Figure 1

Schematic of a possible superconducting stripline cavity implementation of the kicked system. Transmon qubits are centered on each cavity at a and b with an atom-photon coupling $\beta$, and with the intercavity coupling, $\kappa$, controlled by an applied voltage at c.Reuse & Permissions

Figure 2

Classical phase space strobe plots of the dimensionless $E$ field in each cavity over 200 kicks from several initial points. (a) $\kappa \tau =1.3,\beta T=0.1$. In the small-$T$ limit the total energy in the electric field, $E_1^2+E_2^2$, is stable, leading to nonoverlapping rings. (b) $\kappa \tau =0.4,\beta T=1.7$. Phase space is mostly chaotic except for the four regions where the energy in the system is confined mostly to one cavity. As there are four degrees of freedom, and only a single constant of motion, plots of the electric field in each cavity do not convey the entire dynamics.Reuse & Permissions

Figure 3

(a) Classical dynamics: Average $N_2$ over 1000 kicks for points initially at $E_2=\sqrt{2}$. The red regions represent parameters where most of the energy in the system is localized to a single cavity (i.e. the chaotic border). The KAM tori are destroyed with relatively small kick strength at $\beta T=2n\pi$. (b) Quantum dynamics: Average participation number of Floquet states. The regions of localization are qualitatively similar to those in the classical case; however, note that the $T$ scale is different in each graph. Vertical lines mark the location of resonances.Reuse & Permissions

Figure 4

Average participation number and long-term averages of measurable quantities (mean expectation of an ensemble of random states) over increasing $\kappa \tau$ with $\beta T=1.2$. Circles (dashed): $({\sigma }_{z1}^{†}+1)/2$, diamonds (dots): $a_1^{†}{a}_1$, squares (dot-dashed): ${\sigma }_{z1}{\sigma }_{z2}$, triangles (dot-dashed): average participation number.Reuse & Permissions

Figure 5

Evolution of the system initially in $|{\psi }^2\rangle$ over 1000 kicks with $\beta T=1.2$ and (a) $\kappa \tau =0.1$ and (b) $\kappa \tau =0.2$. The blue line is the expectation of excitations in cavity 1. The purple line is the expectation of finding both excitations together in the one cavity.Reuse & Permissions