Entanglement dynamics in chaotic systems

We study quantum chaos for systems with more than one degree of freedom, for which we present an analysis of the dynamics of entanglement. Our analysis explains the main features of entanglement dynamics and identifies entanglement-based signatures of quantum chaos. We discuss entanglement dynamics for a feasible experiment involving an atom in a magneto-optical trap and compare the results with entanglement dynamics for the well-studied quantum kicked top.

Figure 1

Classical Poincaré sections for the AMOL at $E=-280E_R$ for $V_1=160E_R$, ${\Theta }_L=80°$, and ${\mu }_B{B}_x=12E_R$ with (a) ${\mu }_y=0,d{\mu }_y∕dt>0$ and (b) $p=0,dp∕dt>0$.

Figure 2

Entanglement $S$ vs time $\tau =E_{R}t∕\hslash$ in the AMOL for an initial state that is localized on (a) a regular island with $(z∕\lambda ,p∕\hslash k,\theta ,\varphi )=(-0.15,0,1.27,0)$ and (b) the chaotic sea with $(z∕\lambda ,p∕\hslash k,\theta ,\varphi )=(0.06,0,\pi ∕2,0)$. The inset shows the initial increase of entanglement for the regular (solid) and chaotic (dashed) initial states.

Figure 3

Population ${\rho }_{ii}$ vs corresponding eigenenergy $E_i=\hslash {\omega }_i$ for the AMOL with an initial state localized in (a) a regular island with $(z∕\lambda ,p∕\hslash k,\theta ,\varphi )=(-0.15,0,1.27,0)$ and (b) the chaotic sea with $(z∕\lambda ,p∕\hslash k,\theta ,\varphi )=(0.06,0,\pi ∕2,0)$.

Figure 4

(a) For the initial state localized on the regular island the entanglement dynamics (solid curve) can be reproduced by only considering the evolution of the four main pairs of eigenstates (dashed curve). The long term behavior (b) shows quasiperiodic motion with multiple frequencies.

Figure 5

(Color online) Population ${\rho }_{mm}$ vs corresponding eigenphases ${\varphi }_m$ for the QKT with an initial state localized in (a) a regular island and (b) the chaotic sea in Fig. 1 of [6].

Figure 6

(a) For the regular initial state of the QKT the entanglement dynamics (solid curve) can be reproduced by considering the evolution of the three highest weighted eigenstates (dashed curve) in Fig. 5(a). (b) The rise time for the state in the chaotic sea is roughly exponential.