Figure 1

(Color online) Two binary quantum objects interacting through a quantized electromagnetic mode supported by a cavity resonator. The dynamics of such an ideal system is described by the Dicke model.Reuse & Permissions

Figure 2

(Color online) The relevant electronic states of two identical ${{}^{40}\text{C}\text{a}}^{+}$ ions and corresponding couplings provided by an external pump laser and a quantized cavity mode. The excited electronic state decays spontaneously to the ground and to the metastable states, and the cavity mode is damped as well.Reuse & Permissions

Figure 3

(Color online) Scaling of the effective ion-cavity coupling $\left|g_{\text{eff}}\right|$ (middle line for large $\Delta$) and effective spontaneous emission decay rates ${\Gamma }_S^{\left(j\right)}$ (lowest line for large $\Delta$; with ${\beta }^{\left(j\right)}=1$) as a function of the detuning $\Delta$. The isocurves $4\left|{\beta }_T{g}_{\text{eff}}\right|/\kappa =\text{const}$ (thin lines) are parallel to the $\left|g_{\text{eff}}\right|$ curve, so that the weak ion-cavity coupling regime is in the upper right corner and the strong ion-cavity coupling regime in the lower left one. The cavity decay rate $\kappa$ (horizontal line) does not depend on the detuning. The effective spontaneous emission events are suppressed for large detunings.Reuse & Permissions

Figure 4

(Color online) Concurrence as a function of time and the relative coupling strength $r^{\left(1\right)}$ in the weak ion-cavity coupling regime. The dynamics is initially monotonic since the existing superradiant component decays rapidly compared to other dynamical time scales. The subradiant state component decays eventually because of the atomic spontaneous emissions. The best entanglement production occurs with asymmetric couplings $\left(r^{\left(1\right)}\ne 1/\sqrt{2}\right)$. Parameters: $\Delta /{\Delta }_0=100,\kappa /{\kappa }_0=0.1$Reuse & Permissions

Figure 5

(Color online) Dynamics of the concurrence in the weak ion-cavity coupling regime for $r^{\left(1\right)}=0.55$. In the Dicke model with cavity losses (highest line) a stationary value of the concurrence is reached as the superradiant component is overdamped. Parameters: $\Delta /{\Delta }_0=100,\kappa /{\kappa }_0=0.1$ (lowest line, $2\pi /\left|{\Omega }_g\right|=23\mu \text{s}$); $\Delta /{\Delta }_0=1000,\kappa /{\kappa }_0=0.01$ (middle line, $2\pi /\left|{\Omega }_g\right|=230\mu \text{s}$).Reuse & Permissions

Figure 6

(Color online) Average cumulative number of quantum jumps per ensemble member for each decay channel in the weak ion-cavity coupling regime. From above: $C_S^{\left(1\right)}$, $C_S^{\left(2\right)}$, and $a$. Parameters: $\Delta /{\Delta }_0=100,\kappa /{\kappa }_0=0.1$.Reuse & Permissions

Figure 7

(Color online) Concurrence as a function of time for different values of the relative coupling strength $r^{\left(1\right)}$ in the strong ion-cavity coupling regime. Oscillations appear because of a relative phase evolution between the superradiant and subradiant states. Parameters: $\Delta /{\Delta }_0=10$ and $\kappa /{\kappa }_0=0.1$.Reuse & Permissions

Figure 8

(Color online) Time evolution of the concurrence in the strong ion-cavity coupling regime with relative coupling strength $r^{\left(1\right)}=0.46$. For the Dicke model with cavity losses (highest line), the concurrence approaches a constant stationary value after strong oscillations caused by the slowly decaying superradiant component. Parameters: $\Delta /{\Delta }_0=10,\kappa /{\kappa }_0=0.1$ (lowest line, $2\pi /\left|{\Omega }_g\right|=2.7\mu \text{s}$); $\Delta /{\Delta }_0=100,\kappa /{\kappa }_0=0.01$ (middle line, $2\pi /\left|{\Omega }_g\right|=27\mu \text{s}$).Reuse & Permissions

Figure 9

(Color online) Concurrence as a function of time for different values of the detuning ${\delta }_L$ for a homogeneously coupled case $\left(r^{\left(1\right)}=r^{\left(2\right)}=1/\sqrt{2}\right)$. The entanglement generation slows down when passing into the dispersive regime. The resonance is dislocated from the origin because of the Stark shifts. Parameters: $\Delta /{\Delta }_0=10$ and $\kappa /{\kappa }_0=0.1$.Reuse & Permissions

Figure 10

(Color online) Populations of the atomic states ${\rho }_{00,00}$, ${\rho }_{01,01}$, and ${\rho }_{10,10}$ (from above) as a function of time for different values of detuning ${\delta }_L$. Parameters are as in Fig. 9.Reuse & Permissions

Figure 11

(Color online) Dynamics of $\text{Re}\left[{\rho }_{01,10}\right]$, $\text{Im}\left[{\rho }_{01,10}\right]$, and $\left|{\rho }_{01,10}\right|$ (from above) as a function of time for different values of detuning ${\delta }_L$ (observed concurrence is given by $C=2\left|{\rho }_{01,10}\right|$). Parameters are as in Fig. 9.Reuse & Permissions