotic systems. The conjecture has not yet been
validated for realistic systems with interactions. We make progress in this
direction by studying the OTOC in the Dicke model, where two-level atoms
cooperatively interact with a quantized radiation field. For parameters where
the model is chaotic in the classical limit, the OTOC increases exponentially
in time with a rate that closely follows the classical Lyapunov exponent.
