Boosting entanglement between exciton-polaritons with on-off switching of Josephson coupling

We show that the appropriate on-off switching of Josephson coupling between exciton-polaritons in coupled semiconductor microcavities can reveal the full capacity for generating entanglement with a recently proposed method which essentially enhances the nonlinearity of the system. The improvement achieved with this simple modulation of the coupling is substantial over the case where it is kept constant. We also show that even better results can be obtained with the additional on-off switching of the enhanced nonlinearity. The suggested procedure is expected to find also application in other research areas, where nonlinear interacting bosons are encountered.

Figure 1

(a) Constant Josephson coupling (blue line) and modified coupling (11) (red line) for a common duration $\alpha T=2$. The amplitude of the constant pulse is found from (7) to be $u_T=J_T/\alpha =1.2716$, while for the second (nonzero) pulse in the modified coupling it is $u=J/\alpha =1.4$. (b) Corresponding trajectories on the $S_2{S}_3$ plane, where the inner blue trajectory correspond to the constant coupling and the outer red trajectory to the modified coupling.

Figure 2

Logarithmic negativity as a function of duration $\alpha T$. (a) In the absence of dissipation $\mathrm{\Gamma }=0$. The lower blue curve corresponds to the constant coupling with amplitude $u_T=J_T/\alpha$ given in (7), while the upper black curve corresponds to the modified coupling (11) with a delta final pulse (infinite $u=J/\alpha )$. The intermediate red lines correspond to finite values of $u=J/\alpha =1.2,1.4,2$ (from bottom to top). (b) Same as in (a) but in the presence of dissipation $\mathrm{\Gamma }=0.2\alpha$.

Figure 3

Saturation limit of logarithmic negativity as a function of the enhanced nonlinearity amplitude $\alpha$. Red solid line corresponds to on-off switching the Josephson coupling only, Eq. (22), and is restricted to $0<\alpha <J$. Black dashed curve corresponds to the case where both the coupling and the nonlinearity are modulated, Eq. (27), and is depicted for $J\le \alpha \le 2J$. For both cases it is $J/\mathrm{\Gamma }=10$. The vertical black line marks the point $\alpha /J=1$.