Wigner-function nonclassicality as indicator of quantum chaos

We propose a Wigner-function-based parameter that can be used as an indicator of quantum chaos. This parameter is defined as “entropy” from the time dependence of “nonclassicality” proposed by A. Kenfack and K. Życzkowski [J. Opt. B 6, 394 (2004)]. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultrashort external pulses.

Figure 1

Bifurcation diagrams for $\gamma =0.1$. The other parameters are $\chi =1$, $T=\pi$.

Figure 2

Time dependence of the nonclassicality parameter ${\delta }_n\left(\rho \right)$ for various values of $ϵ$, at (a) $ϵ=0.2$, 0.3, 0.4, and at (b) $ϵ=1.24$. Other parameters: $T=\pi$ and $\gamma =0.1$.

Figure 3

Time dependence of the mean energy of the classical system (a) and the mean number of photons (b) for various values of $ϵ$. The parameters $T$ and $\gamma$ are the same as in Fig. 2.

Figure 4

Recurrence plot (a) for the signal presented in Fig. 2b and diagonal line distribution at (b). Time delay is equal to 1, embedding dimension 10. The values of $\gamma$ and $T$ are the same as in Fig. 2.

Figure 5

Entropy of changes for ${\delta }_n\left(\rho \right)$ versus excitation strength $ϵ$. We assume $T=\pi$ and $\gamma =0.1$.