Energy-Tunable Sources of Entangled Photons: A Viable Concept for Solid-State-Based Quantum Relays

We propose a new method of generating triggered entangled photon pairs with wavelength on demand. The method uses a microstructured semiconductor-piezoelectric device capable of dynamically reshaping the electronic properties of self-assembled quantum dots (QDs) via anisotropic strain engineering. Theoretical models based on $\mathbf{k}·\mathbf{p}$ theory in combination with finite-element calculations show that the energy of the polarization-entangled photons emitted by QDs can be tuned in a range larger than 100 meV without affecting the degree of entanglement of the quantum source. These results pave the way towards the deterministic implementation of QD entanglement resources in all-electrically-controlled solid-state-based quantum relays.

Figure 1

(a) Sketch of a QR. Yellow lines represent entanglement. Photodetectors are in black. (b) Implementation with two identical QDs using the $XX\text{−}X\text{−}0$ cascade. ${\sigma }^{+}$ (${\sigma }^{-}$) indicates right (left) circularly polarized photons. A partial BSM is performed via two-photon interference at a beam splitter followed by polarization-resolved detection. (c) Realistic situation for two random QDs. $H(V)$ indicates horizontally (vertically) polarized photons. (d) Sketch of the proposed device. The top and bottom views are depicted on the left and right panel, respectively. Three independent voltages ($V_{1,2,3}$) applied across pairs of legs and the top (grounded) contact allow the in-plane stress in the QD membrane to be controlled. An additional ring contact on top of the membrane enables electric-field control across the QDs. (e) Same as in (b) for two remote QDs embedded in the device shown in (d).

Figure 2

(a) Mismatch between ${\theta }_{+}$ and ${\varphi }_{ϵ}$ in the condition ${\varphi }_{ϵ}={{\varphi }_{ϵ}}^{*}$. The blue (red) line indicates the result for InAs (GaAs) QDs. The inset shows a sketch of a QD featuring $C_1$ symmetry and the stress applied to the QD in terms of $S_1$, $S_2$, and $\varphi$. (b) FSS against the $X$ energy shift ($E_0-E_X$) for an InAs QD with ${\theta }_{+}=16.2°$, with $E_0$ the $X$ energy at zero stress. The colored lines correspond to $S_1$ applied at $\varphi =23°$ (purple line), $\varphi =0°$ (red line), and $\varphi =11°$ (blue line) and with $S_2=0$. The black lines correspond to ${\varphi }_{ϵ}={{\varphi }_{ϵ}}^{*}=18.5°$ and are for $S_2=0$, 0.5, and 1800 MPa, from left to right, respectively. The values of ${{\varphi }_{ϵ}}^{*}$, $\mathrm{\Delta }{p}^{*}$, and $\overline{p}$ at which $s=0$ are also indicated.

Figure 3

(a) FEM simulations of the $S_1$ for two sets of voltages: $(V_1,V_2,V_3)=(0,600,0)\mathrm{V}$ (top) and $(V_1,V_2,V_3)=(600,0,0)\mathrm{V}$ (bottom). The insets show zooms of the central regions and the angle formed by $S_1$ with respect to the [110] direction. We point out that a major stress of 1.8 GPa along the [100] direction corresponds to a major strain of $\sim 1.5\%$. (b) $X$ energy against $\varphi$ and $\mathrm{\Delta }p$ for ($V_1,V_2,V_3$) in the range $\pm 600\mathrm{V}$. A cylindrical coordinate system has been used.