  We discuss a system of a nonlinear Kerr-like oscillator externally pumped by
ultra-short, external, coherent pulses. For such a system, we analyse the
application of the Kullback-Leibler quantum divergence $K[\rho||\sigma]$ to the
detection of quantum chaotic behaviour. Defining linear and nonlinear quantum
divergences, and calculating their power spectra, we show that these parameters
are more suitable indicators of quantum chaos than the fidelity commonly
discussed in the literature, and are useful for dealing with short time series.
Moreover, the nonlinear divergence is more sensitive to chaotic bands and to
boundaries of chaotic regions, compared to its linear counterpart.
