Polarization Engineering in Photonic Crystal Waveguides for Spin-Photon Entanglers

By performing a full analysis of the projected local density of states (LDOS) in a photonic crystal waveguide, we show that phase plays a crucial role in the symmetry of the light-matter interaction. By considering a quantum dot (QD) spin coupled to a photonic crystal waveguide (PCW) mode, we demonstrate that the light-matter interaction can be asymmetric, leading to unidirectional emission and a deterministic entangled photon source. Further we show that understanding the phase associated with both the LDOS and the QD spin is essential for a range of devices that can be realized with a QD in a PCW. We also show how suppression of quantum interference prevents dipole induced reflection in the waveguide, and highlight a fundamental breakdown of the semiclassical dipole approximation for describing light-matter interactions in these spin dependent systems.

Figure 1

(a) Zoom in of a $W1$ PCW made from a suspended slab of GaAs with air holes (marked with dashed blue line), lattice constant $a=250\mathrm{nm}$ and the hole size is $0.34a$. A line of holes is missing through the center forming the waveguide. Gray scale background shows field intensity, red markings show polarization ellipse, where straight lines represent linear polarization. (b) Zoom of specific area where the yellow circle represents the $C$ point and yellow line the ${\mathbf{E}}_y$ polarized point we consider in this Letter. fdtd simulations showing emission from a negatively charged QD at the identified $C$ point for (c) spin-up (${\sigma }_{+}$ polarized), and (d) spin-down (${\sigma }_{-}$ polarized).

Figure 2

Transmitted (blue line) and reflected (dashed red line) intensity as a function of detuning for (a) the linear $E_y$ dipole placed at a point in the PCW with pure $E_y$ polarized light, (b) the ${\sigma }_{+}$ dipole at a ${\sigma }_{+}$ polarized $C$ point, with (c) the accompanying phase shift on the transmitted signal as a function of detuning. (d) An $E_y$ dipole at a ${\sigma }_{+}$ polarized $C$ point. All plots use the $W1$ waveguide shown in Fig. 1, with parameters ${\mathrm{\Gamma }}_0=0.1{\mathrm{\Gamma }}^{\text{hom}}$ and $d_0=30\mathrm{D}$.