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Using a model Hamiltonian for a single-mode electromagnetic field interactingwith a nonlinear medium, we show that quantum expectation values of subsystemobservables can exhibit remarkably diverse ergodic properties even when thedynamics of the total system is regular. The time series of the mean photonnumber is studied over a range of values of the ratio of the strength $\gamma$of the nonlinearity to that of the inter-mode coupling $g$. We obtain the powerspectrum, estimate the embedding dimension of the reconstructed phase space andthe maximal Liapunov exponent $\lambda_{\rm max}$, and find the recurrence-timedistribution of the coarse-grained dynamics. The dynamical behavior ranges fromquasiperiodicity (for $\gamma/g \ll 1$) to chaos as characterized by$\lambda_{\rm max} > 0$ (for $\gamma/g \gtrsim 1$), and is interpreted.

Ergodicity properties of quantum expectation values in entangled states