Perfect Photon Indistinguishability from a Set of Dissipative Quantum Emitters

Abstract

Single photon sources (SPS) based on semiconductor quantum dot (QD) platforms are restricted to low temperature (T) operation due to the presence of strong dephasing processes. Although the integration of QD in optical cavities provides an enhancement of its emission properties, the technical requirements for maintaining high indistinguishability (I) at high T are still beyond the state of the art. Recently, new theoretical approaches have shown promising results by implementing two-dipole-coupled-emitter systems. Here, we propose a platform based on an optimized five-dipole-coupled-emitter system coupled to a cavity which enables perfect I at high T. Within our scheme the realization of perfect I single photon emission with dissipative QDs is possible using well established photonic platforms. For the optimization procedure we have developed a novel machine-learning approach which provides a significant computational-time reduction for high demanding optimization algorithms. Our strategy opens up interesting possibilities for the optimization of different photonic structures for quantum information applications, such as the reduction of quantum decoherence in clusters of coupled two-level quantum systems.

Keywords: photonic integrated circuits; quantum decoherence; quantum optics; single-photon.

Figure 1

(a) The two interacting QEs with $\gamma$ coupled to the cavity field with g are equivalent to a single QE with $2\gamma$ coupled to the cavity with $\sqrt{2}$ g, each sphere represents a single two-level-system. Indistinguishability of the effective QE versus the normalized $\kappa$ and g in the (b) incoherent regime and (c) coherent regime. Contour map of regions with I > 0.9 for different distances between the emitters from $d=6.9\times {10}^{-2}\mathsf{\lambda }$ to $d=8.5\times {10}^{-2}\mathsf{\lambda }$ (d) incoherent regime and (e) coherent regime. (f) Indistinguishability versus normalized g for $d=7.2\times {10}^{-2}\mathsf{\lambda }$ (yellow), $d=7\times {10}^{-2}\mathsf{\lambda }$ (green) and $d=6.9\times {10}^{-2}\mathsf{\lambda }$ (blue); solid lines calculated using Equation (1); colored dots obtained from numerical integration of the Lindblad equation with two QEs.

Figure 2

(a) $\kappa$-parameter space of the stability of rate equations of a single QE system coupled to a cavity. Black dots correspond to bounded points while the gradient colors represent the degree of stability. (b) Characteristic equation of (2) (blue line); tangent line with slope $P^{\prime }\left(0\right)$. The cut of the tangent line with the x-axis is given by $\frac{P\left(0\right)}{P^{\prime }\left(0\right)}$. The arrows indicate consecutive ${\lambda }_n$ values of the iteration process. (c) Indistinguishability versus normalized ${\kappa }_2$ for ${\mathrm{g}}_1$ = (green), 2$\gamma$ (red) and 3$\gamma$ (yellow). (d) Bloch-spheres of the five-QE system with population rate transfers R_ij between each subsystem.

Figure 3

(a) Optimal configuration of the 5-QEs system in a 2D plane for (a) $\kappa =10\gamma$, (b) $\kappa =50\gamma$, (c) $\kappa =100\gamma$, (d) $\kappa =500\gamma$ and (e) $\kappa =1000\gamma$. The circles around each QE position corresponds to the positioning tolerance for having I > 0.9. (f) Indistinguishability versus normalized $\kappa$ and g for the optimized system shown in (a). (g) Field profile ${\left|E\right|}^2$ of the hexagonal PC-cavity-mode with a point source placed at the antinode.

Figure 4

(a) Probability distributions with standard deviation ${\sigma }_n$ for n = 1 …20 for the normalized detuning values $\Delta /\gamma$. At each iteration we set a random $\Delta$ value for each QD according to the corresponding distribution. (b) Average value of the indistinguishability obtained for each of the 20 probability distributions.